Microwave photonics circuit elements will need to be similar to their RF analogs to provide the desired functionality.
One of these analogous circuit elements is a terahertz microwave cavity resonator, which can be integrated onto an IC with standard CMOS processes.
This is one of many circuit elements that can be placed on an IC and used to enable unique applications.
These fibers will soon be integrated into semiconductor wafers as microwave lines to communicate with unique circuit elements like terahertz microcavity resonators.
Microwave components have a lot more going on than what ends up in your microwave oven. Terahertz wave sources, detectors, and components have yet to be miniaturized, and the terahertz portion of the microwave spectrum is still largely unexplored. So far, the best we can do is get into the high GHz (low THz) region for oscillation, detection, and wave manipulation. This region is critical for many applications, including quantum computing, imaging, sensing, and ultra-fast communication.
One fundamental set of components is terahertz microcavity resonators. These components are part of a larger photonics platform and they play analogous roles to RF resonators on a PCB. The simple geometry of these resonators also allows them to be placed on a chip alongside other photonic structures. If you’re a budding photonics engineer, keep reading to learn more about these resonator structures and how they might play a role in current and upcoming photonics systems.
What Are Terahertz Microcavity Resonators?
Much like any other resonator, terahertz microcavity resonators have a fundamental frequency that lies in the terahertz region. In terms of wavelength, a 1 THz wave in air has a wavelength of only 300 microns, which is quite large compared to today’s transistors. These structures provide the same function as well; they allow a wave matching the fundamental frequency or one of its harmonics to excite a high-Q resonance, whereby a standing wave can form in the cavity.
Much like a wave on a string or in a waveguide, this standing wave at one of the eigenfrequencies will have very high intensity due to constructive interference inside the cavity. The very strong, very coherent electromagnetic wave in this structure can then be used for some other application. The challenges in working with these structures are wave generation and detection, both of which need to be solved for terahertz microcavity resonators to be useful at the chip level.
Geometry and Eigenfrequencies
The image below shows a simple rectangular terahertz microcavity resonator and its discrete eigenfrequency spectrum. The eigenfrequencies can be tuned to desired values by adjusting the geometry, just like any other resonator. The equation below applies to a closed rectangular cavity and provides a good first approximation for a slightly lossy cavity (i.e., with high dielectric constant contrast at the edge).
Rectangular terahertz microcavity resonator geometry and eigenfrequencies.
Although a rectangular geometry is shown above, more complex structures may be used for different applications. In a different structure (e.g., circular, hemispherical, or cylindrical) with an open edge, the eigenfrequencies may not obey such a simple equation. Instead, they may be determined from a dispersion relation that is a transcendental equation, which requires a numerical technique to extract specific frequencies. This is a well-known procedure for solving Sturm-Liouville problems in waveguides and resonators.
If you have a much more complex structure that can’t be approximated as a simple shape, the various eigenfrequencies and the spatial distribution of the electromagnetic field can be determined using a 3D field solver (FDFD technique). A field solver you would normally use for IC packages can also be used for modeling terahertz microcavity resonators.
Applications for terahertz microcavity resonators are still being researched, as are the device architectures required for different applications. Some proposed applications of terahertz microcavity resonators include:
Sensing and imaging: High-Q terahertz microcavity resonators can be used for highly coherent imaging and sensing, with applications in molecular detection and biological imaging.
Silicon photonics: While this application area is normally discussed in terms of SMF or MMF wavelengths, devices in this area can also operate at THz frequencies and will need terahertz microcavity resonators to act as filters and amplifiers.
Communication: Currently, the world record for the highest data rate transmission belongs to an experimental wireless system operating at THz frequencies. Miniaturizing these systems at the chip level will require microcavity structures, including terahertz microcavity resonators.
The important advancement provided by these structures is that they can occur on an integrated circuit. Today, these applications still involve large optical systems where an infrared mode comb in a femtosecond soliton laser is used to generate a terahertz wave through interference. Similarly, large systems are also used for the detection and manipulation of terahertz waves. Terahertz microcavity resonators are one class of components that can provide high-Q or low-Q reception of THz frequencies, which can then be passed to a detector element or other photonic circuit.
The range of useful materials for building terahertz microcavity resonators, or for building coupling structures, is also an open research question. Some material platforms used for terahertz microcavity resonators include:
Silicon: This material is the most promising for the fabrication of terahertz devices and their integration alongside other electronic circuits.
GaAs, other III-V’s, and II-VI’s: This promising set of photonic materials has already shown interesting results at ~3 THz frequencies, particularly for the generation of laser light. This material platform is promising for photonics in general.
Photonic crystals: Periodic nanostructures that are fabricated through chemical deposition methods provide a tunable platform for fabricating a range of terahertz devices, including terahertz microcavity resonators.
Dielectrics: This broad range of materials includes oxides, salts, polymers, and other materials that can support transmission or absorption in various THz frequency ranges. For integration, the best set of materials should bond to the industry’s current range of semiconductors.
Microcavity resonator materials should be chosen to integrate into existing semiconductor materials platforms and manufacturing processes.
As your technology and designs push into more advanced spaces with the years to come, more advanced software that can navigate the nuances and challenges of THz components will be necessary. Be sure to prepare adequately as you stay ahead of the frequency curve.


BASIC KNOWLEDGE - SEMICONDUCTORS The workings and applications of semiconductors
Thanks to semiconductors, the world is a safer, smarter and more convenient place. But what are they made of, what do they do, and where are they found?
Without semiconductors, our world would look much more like it did in the late 1950s or early 1960s; we would have no electronic hand calculators, microwave ovens, digital alarm clocks, cellphones, tablets, personal computers, electronically controlled transmissions or washing machines.
What are semiconductors and what do they do?
Semiconductors are the backbone of the information technology and modern electronics industries—and therefore of our society as we know it. Without them, the vast majority of the electronic devices prevalent today would not exist. Despite its status as an essential building block of any electronic device, a semiconductor’s purpose is relatively simple: to allow an amplified current to move along a circuit board, which in turn enables the elements on the circuit board to be powered. Semiconductors are typically made of an insulating material such as silicon, and often have atom-sized impurities mixed in during the production process (known as “doping”) to influence their conductivity depending on the application.
A brief history of semiconductor technology
Semiconductors revolutionized the electronics industry back when the first transistor was developed in the 1940s, as they enabled signals to be amplified to such an extent that they powered an electrical circuit. Scientists soon discovered that semiconductors could be reduced in size, paving the way for the development of computer processors, memory chips, integrated circuits and systems on a chip (SoC). While these devices have gradually became more complex, rugged, efficient and reliable, it’s their reduction in size above all (to a matter of nanometers) that’s enabled a host of technologies to become smaller and more powerful. These technologies, in turn, have opened the door to most of the communication, transportation, entertainment, industry and medical innovations that have helped to shape society over the past 70 years.
Types, groups and classifications
The majority of semiconductor materials are inorganic, and can be divided into two basic groups: intrinsic, where purity is retained, and extrinsic, which are “doped” with impurities to affect the material’s conductivity. They can also be divided by type, namely N-type and P-type. In semiconductors, electrons move across the substrate to holes as part of the process of electrical conductance. N-type semiconductors are made by doping the material with an electron donor element, meaning there are more electrons than holes. In this case, the electrons are known as the majority carriers and the holes as the minority carriers. In P-type semiconductors, the holes are the majority carriers, while the electrons are the minority carriers.
With the advent of the metal-oxide-semiconductor process in the late 1950s, which enabled semiconductors to be miniaturized for the first time, silicon became the most commonly used element in their production. This is due to its ease of production and strong electrical and mechanical characteristics. Other semiconductor materials include: gallium arsenide, which is used in radio-frequency modules and is difficult to produce; germanium, which was used in early transistor technology (along with lead sulfide); silicon carbide; gallium phosphide; and cadmium sulfide.
One semiconductor material that’s gaining ground in the field of electronics is gallium nitride (GaN). Hailed as the silicon of the future, gallium nitride semiconductors are highly temperature resistant, conduct more current, improve power density and are more efficient overall. The material has found major support within the aerospace industry, and is now increasingly being used in household appliances and road vehicles.
