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arxiv-677401 | quant-ph/0703107 | Quantum Key Distribution with Classical Bob | <|reference_start|>Quantum Key Distribution with Classical Bob: Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? We present a protocol with this constraint, and prove its robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate users could notice.<|reference_end|> | arxiv | @article{boyer2007quantum,
title={Quantum Key Distribution with Classical Bob},
author={Michel Boyer, Dan Kenigsberg and Tal Mor},
journal={arXiv preprint arXiv:quant-ph/0703107},
year={2007},
doi={10.1103/PhysRevLett.99.140501},
archivePrefix={arXiv},
eprint={quant-ph/0703107},
primaryClass={quant-ph cs.CR}
} | boyer2007quantum |
arxiv-677402 | quant-ph/0703112 | Graphs, Quadratic Forms, and Quantum Codes | <|reference_start|>Graphs, Quadratic Forms, and Quantum Codes: We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illustrate our results.<|reference_end|> | arxiv | @article{grassl2007graphs,,
title={Graphs, Quadratic Forms, and Quantum Codes},
author={Markus Grassl, Andreas Klappenecker, Martin Roetteler},
journal={Proceedings 2002 IEEE International Symposium on Information
Theory (ISIT 2002), Lausanne, Switzerland, June/July 2002, p. 45},
year={2007},
doi={10.1109/ISIT.2002.1023317},
archivePrefix={arXiv},
eprint={quant-ph/0703112},
primaryClass={quant-ph cs.IT math.IT}
} | grassl2007graphs, |
arxiv-677403 | quant-ph/0703113 | Quantum Convolutional BCH Codes | <|reference_start|>Quantum Convolutional BCH Codes: Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes. These codes have the property that they contain their Euclidean, respectively Hermitian, dual codes. Hence, they can be used to define quantum convolutional codes by the stabilizer code construction. We compute BCH-like bounds on the free distances which can be controlled as in the case of block codes, and establish that the codes have non-catastrophic encoders.<|reference_end|> | arxiv | @article{aly2007quantum,
title={Quantum Convolutional BCH Codes},
author={Salah A. Aly, Markus Grassl, Andreas Klappenecker, Martin Roetteler,
Pradeep Kiran Sarvepalli},
journal={Proceedings 2007 Canadian Workshop on Information Theory (CWIT
2007), Edmonton, Canada, June 2007, pp. 180-183},
year={2007},
doi={10.1109/CWIT.2007.375730},
archivePrefix={arXiv},
eprint={quant-ph/0703113},
primaryClass={quant-ph cs.IT math.IT}
} | aly2007quantum |
arxiv-677404 | quant-ph/0703141 | Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries | <|reference_start|>Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries: Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model in which the goal is to compute functions of N by N ``black box'' unitary matrices drawn from a set of such matrices, a problem with applications to determining properties of quantum physical systems. We characterize the existence of an algorithm for such a query problem, with given error and number of queries, as equivalent to the feasibility of a certain set of semidefinite programming constraints, or equivalently the infeasibility of a dual of these constraints, which we construct. Relaxing the primal constraints to correspond to mere pairwise near-orthogonality of the final states of a quantum computer, conditional on black-box inputs having distinct function values, rather than bounded-error determinability of the function value via a single measurement on the output states, we obtain a relaxed primal program the feasibility of whose dual still implies the nonexistence of a quantum algorithm. We use this to obtain a generalization, to our not-necessarily-commutative setting, of the ``spectral adversary method'' for quantum query lower bounds.<|reference_end|> | arxiv | @article{barnum2007semidefinite,
title={Semidefinite programming characterization and spectral adversary method
for quantum complexity with noncommuting unitary queries},
author={Howard N. Barnum},
journal={arXiv preprint arXiv:quant-ph/0703141},
year={2007},
archivePrefix={arXiv},
eprint={quant-ph/0703141},
primaryClass={quant-ph cs.CC}
} | barnum2007semidefinite |