A constant companion in everyday life
Once reserved for televisions and radios, semiconductors are now unavoidable in day-to-day life. From making toast in the morning to switching on a light, checking the weather or reading an e-book, even the most banal activities are made possible thanks to semiconductors. They’re the reason why smartphones are more powerful than the supercomputers of 20 years ago, why cars will soon be able to drive themselves, and why it’s possible to communicate with people instantly all over the world. Semiconductors are as critical to modern life as air or water—and with artificial intelligence, quantum computing and advanced wireless networks on the horizon, their importance won’t be diminishing any time soon.
It’s a little known fact that Britney Spears is an expert in semiconductor physics. (Yes, you read that right.) Britney Spears knows the ins and outs of the vital laser components that have made it possible to hear her super music in a digital format.


What is quantum computing and why does the future of Earth depend on it?
Computing power is reaching a crisis point. If we continue to follow the trend in place since computers were introduced, by 2040, we will not have the capability to power all of the world’s machines, unless we can crack quantum computing.
Quantum computers promise faster speeds and more robust security than their classical counterpart, and scientists have been striving to create a quantum computer for decades.
What is quantum and how does it help us?
Quantum computing differs from classical computing in one fundamental way—the way information is stored. Quantum computing makes the most of a strange property of quantum mechanics, called superposition. It means one ‘unit’ can hold much more information than the equivalent found in classical computing.
Information gets stored in ‘bits’ in state ‘1‘ or ‘0,’ like a light switch that turns on or off. By contrast, quantum computing can include a unit of information that can be ‘1,’ ‘0,’ or a superposition of the two states.
Think of a superposition as a sphere. ‘1‘ is written at the north pole, and ‘0‘ is written at the south—two classical bits. However, a quantum bit (or qubit) can be found anywhere between the poles.
“Quantum bits that can be on and off at the same time, provide a revolutionary, high-performance paradigm where information is stored and processed more efficiently,” said Dr. Kuei-Lin Chiu to Alphr in 2017. Dr. Chiu was a researcher for the quantum mechanical behavior of materials at the Massachusetts Institute of Technology.
The ability to store a much higher amount of information in one unit means quantum computing can be faster and more energy-efficient than computers we use today. So why is it so hard to achieve?
Qubits, the backbone of a quantum computer, are tricky to make and, once established, are even harder to control. Scientists must get them to interact in specific ways that would work in a quantum computer.
Researchers have tried using superconducting materials, ions held in ion traps, individual neutral atoms, and molecules of varying complexity to build them. However, making them hold onto quantum information for a long time is proving difficult.
In recent research, scientists at MIT devised a new approach, using a cluster of simple molecules made of just two atoms as qubits.
“We are using ultracold molecules as ‘qubits’” Professor Martin Zwierlein, lead author of the paper, told Alphr in 2017. “Molecules have long been proposed as a carrier of quantum information, with very advantageous properties over other systems like atoms, ions, superconducting qubits, etc. “Here, we show for the first time, that you can store such quantum information for extended periods in a gas of ultracold molecules. Of course, an eventual quantum computer will have to also make calculations, for example, have the qubits interact with each other to realize so-called “gates.” Zwierlein continued, “But first, you need to show that you can even hold on to quantum information, and that’s what we have done.”
The qubits created at MIT held onto the quantum information longer than previous attempts, but still only for one second. This timeframe might sound short, but it is “in fact on the order of a thousand times longer than a comparable experiment that has been done,” explained Zwierlein.
More recently, researchers from the University of New South Wales made a significant breakthrough in the push towards quantum computing. They invented a new type of qubit called a flip-flop qubit, which uses the electron and the nucleus of a phosphorus atom. They are controlled by an electrical signal instead of a magnetic one, making them easier to distribute. The ‘flip-flop’ qubit works by pulling the electron away from the nucleus using an electric field, creating an electric dipole.
It is not just qubits, however, that scientists need to figure out. They also need to determine the material to make quantum computing chips successfully.
Chiu’s paper, published earlier in 2017, found ultra-thin layers of materials that could form the basis for a quantum computing chip. Chiu said to Alphr, “The interesting thing about this research is how we choose the right material, find out its unique properties, and use its advantage to build a suitable qubit.”
“Moore’s Law predicts that the density of transistors on silicon chips doubles approximately every 18 months,” Chiu told Alphr. “However, these progressively shrunken transistors will eventually reach a small scale where quantum mechanics play an important role.”
Moore’s Law, which Chiu referred to, is a computing term developed by Intel co-founder Gordon Moore in 1970. It states that the overall processing power for computers doubles about every two years. As Chiu states, the chips’ density decreases—a problem that quantum computing chips can potentially answer.
Is quantum computing the ultimate vaporware?
What is vaporware?
In case you never heard of the term vaporware, it is essentially a software-related product that is advertised but not yet available or possibly never becomes available. An example is a software product that was heavily marketed but never saw the light of day.
Despite people making optimistic predictions for decades about the impact of quantum computers, and the various advancements in business and research environments, how close are we to achieving the dream of quantum computing? Is this situation a prediction of future vaporware, or will it become something of use?
We delve into the reality of quantum computing in another article. In summary, a quantum computer will likely perform a very unrealistic computation faster than a conventional computer in the next year or two. However, it won’t be a straightforward process, and it won’t be cheap or beneficial for everyday consumers.


Moving quantum computation from the labs and into the real world will require more precise ways to measure performance. Researchers at the Department of Energy’s Oak Ridge National Laboratory have taken a step in that direction by developing a quantum chemistry simulation benchmark to evaluate the performance of quantum devices and guide the development of applications for future quantum computers, according to a news release.
Quantum computers use the laws of quantum mechanics and units known as qubits to greatly increase the threshold at which information can be transmitted and processed. Whereas traditional “bits” have a value of either 0 or 1, qubits are encoded with values of both 0 and 1, or any combination thereof, allowing for a vast number of possibilities for storing data.
While still in their early stages, quantum systems have the potential to be exponentially more powerful than today’s leading classical computing systems and promise to revolutionize research in materials, chemistry, high-energy physics, and across the scientific spectrum.
But because these systems are in their relative infancy, understanding what applications are well suited to their unique architectures is considered an important field of research.
“We are currently running fairly simple scientific problems that represent the sort of problems we believe these systems will help us to solve in the future,” said ORNL’s Raphael Pooser, principal investigator of the Quantum Testbed Pathfinder project. “These benchmarks give us an idea of how future quantum systems will perform when tackling similar, though exponentially more complex, simulations.”
Pooser and his colleagues calculated the bound state energy of alkali hydride molecules on 20-qubit IBM Tokyo and 16-qubit Rigetti Aspen processors. These molecules are simple and their energies well understood, allowing them to effectively test the performance of the quantum computer.
By tuning the quantum computer as a function of a few parameters, the team calculated these molecules’ bound states with chemical accuracy, which was obtained using simulations on a classical computer. Of equal importance is the fact that the quantum calculations also included systematic error mitigation, illuminating the shortcomings in current quantum hardware.
Systematic error occurs when the “noise” inherent in current quantum architectures affects their operation. Because quantum computers are extremely delicate (for instance, the qubits used by the ORNL team are kept in a dilution refrigerator at around 20 millikelvin (or more than -450 degrees Fahrenheit), temperatures and vibrations from their surrounding environments can create instabilities that throw off their accuracy. For instance, such noise may cause a qubit to rotate 21 degrees instead of the desired 20, greatly affecting a calculation’s outcome.
“This new benchmark characterizes the ‘mixed state,’ or how the environment and machine interact, very well,” Pooser said. “This work is a critical step toward a universal benchmark to measure the performance of quantum computers, much like the LINPACK metric is used to judge the fastest classical computers in the world.”
While the calculations were fairly simple compared to what is possible on leading classical systems such as ORNL’s Summit, currently ranked as the world’s most powerful computer, quantum chemistry, along with nuclear physics and quantum field theory, is considered a quantum “killer app.” In other words, it is believed that as they evolve quantum computers will be able to more accurately and more efficiently perform a wide swathe of chemistry-related calculations better than any classical computer currently in operation, including Summit.
“The current benchmark is a first step towards a comprehensive suite of benchmarks and metrics that govern the performance of quantum processors for different science domains,” said ORNL quantum chemist Jacek Jakowski. “We expect it to evolve with time as the quantum computing hardware improves. ORNL’s vast expertise in domain sciences, computer science and high-performance computing make it the perfect venue for the creation of this benchmark suite.”
ORNL has been planning for paradigm-shifting platforms such as quantum for more than a decade via dedicated research programs in quantum computing, networking, sensing and quantum materials. These efforts aim to accelerate the understanding of how near-term quantum computing resources can help tackle today’s most daunting scientific challenges and support the recently announced National Quantum Initiative, a federal effort to ensure American leadership in quantum sciences, particularly computing.
Such leadership will require systems like Summit to ensure the steady march from devices such as those used by the ORNL team to larger-scale quantum systems exponentially more powerful than anything in operation today.
Access to the IBM and Rigetti processors was provided by the Quantum Computing User Program at the Oak Ridge Leadership Computing Facility, which provides early access to existing, commercial quantum computing systems while supporting the development of future quantum programmers through educational outreach and internship programs. Support for the research came from DOE’s Office of Science Advanced Scientific Computing Research program.
“This project helps DOE better understand what will work and what won’t work as they forge ahead in their mission to realize the potential of quantum computing in solving today’s biggest science and national security challenges,” Pooser said.
Next, the team plans to calculate the exponentially more complex excited states of these molecules, which will help them devise further novel error mitigation schemes and bring the possibility of practical quantum computing one step closer to reality.
UT-Battelle manages ORNL for DOE’s Office of Science. The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, please visit https://science.energy.gov/.


When it comes to studying transportation systems, stock markets and the weather, quantum mechanics is probably the last thing to come to mind.
However, scientists at Australia’s Griffith University and Singapore’s Nanyang Technological University have just performed a ‘proof of principle’ experiment showing that when it comes to simulating such complex processes in the macroscopic world quantum mechanics can provide an unexpected advantage.
Griffith’s Professor Geoff Pryde, who led the project, says that such processes could be simulated using a “quantum hard drive”, much smaller than the memory required for conventional simulations.
“Stephen Hawking once stated that the 21st century is the ‘century of complexity’, as many of today’s most pressing problems, such as understanding climate change or designing transportation system, involve huge networks of interacting components,” he says.
“Their simulation is thus immensely challenging, requiring storage of unprecedented amounts of data. What our experiments demonstrate is a solution may come from quantum theory, by encoding this data into a quantum system, such as the quantum states of light.”
Einstein once said that “God does not play dice with the universe,” voicing his disdain with the idea that quantum particles contain intrinsic randomness.
“But theoretical studies showed that this intrinsic randomness is just the right ingredient needed to reduce the memory cost for modelling partially random statistics,” says Dr Mile Gu, a member of the team who developed the initial theory.
In contrast with the usual binary storage system – the zeroes and ones of bits – quantum bits can be simultaneously 0 and 1, a phenomenon known as quantum superposition.
The researchers, in their paper published in Science Advances, say this freedom allows quantum computers to store many different states of the system being simulated in different superpositions, using less memory overall than in a classical computer.
The team constructed a proof-of-principle quantum simulator using a photon – a single particle of light – interacting with another photon.
The data showed that the quantum system could complete the task with much less information stored than the classical computer– a factor of 20 improvements at the best point.
“Although the system was very small – even the ordinary simulation required only a single bit of memory – it proved that quantum advantages can be achieved,” Pryde says.
“Theoretically, large improvements can also be realised for much more complex simulations, and one of the goals of this research program is to advance the demonstrations to more complex problems.”
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A device that eavesdrops on the quantum whispers of atoms could form the basis of a new type of quantum computer.
Stanford physicists have developed a “quantum microphone” so sensitive that it can measure individual particles of sound, called phonons.
The device, which is detailed July 24 in the journal Nature, could eventually lead to smaller, more efficient quantum computers that operate by manipulating sound rather than light.
“We expect this device to allow new types of quantum sensors, transducers and storage devices for future quantum machines,” said study leader Amir Safavi-Naeini, an assistant professor of applied physics at Stanford’s School of Humanities and Sciences.
Quantum of motion
First proposed by Albert Einstein in 1907, phonons are packets of vibrational energy emitted by jittery atoms. These indivisible packets, or quanta, of motion manifest as sound or heat, depending on their frequencies.
Like photons, which are the quantum carriers of light, phonons are quantized, meaning their vibrational energies are restricted to discrete values – similar to how a staircase is composed of distinct steps.
“Sound has this granularity that we don’t normally experience,” Safavi-Naeini said. “Sound, at the quantum level, crackles.”
The energy of a mechanical system can be represented as different “Fock” states – 0, 1, 2, and so on – based on the number of phonons it generates. For example, a “1 Fock state” consist of one phonon of a particular energy, a “2 Fock state” consists of two phonons with the same energy, and so on. Higher phonon states correspond to louder sounds.
Until now, scientists have been unable to measure phonon states in engineered structures directly because the energy differences between states – in the staircase analogy, the spacing between steps – is vanishingly small. “One phonon corresponds to an energy ten trillion trillion times smaller than the energy required to keep a lightbulb on for one second,” said graduate student Patricio Arrangoiz-Arriola, a co-first author of the study.
To address this issue, the Stanford team engineered the world’s most sensitive microphone – one that exploits quantum principles to eavesdrop on the whispers of atoms.
In an ordinary microphone, incoming sound waves jiggle an internal membrane, and this physical displacement is converted into a measurable voltage. This approach doesn’t work for detecting individual phonons because, according to the Heisenberg uncertainty principle, a quantum object’s position can’t be precisely known without changing it.
“If you tried to measure the number of phonons with a regular microphone, the act of measurement injects energy into the system that masks the very energy that you’re trying to measure,” Safavi-Naeini said.
Instead, the physicists devised a way to measure Fock states – and thus, the number of phonons – in sound waves directly. “Quantum mechanics tells us that position and momentum can’t be known precisely – but it says no such thing about energy,” Safavi-Naeini said. “Energy can be known with infinite precision.”
The quantum microphone the group developed consists of a series of supercooled nanomechanical resonators, so small that they are visible only through an electron microscope. The resonators are coupled to a superconducting circuit that contains electron pairs that move around without resistance. The circuit forms a quantum bit, or qubit, that can exist in two states at once and has a natural frequency, which can be read electronically. When the mechanical resonators vibrate like a drumhead, they generate phonons in different states.
“The resonators are formed from periodic structures that act like mirrors for sound. By introducing a defect into these artificial lattices, we can trap the phonons in the middle of the structures,” Arrangoiz-Arriola said.
Like unruly inmates, the trapped phonons rattle the walls of their prisons, and these mechanical motions are conveyed to the qubit by ultra-thin wires. “The qubit’s sensitivity to displacement is especially strong when the frequencies of the qubit and the resonators are nearly the same,” said joint first-author Alex Wollack, also a graduate student at Stanford.
However, by detuning the system so that the qubit and the resonators vibrate at very different frequencies, the researchers weakened this mechanical connection and triggered a type of quantum interaction, known as a dispersive interaction, that directly links the qubit to the phonons.
This bond causes the frequency of the qubit to shift in proportion to the number of phonons in the resonators. By measuring the qubit’s changes in tune, the researchers could determine the quantized energy levels of the vibrating resonators – effectively resolving the phonons themselves.
“Different phonon energy levels appear as distinct peaks in the qubit spectrum,” Safavi-Naeini said. “These peaks correspond to Fock states of 0, 1, 2 and so on. These multiple peaks had never been seen before.”
Mechanical quantum mechanical
Mastering the ability to precisely generate and detect phonons could help pave the way for new kinds of quantum devices that are able to store and retrieve information encoded as particles of sound or that can convert seamlessly between optical and mechanical signals.
Such devices could conceivably be made more compact and efficient than quantum machines that use photons, since phonons are easier to manipulate and have wavelengths that are thousands of times smaller than light particles.
“Right now, people are using photons to encode these states. We want to use phonons, which brings with it a lot of advantages,” Safavi-Naeini said. “Our device is an important step toward making a ‘mechanical quantum mechanical’ computer.”
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This article will be dealing with how computers calculate trigonometric ratios, logarithms, and exponents. We will be exploring the mathematics behind these functions and shall end with a proof for the famous e^πi = -1. The article would be a pretty light read for anyone familiar with basic differentiation formulas such as those for cos(x), sin(x), and e^x. Even if the reader isn’t aware of these formulas, I’ve tried my best to make the article approachable for a general audience.