arxiv-677405 | quant-ph/0703181 | Quantum Block and Convolutional Codes from Self-orthogonal Product Codes | <|reference_start|>Quantum Block and Convolutional Codes from Self-orthogonal Product Codes: We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we can derive ordinary quantum error-correcting codes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that the product construction cannot improve the rate in the classical case, we show that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is obtained by the product of a code [[5,1,3]]_2 with a suitable code.<|reference_end|> | arxiv | @article{grassl2007quantum,
title={Quantum Block and Convolutional Codes from Self-orthogonal Product Codes},
author={Markus Grassl, Martin Roetteler},
journal={Proceedings 2005 IEEE International Symposium on Information
Theory (ISIT 2005), Adelaide, Australia, September 2005, pp. 1018-1022},
year={2007},
doi={10.1109/ISIT.2005.1523493},
archivePrefix={arXiv},
eprint={quant-ph/0703181},
primaryClass={quant-ph cs.IT math.IT}
} | grassl2007quantum |
arxiv-677406 | quant-ph/0703182 | Constructions of Quantum Convolutional Codes | <|reference_start|>Constructions of Quantum Convolutional Codes: We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum convolutional code by applying a product code construction to an arbitrary classical convolutional code and an arbitrary quantum block code. We show that the resulting codes have highly structured and efficient encoders. Furthermore, we show that the resulting quantum circuits have finite depth, independent of the lengths of the input stream, and show that this depth is polynomial in the degree and frame size of the code.<|reference_end|> | arxiv | @article{grassl2007constructions,
title={Constructions of Quantum Convolutional Codes},
author={Markus Grassl, Martin Roetteler},
journal={Proceedings 2007 IEEE International Symposium on Information
Theory (ISIT 2007), Nice, France, June 2007, pp. 816-820},
year={2007},
doi={10.1109/ISIT.2007.4557325},
archivePrefix={arXiv},
eprint={quant-ph/0703182},
primaryClass={quant-ph cs.IT math.IT}
} | grassl2007constructions |
arxiv-677407 | quant-ph/0703215 | Classical Interaction Cannot Replace a Quantum Message | <|reference_start|>Classical Interaction Cannot Replace a Quantum Message: We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model.<|reference_end|> | arxiv | @article{gavinsky2007classical,
title={Classical Interaction Cannot Replace a Quantum Message},
author={Dmytro Gavinsky},
journal={arXiv preprint arXiv:quant-ph/0703215},
year={2007},
archivePrefix={arXiv},
eprint={quant-ph/0703215},
primaryClass={quant-ph cs.CC}
} | gavinsky2007classical |
arxiv-677408 | quant-ph/9603004 | Is Quantum Bit Commitment Really Possible? | <|reference_start|>Is Quantum Bit Commitment Really Possible?: We show that all proposed quantum bit commitment schemes are insecure because the sender, Alice, can almost always cheat successfully by using an Einstein-Podolsky-Rosen type of attack and delaying her measurement until she opens her commitment.<|reference_end|> | arxiv | @article{lo1996is,
title={Is Quantum Bit Commitment Really Possible?},
author={Hoi-Kwong Lo and H. F. Chau},
journal={Phys. Rev. Lett. 78, 3410 (1997)},
year={1996},
doi={10.1103/PhysRevLett.78.3410},
archivePrefix={arXiv},
eprint={quant-ph/9603004},
primaryClass={quant-ph cs.CR}
} | lo1996is |
arxiv-677409 | quant-ph/9604007 | A decision procedure for unitary linear quantum cellular automata | <|reference_start|>A decision procedure for unitary linear quantum cellular automata: Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution operator has to be a unitary transformation. In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary. The complexity of the algorithm is O(n^((3r-1)/(r+1))) = O(n^3) in the algebraic computational model if the automaton has a continuous neighborhood of size r, where $n$ is the size of the input.<|reference_end|> | arxiv | @article{durr1996a,
title={A decision procedure for unitary linear quantum cellular automata},
author={Christoph Durr (LRI), Miklos Santha (CNRS)},
journal={Proceeding of the 37th IEEE Symposium on Foundations of Computer
Science, 38--45, 1996},
year={1996},
archivePrefix={arXiv},
eprint={quant-ph/9604007},
primaryClass={quant-ph cs.CC}
} | durr1996a |
arxiv-677410 | quant-ph/9607014 | A Quantum Algorithm for Finding the Minimum | <|reference_start|>A Quantum Algorithm for Finding the Minimum: We give a quantum algorithm to find the index y in a table T of size N such that in time O(c sqrt N), T[y] is minimum with probability at least 1-1/2^c.<|reference_end|> | arxiv | @article{durr1996a,