Let’s start by talking about polynomial. A polynomial is any function of a variable that involves only multiplication, subtraction, and addition. Polynomials are of different degrees and the degree of the polynomial is the highest power of the variable in the function. We denote the function by f(x) and it represents the mathematical processes we are carrying out on our variable x. Now our n-degree polynomial is given by :
Imagine you are struck by the particularly brilliant thought which makes you ask if you can represent any function f(x) as one of these polynomials. For whatever reason, you decide that you shall first try to express sin(x) and cos(x) as one of these polynomials. You enthusiastically write down your first equation
You cleverly come up with the idea of plugging in x as zero to eliminate all the x terms as zero to any power is zero in our polynomial.
Now that we’ve gotten the constant out of the way, you now get down to the task of figuring out each of the coefficients for this polynomial. You learned somewhere that the derivative of sin(x), represented by d(sin(x))/dx = cos(x) and also conveniently learned that the derivative of ax^n, given by d(ax^n)/dx = (n)(a)(x^n-1) and know that the derivative of a constant c is zero. You write them down to remember these results along with a few other things you learned that you think might be useful.
Since you know that cos(0) = 1, you go ahead and differentiate the equation f(x) and write it as f ‘(x) to get a new equation you can work with:
You go ahead and continue differentiation multiple times and get :
You notice that this is an infinite process, but the coefficients of every term with an even power are zero and that only the terms with odd powers of x remain. The odd powers of x seem to be the ones remaining and their coefficients seem to be of the form 1/(the power’s factorial) or- 1/(the power’s factorial ).The plus and minus alternate with every second term being negative. Factorial is the multiplication of all the natural numbers( in this case ) from one up to the number itself and is represented as the number followed by an exclamation mark. For example 1! = 1, 2! = 2(1), 3! = (3)(2)(1) , 4! = 4(3)(2)(1), and in general k! = k(k-1)(k-2)….(1). So you write down your observations:
With that, you have converted sin(x), a function seemingly related only to triangles and circles into an infinite polynomial in which substituting any x will get you closer and closer to the value of sin(x) with the more terms you choose to add.
Following a similar process for cos(x), we can obtain it’s polynomial and with some knowledge of limits of a function and such, we can also obtain the polynomial for e^x.
Indeed, these exact formulas were the one’s calculators used to compute sin(x), cos(x), tan(x), or any number to another power. For exponentiation:
The calculator calculates the value of log(k) and then substitutes xlog(k) into the e^x expansion.
The above approach should also help you better grasp the fact that exponentiation isn’t just repeated multiplication and how raising numbers to the power of a fraction like 1/2 might not make sense under repeated multiplication, but makes sense when we think about the number as an input to our polynomial, which we then know how to work with. The precision of your calculator naturally depends on how many of these terms in the expansion it adds up but the infinite sum can be approximated pretty well with just a few terms as these terms get exponentially smaller and converge at a value.
Now that we have managed to make exponentiation a polynomial, it would seem less absurd to input a complex number as the exponent due to the fact that the solutions/zeroes of several polynomials are often complex numbers. Flowing with this train of thought, let’s try raising e to the power of i, where i is the square root of -1.
Now stare at our final expression for a while and try to notice some patterns and try simplifying this into two other infinite polynomials that we have discussed below.
If you spotted it then great, but if not, here’s how it breaks down:
With that, we have just defined a way to raise any number to a complex number.
Now, let me prove what was promised in the title:
We have just proved a result that many argue is the most beautiful result in all of mathematics, but we have more important things to think about.
Let us look at what this means for any complex number z and it’s representation in the argand plane, where the usual y-axis is replaced by an imaginary axis which tells us the value b if z = x + yi. Much the same way we plot any point (x,y), a complex number x + yi can be represented by a line from the origin to the point (x,y). We call the length of this line the modulus of the complex number and the angle it makes with the x-axis it’s argument.
This means that any complex number z can be written as |z| e^i𝞱 which would imply that the complex number z is the radius of a circle centered at the origin, with the length of the radius being |z| and the angle it’s the radius at angle 𝞱 with the x-axis. The x value of the complex number is |z|(cos(𝞱 )) and the y value is |z|(sin(𝞱 )). This leads us to z = |z| cos(𝞱 ) + |z| i sin(𝞱 ).
This greatly simplifies the multiplication of complex numbers as:
This shows us that if we take any line which represents a complex number, and multiply it by another number, it gets scaled( stretched or squished ) by the modulus of the second number and then rotated by an angle equal to the argument of the second complex number. This can be used in the scaling and rotation of objects or images by assigning each point or pixel a specific complex number and then multiplying it by a complex number whose argument is the angle you want to rotate by and whose modulus is the desired resizing scaling amount. These results are also quite significant for 2-D rotational motion in Newtonian mechanics, and the development of vectors and vector analysis, in fact, comes from complex numbers and higher dimension complex number systems called quaternions.
I encourage the reader to try and code functions, recursive, or otherwise to compute the sin, cos, or log values using the polynomials I have mentioned today. You might also have several useful and key insights by thinking about the rotation properties I mentioned above and how they might help you calculate the nth-roots of real numbers by thinking of the real numbers as having arg(nπ) where n belongs to the integers. The same line of reasoning will also help you understand why complex roots to polynomials always come in pairs of two with both being conjugates. I encourage you to also go through the links I have provided below for better depth and understanding of the results I have used today and they will certainly help you see the bigger picture when it comes to the importance of these formulas. I would like to cover more serious topics by talking about things like quantum computing, the Fourier series, Fermat’s little theorem, and other crucial mathematical results that play a big role in modern computers. Hence, the articles I plan on writing will be pretty long and technical so please let me know if those are some topics you might be interested in. I mentioned that these polynomials were used in calculators initially, nowadays there are optimizations and matrices that can be used for computations, topics that I might cover in future articles.
~ Koka Sathwik


Quantum computing is hailed as the future holy grail of information processing. However, quantum computing machines are very complex, delicate, and cumbersome. They also require exotic materials such as superconducting metals or levitated atoms. But new developments demonstrated in two recently published studies may prove revolutionary — they suggest that quantum states can be controlled in regular, everyday devices.
Quantum mechanics in classical semiconductors
It’s difficult to grasp just how quantum computers work, but if we were to simplify things, the gist would be that digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), whereas quantum computers use qubits, also known as quantum bits.
A qubit is the quantum analog of the digital bit that encodes information in 1s and 0s. The crucial difference is that a quantum bit can exist in both states at the same time due to a quantum quirk called superposition.
It’s akin to saying that a switch is both on and off at the same time or that water is both flowing and not flowing through a pipe simultaneously — which, in day to day life, makes absolutely no sense, but in the quantum domain, few things are reasonable.
Two-qubits can perform operations on four values, three on eight values and so on in powers of two. Today’s computers have millions of transistors. Now imagine a quantum logic gate that works with millions of qubits. The computing force would be unheard of, allowing scientists to solve currently intractable problems and perform complex models that take longer than the age of the universe for today’s fastest supercomputers to process.
Although classical computing systems have always been thought of as under-equipped to read and maintain quantum states, scientists at the University of Chicago’s Pritzker School of Molecular Engineering showed that this isn’t necessarily true.
“The ability to create and control high-performance quantum bits in commercial electronics was a surprise,” said lead investigator David Awschalom, professor of molecular engineering at the University of Chicago. “These discoveries have changed the way we think about developing quantum technologies—perhaps we can find a way to use today’s electronics to build quantum devices.”
Awschalom and colleagues published a paper in the journal Science, demonstrating they could electrically control quantum states embedded in silicon carbide. Immediately, this opens the possibility of designing quantum computers based on traditional materials, which could vastly accelerate their development.
What’s more, quantum states in silicon carbide emit single particles of light with a wavelength near the telecommunications band.
“This makes them well suited to long-distance transmission through the same fiber-optic network that already transports 90 percent of all international data worldwide,” said Awschalom, who is also a senior scientist at Argonne National Laboratory and director of the Chicago Quantum Exchange.
In a second paper, which was published in Science Advances, the researchers were able to combine these light particles with existing electronics to make a “quantum FM radio”. They claim that just like the information that plays music in your car is transmitted through the air over long distances, so can quantum information be exchanged wirelessly.
One important challenge that researchers managed to overcome was quantum noise. Common semiconductor devices have impurities, which can scramble quantum information by adding noise to the electrical environment. This is why quantum research exclusively uses pure materials that are free of fluctuating fields. But, the researchers managed to eliminate noise in the quantum signal by employing one of the most basic electronics components — the diode, a one-way switch for current.
“In our experiments, we need to use lasers, which unfortunately jostle the electrons around. It’s like a game of musical chairs with electrons; when the light goes out everything stops, but in a different configuration,” said graduate student Alexandre Bourassa. “The problem is that this random configuration of electrons affects our quantum state. But we found that applying electric fields removes the electrons from the system and makes it much more stable.”
For decades, consumers have enjoyed the dividends of Moore’s Law — an empirical observation that states the number of transistors in an integrated circuit doubles every two years or so. This prediction has proven true ever since it was first proposed by American engineer Gordon Moore in 1965. However, there’s a physical limit to how many transistors you can cram into a chip — and in a decade we should all be feeling it. But, by integrating quantum mechanics with classical semiconductor technology, these new developments suggest that we might not only avoid Moore’s brick wall but scale computing power to incredible heights.
“This work brings us one step closer to the realization of systems capable of storing and distributing quantum information across the world’s fiber-optic networks,” Awschalom said. “Such quantum networks would bring about a novel class of technologies allowing for the creation of unhackable communication channels, the teleportation of single electron states and the realization of a quantum internet.”
This is a syndicated post. Read the original post at Source link .


The photon is a sine wave related to the E and B fields, but only of one period. As an open string it has two ends. The question is, what does their physical reality look like? First, two parallel photons of the same wavelength are to be investigated. From the chapter about neutrinos as oscis it can be deduced that their approach can never be total. According to the dilemma of QT, this behavior cannot be attributed to the photon as a quantum, but is owed to field theory. After the dilemma of the QT, annihilation cannot occur in any case.
So it just seems like there's zero point fluctuation. But after the TO they do not exist!
Polarisation: Simply changing the right angle between the E and B fields is not allowed after the QT dilemma, but the right angle refers to the unbent space-time. Polarization can also be generated with photons twisted against each other. After the last chapter, however, no mathematically correct rotary polarization can occur. This should be observable experimentally! Polarization and torsion of the wave in the gravitational field are to be distinguished. In the latter case, the wave appears rotated in the before-after comparison.
Shortest wavelength: It is determined in the TO by the minimum radius of curvature of the circular wave in the plane of the E field. The reason for this is that quantum processes cannot have a smaller wavelength.
With 5,876516699923 10-16 m as minimum radius is λ0 = 3,69232433863517 10-15 m,and thus E0 = h c/λ0 = 0,33578900862721 GeV (in the gamma radiation range).
The quantum number, which stands for the area integral of the sine wave, was determined arbitrarily. The area remains intact if the wavelength and amplitude are changed in inverse proportion. One more comment on the maximum energy of photons: Photons can link up. It is then a quantum object.
The behavior of the graph is more complex because the amplitude influences its length change. The reference figure is the extension factor λ'. It sets the length difference of graph and wavelength in relation to the wavelength, which should be in the counter of the quotient. Its function curve as a function of amplitude a is known:
If a < 1, their function value runs asymptotically against 0,25,if a > 1, it runs asymptotically against 0, which means that a = 1 is a turning point.Even if λ0' still increases with increasing wavelength,
remains λ0' under λ0' ‧ 1,16, because 0,25/0,216... = 1,15739... < 1,16.
The shortest wavelength is identified with a = 1, because then the extreme values lie on top of each other. If a were greater than 1, there would have to be an effect that can be associated with the turning point. This is not known. The arguments are admittedly weak, but perhaps a stronger argument will be found.
For the shortest wavelength λ0 = 3,69232433863517 10-15 m is then λ0' = 0,2160028025443.
The wavelength of the photon must remain constant in empty space. In the prestressed space-time continuum, this can only be ensured by limiting the oscillation space to the wavelength, which again results in the principle of constriction. The corresponding space-time line is constricted to the wavelength based on the length of the graph.
With wD = - 1,09020236896306 10-11 kgm/s2 as the energy density of the space-time line,
it is possible to for the photon with the shortest wavelength, establish the following energy equation:
E0 ART + E0 kin = wD λ0 λ0' + E0 kin = -8,69493521355215 10-27 kgm²/s² + E0 kin = 0,where E0 ART corresponds to a mass defect of -6,03829837739599 10-25 eV/c².
Even the longest wavelength photon thus remains below 1.16 times this value! The above equation must give 0 because the TO does not allow a negative energy balance (no zero fluctuation). So the photon is only massless at c - see also INTERPRETATION OF THE MASS. The first summand is the energy with which the photon counteracts its extension (holding the wavelength). With a higher negative energy density, this no longer works, which leads to a redshift. The above equation can also be interpreted differently. With the extension factor λ0' the photon is ironed (amplitude = 0). Thus, the photon once again confirms the conclusion that the universe has an event horizon. If, conversely, the rest mass were known, wD could be confirmed.
Gravitational and electromagnetic field theories show a relationship. This is reflected in the gravitational shift of the wavelength and the gravitational lens effect. Due to this relationship, it cannot be ruled out that they may have a resonant effect. The damping factors must be determined for this purpose. Since a photon remains photon as long as it is not absorbed, its electromagnetic damping is 0. A resonance catastrophe cannot occur with the dilemma of QT at the quantum level!
If the damping in the gravitational space were to be √½, the resonance increase would be 1. Thus the resonance amplitude would decrease exactly to the same extent as the effect of gravity. At stronger damping, gravity waves would not be detectable as forced swinging of astronomic events. In order not to have to think about a solution to Einstein's field equations, it is first a question of the prerequisite that leaves the constriction area unchanged. Its relativistic compression is of no interest. In any case, this requires that the divergence of the vector field at the ends of the constriction must remain 0 at certain points, because this is the only way to maintain the one-sided unsteadiness at the ends of the electromagnetic wave. Einstein's field equations allow this (conservation of energy and impulses).
If one considers the preservation of the constriction under the aspect of the resonance,
then the damping must be √½, because only in this way the divergence remains 0.
Divergence 0 affects the problem known as the classical borderline case of the harmonic oscillator. Classically interpreted, this results in a sharply defined oscillation. In quantum mechanics this becomes the wave equation (see right). The wave oscillates beyond the boundary, which can no longer correspond to quantum reality with the TO. Combined, the above dampings lead to resonance in the one room of the TO, which is actually a sandwich of rooms - see SEPARATION OF ROOMS. This explains the spooky distant effect of the photon. Since the oscillation propagates gravitatively with c, the oscillation is at the latest there, where the photon is, which reminds of the fairy tale "The rabbit and the hedgehog".
Quantum entanglement turns out to be a resonance event, and the ERP paradox is no longer one!
last modification 24.02.2019


First, let’s start by analyzing the concept and components of classical computing. Classic computers will obey the principles of classical physics. A classical computer will perform operations using information stored in the form of bits; whose value is either zero (0) or one (1). Now, when we program a classical computer; we will have a CPU which has an input, an output, and software which regulates the CPU. This is called a Turing Machine, which also happens to be the substructure of your cell phones and laptops computing power. In spite of the relative simplicity, a Turing machine may be constituted to simulate any given computer algorithm’s logic. Unfortunately, even as classical computers have become faster and more concise; they are unable to solve arithmetic like factoring massive integers effectively.
In quantum computing, instead of having information stored in the form of bits, we have a new unit called a qubit or quantum bit, which carries quantum information. In a classical system a bit can only be in two positions; either up or down (commonly represented as a zero or one). In quantum computing, the qubit can be in any superposition of both at the same time.
Qubits can be in the in the given states |0} and |1} (note: 0 and 1 are not always the given values for a qubit, various others may be used but with the same result) as well as any addition of the two; which will yield another valid quantum state x|0} + y|1} where the two variables x and y represent complex numbers.
With this basic knowledge, we can analyze the processor inside a quantum computer; specifically the D Wave quantum computer.
The Elementary Units of Quantum Computing
In the introduction, we covered how we can represent qubits symbolically as a 0 or 1, as well as a superposition
of both of the states. We will now cover how qubits are constructed as well as their appearance.
In conventional computing, we are using the CMOS transistors to encode bits of information. This is done by regulating the voltage to transistors that are fitted with a bus to determine whether the state is a 0 or 1.
Quantum transistors are somewhat similar, yet vastly different than our current CMOS transistors. Interference refers to the actual electrons, and how they act as waves that create interference patterns to cause quantum effects to occur. This is the basis of quantum computing (basically a quantum transistor.) The electron behaves as a qubit due to the nature of the material called niobium; which is what the gold loop is made of. When the niobium is cooled to reach its critical temperature; it will manifest the qualities of quantum mechanics.