title={A Quantum Algorithm for Finding the Minimum},
author={Christoph Durr and Peter Hoyer},
journal={arXiv preprint arXiv:quant-ph/9607014},
year={1996},
archivePrefix={arXiv},
eprint={quant-ph/9607014},
primaryClass={quant-ph cs.DS}
} | durr1996a |
arxiv-677411 | quant-ph/9611031 | Insecurity of Quantum Secure Computations | <|reference_start|>Insecurity of Quantum Secure Computations: It had been widely claimed that quantum mechanics can protect private information during public decision in for example the so-called two-party secure computation. If this were the case, quantum smart-cards could prevent fake teller machines from learning the PIN (Personal Identification Number) from the customers' input. Although such optimism has been challenged by the recent surprising discovery of the insecurity of the so-called quantum bit commitment, the security of quantum two-party computation itself remains unaddressed. Here I answer this question directly by showing that all ``one-sided'' two-party computations (which allow only one of the two parties to learn the result) are necessarily insecure. As corollaries to my results, quantum one-way oblivious password identification and the so-called quantum one-out-of-two oblivious transfer are impossible. I also construct a class of functions that cannot be computed securely in any ``two-sided'' two-party computation. Nevertheless, quantum cryptography remains useful in key distribution and can still provide partial security in ``quantum money'' proposed by Wiesner.<|reference_end|> | arxiv | @article{lo1996insecurity,
title={Insecurity of Quantum Secure Computations},
author={Hoi-Kwong Lo (HP Labs, Bristol and University of Santa Barbara)},
journal={arXiv preprint arXiv:quant-ph/9611031},
year={1996},
doi={10.1103/PhysRevA.56.1154},
archivePrefix={arXiv},
eprint={quant-ph/9611031},
primaryClass={quant-ph cs.CR}
} | lo1996insecurity |
arxiv-677412 | quant-ph/9703009 | Reversible Simulation of Irreversible Computation by Pebble Games | <|reference_start|>Reversible Simulation of Irreversible Computation by Pebble Games: Reversible simulation of irreversible algorithms is analyzed in the stylized form of a `reversible' pebble game. While such simulations incur little overhead in additional computation time, they use a large amount of additional memory space during the computation. The reacheable reversible simulation instantaneous descriptions (pebble configurations) are characterized completely. As a corollary we obtain the reversible simulation by Bennett and that among all simulations that can be modelled by the pebble game, Bennett's simulation is optimal in that it uses the least auxiliary space for the greatest number of simulated steps. One can reduce the auxiliary storage overhead incurred by the reversible simulation at the cost of allowing limited erasing leading to an irreversibility-space tradeoff. We show that in this resource-bounded setting the limited erasing needs to be performed at precise instants during the simulation. We show that the reversible simulation can be modified so that it is applicable also when the simulated computation time is unknown.<|reference_end|> | arxiv | @article{li1997reversible,
title={Reversible Simulation of Irreversible Computation by Pebble Games},
author={Ming Li (University of Waterloo), John Tromp (CWI), Paul Vitanyi (CWI
and University of Amsterdam)},
journal={Physica D120 (1998) 168-176},
year={1997},
doi={10.1016/S0167-2789(98)00052-9},
number={CWI Tech Report 1996},
archivePrefix={arXiv},
eprint={quant-ph/9703009},
primaryClass={quant-ph cs.CC cs.DS}
} | li1997reversible |
arxiv-677413 | quant-ph/9703022 | Reversibility and Adiabatic Computation: Trading Time and Space for Energy | <|reference_start|>Reversibility and Adiabatic Computation: Trading Time and Space for Energy: Future miniaturization and mobilization of computing devices requires energy parsimonious `adiabatic' computation. This is contingent on logical reversibility of computation. An example is the idea of quantum computations which are reversible except for the irreversible observation steps. We propose to study quantitatively the exchange of computational resources like time and space for irreversibility in computations. Reversible simulations of irreversible computations are memory intensive. Such (polynomial time) simulations are analysed