Our classic transistors will encode in two states by regulating voltages. The SQUID will encode the two states into magnetic fields which are designated down or up. The two states are given as -1, +1 in which the qubit can be in superposition of both. This is done by combining the Josephson Effect (or the phenomenon of supercurrent) and the quantization of flux. BCS pairs are tunneled through a weak link (which in this case would be a weak insulating barrier) between the niobium. For each current below a given critical value, a supercurrent will be established between the two superconductors and will yield no voltage across the Josephson junction. Any time a current is larger than the critical value, a voltage will be read across the junction.
The qubits need to be linked together in a fashion that is capable of relaying information. The qubits are attached together by couplers which are also made from superconducting material. When we combine the qubits and couplers together we are capable of creating a programmable structure of quantum mechanics.
The superconducting qubit is formed into rectangles; with each of the dots representing a coupler. These couplers would in a sense couple the data or variables in an equation making it more efficient to solve.
Unfortunately, there are more components needed to create a functional quantum processor. Much of the structure and circuitry that outlines the qubits are composed of switches that function by the Josephson Effect. This circuitry directs the information from the qubits into various memory components which store the data into a magnetized medium. Each of the qubits is equipped with read-out apparatuses. The read-out will take the vector from the coherent superposition state and project it into a pure zero or one state while losing the phase information. The probability of projection into zero or one state is taken by repeating the procedure many times and averaging the result. These apparatuses will be inoperative while calculations are being made for the qubits to prevent the quantum behavior from being changed. Once calculations have been completed, and after each qubit has established itself into a classical state, the recorded data is converted into a chain of classical bits which can then be read by the user.
The structure of the processor is different from the typical silicon processor in that each qubit has individual memory devices instead of large cache areas.
Quantum processing has been speculated to be able to utilize computing power massive orders of magnitude more than our conventional computers. If we take a coherent state qubit system with X qubits then we can superpose 2X different sequences of bits (remember that each additional qubit will yield twice as many values, which is where the 2X comes from.) Now to equate that to conventional computers we take the difference in energy levels of the qubit, in this case, it happens to be in the gigahertz region; which gives us 2X gigahertz. This means with 20 qubits a quantum processor could process approximately 2^20 operations per second. We can conclude that quantum processors have a substantially greater potential than that of conventional computers.
Recently the Dwave 2X system was manufactured and is considered to be the most powerful quantum computer to date. It happens to operate at 0.015° above absolute zero, and its processor generates no heat. The system is comprised of over 1000 qubits that operate near absolute zero to generate a massive amount of quantum effects. To put this into perspective, the system can search through 2^1000 solutions at once; which is more than every particle in the universe. The Dwave 2X has a rumored list price north of $15,000,000, and has been released for general availability.


Can quantum technology improve the performance of batteries? The answer is yes. A project led by researchers at the University of Sussex is using quantum sensors to measure battery behavior, with the expectation that the resulting data can be used to improve battery technology.
The project has been awarded with the University of Birmingham’s Partnership Resource Funding, UK Quantum Technology Hub Sensors and Timing. The project team also includes the Universities of Strathclyde and Edinburgh as part of the consortium.
The project addresses a crucial need to increase energy density, durability and safety in batteries, thus driving the industrial revolution towards an increasingly green ecosystem. To achieve these and other green goals, intensive research and development in these areas are needed while implementing environmental policies.
In an interview with EE Times, Peter Kruger, research professor of experimental physics at the University of Sussex, highlighted how batteries seem to be the first big market for quantum battery sensors, as EVs require large battery packs with high storage capacity. “That would mean the first significant commercial impact of quantum sensors,” said Kruger.
Battery and quantum technology
New electric vehicle control systems, including regenerative braking systems, start & stop functionality, and the electric motors that drive the wheels, all require accurate measurement and control of electrical inputs to optimize performance and avoid catastrophic failure.
An essential part of these systems is the battery current measurement sensor, which measures the battery charge and discharge level and its state of health. There are several existing technologies to create a good current sensor for vehicle battery monitoring.
At the same time, simulating the chemical structure of batteries using quantum computing makes it possible to apply these algorithms to reproduce the chemical composition inside a battery according to various criteria, such as weight reduction, maximum density, and cell assembly. This speeds up the industrialization of the battery pack itself.
The University of Sussex project
The goal of the project is to implement quantum magnetometer technology to examine if microscopic battery current flows accurately. In this way, rapid assessments of the chemistries of new and existing batteries will accelerate the creation of superior battery technology, thereby facilitating electrification.
A magnetometer is an instrument with a single sensor that measures magnetic flux density. Quantum magnetometers are based on the spin of subatomic particles. The coupling of each particle magnetic moment with the applied field is quantized or limited to a discrete set of values as determined by the laws of quantum mechanics.
Kruger pointed out that there have been many cases of lithium battery failures in recent years that have made the headlines, such as the case of Samsung’s Galaxy Note 7 smartphone. Monitoring the current flow could allow preventive actions to be taken before these battery failures occur. A quantum sensor could provide batteries with a some sort of intelligence by monitoring their health and reducing the most worn cells load.
“Current battery monitoring solutions mainly focus on measuring the voltage across batteries. This gives a good indication of the charge left inside a battery, and by measuring these voltages during many subsequent charge/discharge cycles, the charge capacity can be monitored as the battery degrades,” said Kruger.
He added, “While these measurements are useful to monitor the battery state of health, they do not tell us much about what is going on inside the battery. The quantum systems in development allow the magnetic fields generated by the battery to be measured, which are used to deduce the electrical currents that flow through the battery. This system acts as a “magnetic camera”, able to peer inside the battery.”
The research group’s aim is to develop small, low-power, portable devices that require no infrastructure and minimal running costs, thus being suitable for economic production.
The academics will also work closely with CDO2, Magnetic Shields Ltd and QinetiQ to achieve their goal. Magnetic Shields Ltd will provide the magnetic noise-free environment required to allow the sensor technology to be tested with unprecedented sensitivity.
“Large application is in the research sector, where battery manufacturers can bench-test different chemistries and cell geometries. The sensors could send diagnostic information to the on-board computer of an EV and could reduce the service interval as manual check-ups are no longer required. Battery farms are being developed as a form of renewable energy storage, and the technology can be adapted to be used as a smart-charging system, as well as monitoring the battery state of health,” said Kruger.
The big challenge at the moment is focused on raising the capacity of the batteries. “Technology-wise the sensors are not just sensitive to magnetic fields from the battery, but from all ferromagnetic substances. Much of the work we carry out is in the design of the sensors, and looking at how we can shield them from external magnetic sources. We have to think about how the system will be able to filter out the magnetic fields generated by the car’s electric motor, or quick changes in magnetic fields as around a ton of metal passes the sensor each time a car passes in the other direction. A full supply chain for all relevant components needs to be established. We’re well underway doing that through concurrent Industrial Strategy funding,” said Kruger.
Batteries are the key to decarbonization, but improvements are needed in both chemistry and boundary technology. Lithium-ion batteries are still the gold standard technology in this field, and have come a long way. Checking each battery is an operation that has to take into account many factors, such as leaks and imperfections, which adversely affect the performance of the entire system, whether it is an electric vehicle or a simple consumer device.
The article originally published at sister publication EE Times.


Data storage is the containment of any type of information in a particular location. Though today it is typically used to describe storing applications, files and other computing resources, it has existed as long as humans have. Data has been commonly stored and managed by memorizing, carving, writing, recording sound and video, printing type, taping, programming, creating files and powering servers.
It is estimated that the world will create 44 zettabytes of data in 2020; that’s 687 billion times larger than the data contained in all the scrolls in the Great Library of Alexandria, the largest library of the ancient world. And that number grows exponentially every year. Storing, managing and securing all that data requires enormous computing power and physical storage devices such as hard drives, flash memory, solid state drives and data tapes, whether on laptops, mobile devices or on servers in a cloud or data center. It also makes issues such as data storage integrity, reliability, and compatibility extremely important; nothing less than preserving the record of our civilization is at stake.
Historical data storage
Ancient data storage was both thorough and intricate. Ancient tribes memorized lengthy pieces of history and literature and handed them down through generations by regular recitation and practice. The Bible records data about the 12 tribes of Israel and head-counted certain tribe members. Thousands of years later, that data is preserved. Ancient people carved drawings, writing and numerical values on cave walls, stone tablets and pieces of clay, many of which still exist. The abacus and other calculation methods managed numerical data.
The Antikythera mechanism (photo at right courtesy Giovanni Dall’Orto) was an advanced time-tracking tool that used computing processes, dials, and gears to track astronomical movement and calendar dates. It was found in 1900 on a sunken ship near a Greek island. It is known as the first analog computer. The Antikythera mechanism produced data about the stars and the calendar years in advance. The advanced design of this computing tool suggested that it was not the first one to be designed.
Medieval data storage is less notable (years 500-1300 AD were not called the Dark Ages mistakenly), perhaps partly because ancient invention sank into oblivion for many years and historical records from medieval times are more fuzzy. (After the aforementioned Antikythera mechanism, similar machines didn’t appear to be invented for a good 1,300 years). However, the popularity of writing on parchment and the development of books marked an important step in storing data. During this period, as monks and scribes painstakingly created books filled with color and design, data storage became a work of art as well as a method of recording information.
In the 15th century, Gutenberg invented the printing press. Typesetting allowed people to make information much more available much more quickly. Though books were considered the property of the extremely wealthy or at least well-to-do for centuries more, they put physical copies of data into many more people’s hands. This not only increased the development of learning but also provided all people with the opportunity to analyze governmental and philosophical processes for themselves and challenge injustice.
During the industrial age, multiple inventors created machines that performed calculations and stored information; notably, Charles Babbage, in the 19th century, designed an early computer. The term business intelligence came into use in the mid-19th century, initiated by carefully discerned statistics and indicating the storage and analysis of data. Computing machines became very important in the world wars, in which they assisted in breaking codes, planning attacks and dropping bombs.
A side note regarding the most advanced kind of data storage: Though it may seem overly straightforward, the brain is much more advanced than any computer or network in its ability to process and use data (artificial intelligence is one of the more advanced forms of technology, and even it can only hope to catch up with the brain). The human mind can store data through memorization (as mentioned earlier) and through naturally intaking information. The brain manages the inner workings of many different systems through electric signals and stores data through its natural processing and advanced analytics system.
Pre-digital data, file and image storage
Before data storage providers went digital, there were a few providers who specialized in safeguarding data and files on paper, on film, in images, on objects and in other formats. Most of these companies are still in business, because not everything that needs to be stored and protected is in a computer system. Companies such as Iron Mountain (started up in 1951) and competitors Access Information Management, Hewlett Packard Enterprise, H3C and CoreSite Realty are known to build and maintain super-secure storage facilities–both above and below ground–in order to safeguard valuable public and private information and artifacts. These storage providers still play an important role in real-world use cases.
For example, Iron Mountain protects a high percentage of Hollywood movie history–thousands of cans of physical film dating back to the late 19th century–in an underground vault in the West Los Angeles area. Iron Mountain and others also store a great deal of information and artifacts for the federal, state and local governments.
Computer data storage
In a modern computer, a central processing unit (CPU) is the control center for the computer, giving commands that the computer then executes. It is connected to primary storage, or main memory. Random access memory (RAM), part of main memory, processes data that the CPU requests, but it cannot process much at once. Secondary storage, however, stores data in the background, where it can be accessed by computer memory and brought into primary storage, or RAM, for processing. Multiple types of hardware are available for storing and processing data. Hard disks store more data than soft disks and can process information more quickly. Soft (floppy) disks, though easier to transport and purchase, are much less secure.
Direct-attached storage refers to data storage that’s attached to a computer or server rather than over a network. This makes it readily available, which is beneficial if a network is down and a user needs to access data. Solid state drives (SSDs) are just one example of direct-attached storage: external hard drives, which can be an SSD or hard disk drive, plug into a computer, allowing users to instantly access the data stored within the drive.
Software-defined storage (SDS) manages software and hardware, such as servers in a data center, from a distance. SDS can control multiple environments and allows flexible data storage (on servers, pieces of hardware, virtual machines, etc). It’s more abstract than on-premises storage, but it also provides many more compute resources and greater flexibility.
Data centers were initially developed in the mid-1900s (perhaps initially modeled after ENIAC â€” photo at right â€” one of the first computers), but their usage grew much more quickly in the late 1990s. As demand for computing skyrocketed, huge infrastructures were built to meet the need. Now data centers exist physically and virtually. Google has 11 physical centers in the United States alone and 19 globally (as of 2020). Data centers require enormous amounts of management, cooling and security monitoring; they must also be placed in locations with minimal natural disaster tendencies.
Modern data storage concerns
Though the flexibility and agility of data storage has improved through software-defined and hybrid cloud environments, this doesn’t solve the problem of obsolete storage methods. Throughout history, storage methods have increasingly become less sturdy, if also easier to use.
Storing data through technology is still relatively abstract compared to previous methods of storageâ€”such as rock carving, which could only be lost if physically misplaced or damaged over hundreds of years of weather.
In contrast, technology becomes obsolete so quickly (more so than paper, which came before it), and users run the risk of losing their information if they can’t find a new location to properly store and process it. Different formats and generations of technology make old files obsolete quickly, and occasionally unreadable, necessitating the migration of data from one generation of technology to the next. Videos are one example: they’re challenging to transfer between mediums, and the technology that reads them (VHS and DVD drives, for example) can fail and storage devices deteriorate over time.
Even with the significant expansion of the cloud, computing processes still have to run on servers, and if technology shifts further, users may struggle to save all of their important data. And error rates during storage and transmission are also a threat to the integrity of data – if enough bits flip from 0 to 1 or vice versa, a file may become unreadable. While quantum computing is an attempt to move beyond the limits of modern data storage and computing, at its most basic level, data storage remains a digital process, defined by just two binary values, 1 and 0.
One of the most common types of enterprise data storage–RAID, or redundant array of independent disks–is an attempt to limit the risk of disk failures by spreading out data and duplicating it. Backup is an essential data protection strategy and can even help fight security threats, such as ransomware. The more amounts of data people store, the more information they risk losing, and the more they need strategies to protect and preserve it.
The importance of backing up data has increased as users rely further on technology. Accessing data in the cloud (using Google Drive to create documents, for example) is one helpful method, but it’s also important to save files on an external device such as a hard drive. The most important files should ideally be kept physically outside a computer network (in print form). You could also attempt carving them into a rock, depending on the relative importance of the file.


'Molecular spintronics': New technology offers hope for quantum computing
Quantum computers, which work according to the strange rules of quantum mechanics, may one day revolutionize the world. Once we have managed to build a powerful working machine, it will be able to solve some problems that take today's computers millions of years to compute.
Computers use bits (zero or one) to encode information. Quantum computers use "qubits"—which can take any value between zero and one—giving them huge processing power. But quantum systems are notoriously fragile, and although progress has been made to build working machines for some proposed applications, the task remains difficult. But a new approach, dubbed molecular spintronics, offers fresh hope.
In 1997, theoretical physicists Daniel Loss and David DiVincenzo laid down the general rules necessary for creating a quantum computer. While normal electronic devices use electric charge to represent information as zeros and ones, quantum computers often use electron "spin" states to represent qubits.
Spin is a fundamental quantity we've learned about through quantum mechanics. Unfortunately, it lacks an accurate counterpart in everyday experience, even though an analogy of a planet spinning on its own axis is sometimes used.
We do know that electrons spin in two different directions or "states" (dubbed up and down). According to quantum mechanics, each electron in a material spins in a combination (superposition) of these states—a certain bit up and a certain bit down. That's how you can get so many values rather than just zero or one.
Among the five requirements for building a quantum computer developed by Loss and DiVincenzo included the possibility of scaling up the system. More qubits mean more power. Another was making information survive for reasonable amounts of time once encoded, while others concerned the initialization, manipulation and read-out of the physical system.
Although originally conceived for a quantum computer based on electron spins in tiny particles of semiconductors, the proposal has now been implemented across many physical systems, including trapped ions, superconductors and diamonds.
But, unfortunately, these require a near perfect vacuum, extremely low temperatures and no disturbances to operate. They are also hard to scale up.
Spintronics is a form of electronics based on spin rather than charge. Spin can be measured because it generates tiny magnetic fields. This technology, which often uses semiconductors for manipulating and measuring spin, has already had a huge impact on improving hard drive information storage.
Now, scientists are realizing that spintronics can also be done in organic molecules containing rings of carbon atoms. And that connects it with a whole other research field called molecular electronics, which aims to build electronic devices from single molecules and films of molecules.
The combination has proven useful. By carefully controlling and manipulating an electron's spin within a molecule, it turns out we can actually do quantum computations. The preparation and readout of the electron's spin state on molecules is made by zapping them with electric or magnetic fields.
Carbon-based organic molecules and polymer semiconductors also address the criteria of being easy to scale up. They do this through an ability to form molecular frameworks, within which molecular qubits sit in close proximity with each other. The tiny size of a single molecule automatically favors packing large numbers of them together on a small chip.
In addition, organic materials disturb quantum spins less than other electronic materials do. That's because they are composed of relatively light elements such as carbon and hydrogen, resulting in weaker interactions with the spinning electrons. This avoids its spins from easily flipping state, causing them to be preserved for long periods of up to several microseconds.
In one propeller-shaped molecule, this duration can even be up to a millisecond. These relatively long times are sufficient for operations to be performed—another great advantage.
But we still have much left to learn. In addition to understanding what causes extended spin lifetimes on organic molecules, a grasp on how far these spins can travel within organic circuits is necessary for building efficient spin-based electronic circuits. The figure below shows some of our concepts for exploratory organic spintronic devices towards this goal.
There are also major challenges in getting such devices to work efficiently. The charged electrons that carry spins in an organic material constantly hop from molecule to molecule as they move. This hopping activity is unfortunately a source of electrical noise, making it difficult to electrically measure small spin current signatures using conventional architectures. That said, a relatively new technique known as spin pumping might prove suitable for generating spin currents with low noise in organic materials.
Another problem when trying to make organic molecules serious candidates within future quantum technologies is the ability to coherently control and measure spins on single molecules, or on a small number of molecules. This grand challenge is currently seeing tremendous progress. For example, a simple program for a quantum computer known as "Grover's search algorithm" was recently implemented on a single magnetic molecule. This algorithm is known to significantly reduce the time necessary to perform a search on an unsorted database.
In another report, an ensemble of molecules were successfully integrated into a hybrid superconducting device. It provided a proof-of-concept in combining molecular spin qubits with existing quantum architectures.
Much is left to be done, but in the current state of play, molecular spin systems are fast finding several new applications in quantum technologies. With the advantage of small size and long-lived spins, it is only a matter of time before they cement their spot in the roadmap for quantum technologies.


Chasing clues about the infant universe in relic light known as the cosmic microwave background, or CMB, scientists are devising more elaborate and ultrasensitive detector arrays to measure the properties of this light with increasing precision.
To meet the high demand for these detectors that will drive next-generation CMB experiments, and for similar detectors to serve other scientific needs, researchers at the Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) are pushing to commercialize the manufacturing process so that these detectors can be mass-produced quickly and affordably.
The type of detector they are working to commercialize incorporates sensors that, when chilled to far-below-freezing temperatures, operate at the very edge of superconductivity—a state in which there is zero electrical resistance. Incorporated in the detector design is transition-edge sensor (TES) technology that can be tailored for ultrahigh sensitivity to temperature changes, among other measurements.
The team is also working to commercialize the production of ultraprecise magnetic field sensors known as SQUIDs (superconducting quantum interference devices).
In the current TES detector design, each detector array is fabricated on a silicon wafer and contains about 1,000 detectors. Hundreds of thousands of these detectors will be needed for a massive next-generation CMB experiment, dubbed CMB-S4.
The SQUID amplifiers are designed to enable low-noise readout of signals from the detectors. They are intended to be seated near the detectors to simplify the assembly process and the operation of the next-generation detector arrays.
More exacting measurements of the CMB light’s properties, including specifics on its polarization—directionality in the light—can help scientists peer more deeply into the universe’s origins, which in turn can lead to more accurate models and a richer understanding of the modern universe.
Berkeley Lab researchers have a long history of pioneering achievements in the in-house design and development of new detectors for particle physics, nuclear physics, and astrophysics experiments. And while the detectors can be built in-house, scientists also considered the fact that commercial firms have access to state-of-the-art, high-throughput microfabricating machines and expertise in larger-scale manufacturing processes.
So Aritoki Suzuki, a staff scientist in Berkeley Lab’s Physics Division, for the past several years has been working to transfer highly specialized detector fabrication techniques needed for new physics experiments to industry. The goal is to determine if it’s possible to produce a high volume of detector wafers more quickly, and at lower cost, than is possible at research labs.
“What we are building here is a general technique to make superconducting devices at a company to benefit areas like astrophysics, the search for dark matter, quantum computing, quantum information science, and superconducting circuits in general,” said Suzuki, who has been working on advanced detector R&D for about a decade.
This breed of sensors has also been enlisted in the hunt for a theorized nuclear process called neutrinoless double-beta decay that could help solve a riddle about the abundance of matter over antimatter in the universe, and whether the ghostly neutrino particle is its own antiparticle.
Progress toward commercial production of the specialized detectors has been promising. “We have demonstrated that detector performance from commercially fabricated detectors meet the requirements of typical CMB experiments,” Suzuki said.
Work is underway to build the prototype detectors for a planned CMB experiment in Chile known as the Simons Observatory that may incorporate the commercially produced detectors.
About 3 miles above sea level, in the Atacama Desert of Northern Chile, researchers have worked on successive generations of TES-based detector arrays for CMB-related experiments including POLARBEAR, POLARBEAR-2, the Simons Array, and the Simons Observatory.
A detector array for two telescopes that are part of the POLARBEAR-2 and Simons Array experiments is now being fabricated at UC Berkeley’s Marvell Nanofabrication Laboratory by Berkeley Lab and UC Berkeley researchers. The effort will ultimately produce 7,600 detectors apiece for three telescopes. The first telescope in the Simons Array has just begun its commissioning run.
The Simons Observatory project, which is now in a design and prototyping phase, will require about 80,000 detectors, half of which will be fabricated at the Marvell Nanofabrication Laboratory.
These experiments are driving toward a CMB-S4 experiment that will combine detector arrays in Chile and near the South Pole to better resolve the cosmic microwave background and possibly help determine whether the universe underwent a brief period of incredible expansion known as inflation in its formative moments.
The commercial fabrication effort is intended to benefit this CMB-S4 experiment, which will require a total of about 500,000 detectors. The current design calls for about 400 detector wafers that will each feature more than 1,000 detectors arranged on hexagonal silicon wafers measuring about six inches across. The wafers are designed to be tiled together in telescope arrays.
Suzuki, who is part of a scientific board working on CMB-S4 along with other Berkeley Lab scientists, is collaboring with Adrian Lee, another board member who is also a physicist at Berkeley Lab and a UC Berkeley physics professor. It was Lee who pioneered microfabrication techniques at UC Berkeley to help speed the production of TES-containing detectors.
In addition to the detector production at UC Berkeley’s nanofabrication laboratory, researchers have also built specialized superconducting readout electronics in a nearly dustless clean room space within the Microsystems Laboratory at Berkeley Lab.
Before the introduction of higher-throughput manufacturing processes, detectors “were made one by one, by hand,” Suzuki noted.
Suzuki labored to develop the latest 6-inch wafer design, which offers a production throughput advantage over the previously used 4-inch wafer designs. Older wafers had only about 100 detectors, which would have required the production of many more wafers to fully outfit a CMB-S4 experiment.
The current detector design incorporates niobium, a superconducting metal, and other uncommon metals like palladium and manganese-doped aluminum alloy.
“These are very unique metals that normally companies don’t touch. We use them to achieve the unique properties that we desire for these detectors,” Suzuki said.
The effort has benefited from a Laboratory Directed Research and Development grant that Lee received in 2015 to explore commercial fabrication of the detectors. Also, the research team has received support from the federally supported Small Business Innovation Research program, and Suzuki has also received support from the DOE Early Career Research Program.
Suzuki has worked with Hypres Inc. of New York and STAR Cryoelectronics of Santa Fe, New Mexico, on the fabrication processes for the detectors, and worked with the University of New Mexico and STAR Cryoelectronics on the SQUID amplifiers. Suzuki said that working with the companies has been a productive process. “They gave us a lot of ideas,” he said, to help improve and streamline the processes.
The industry-produced SQUID amplifiers will be used in one of the telescopes of the POLARBEAR-2/Simons Array experiment, Suzuki noted, and the design of these amplifiers could drive improvements in the readout electronics of a CMB-S4 experiment.
As a next step in the effort to commercially fabricate detectors, a test run is planned this year to demonstrate fabrication quality and throughput.