here in terms of `reversible' pebble games. We show that Bennett's pebbling strategy uses least additional space for the greatest number of simulated steps. We derive a trade-off for storage space versus irreversible erasure. Next we consider reversible computation itself. An alternative proof is provided for the precise expression of the ultimate irreversibility cost of an otherwise reversible computation without restrictions on time and space use. A time-irreversibility trade-off hierarchy in the exponential time region is exhibited. Finally, extreme time-irreversibility trade-offs for reversible computations in the thoroughly unrealistic range of computable versus noncomputable time-bounds are given.<|reference_end|> | arxiv | @article{li1997reversibility,
title={Reversibility and Adiabatic Computation: Trading Time and Space for
Energy},
author={Ming Li (University of Waterloo), Paul Vitanyi (CWI and University of
Amsterdam)},
journal={Proc. Royal Society of London, Series A, 452(1996), 769-789},
year={1997},
doi={10.1098/rspa.1996.0039},
archivePrefix={arXiv},
eprint={quant-ph/9703022},
primaryClass={quant-ph cs.CC cs.CE cs.DS}
} | li1997reversibility |
arxiv-677414 | quant-ph/9712040 | Computing Local Invariants of Qubit Systems | <|reference_start|>Computing Local Invariants of Qubit Systems: We investigate means to describe the non-local properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple qubits. We compute invariant polynomials, i. e., polynomial functions of the entries of the density operator which are invariant under local unitary operations. As an example, we consider a system of two qubits. We compute the Molien series for the corresponding representation which gives information about the number of linearly independent invariants. Furthermore, we present a set of polynomials which generate all invariants (at least) up to degree 23. Finally, the use of invariants to check whether two density operators are locally equivalent is demonstrated.<|reference_end|> | arxiv | @article{grassl1997computing,
title={Computing Local Invariants of Qubit Systems},
author={Markus Grassl, Martin Roetteler, and Thomas Beth (Universitaet
Karlsruhe)},
journal={Phys.Rev.A58:1833-1839,1998},
year={1997},
doi={10.1103/PhysRevA.58.1833},
archivePrefix={arXiv},
eprint={quant-ph/9712040},
primaryClass={quant-ph cs.ET}
} | grassl1997computing |
arxiv-677415 | quant-ph/9802028 | Analogue Quantum Computers for Data Analysis | <|reference_start|>Analogue Quantum Computers for Data Analysis: Analogue computers use continuous properties of physical system for modeling. In the paper is described possibility of modeling by analogue quantum computers for some model of data analysis. It is analogue associative memory and a formal neural network. A particularity of the models is combination of continuous internal processes with discrete set of output states. The modeling of the system by classical analogue computers was offered long times ago, but now it is not very effectively in comparison with modern digital computers. The application of quantum analogue modelling looks quite possible for modern level of technology and it may be more effective than digital one, because number of element may be about Avogadro number (N=6.0E23).<|reference_end|> | arxiv | @article{vlasov1998analogue,
title={Analogue Quantum Computers for Data Analysis},
author={Alexander Yu. Vlasov (FCR/IRH, St.-Petersburg, Russia)},
journal={arXiv preprint arXiv:quant-ph/9802028},
year={1998},
number={QCY-VAY12-291297},
archivePrefix={arXiv},
eprint={quant-ph/9802028},
primaryClass={quant-ph cs.CV}
} | vlasov1998analogue |
arxiv-677416 | quant-ph/9802049 | Quantum Lower Bounds by Polynomials | <|reference_start|>Quantum Lower Bounds by Polynomials: We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions (i.e. problems involving a promise on the input) by Deutsch and Jozsa and by Simon cannot be obtained for any total function: if a quantum algorithm computes some total Boolean function f with bounded-error using T black-box queries then there is a classical deterministic algorithm that computes f exactly with O(T^6) queries. We also give asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings. Finally, we give new precise bounds for AND, OR, and PARITY. Our results are a quantum extension of the so-called polynomial method, which has been successfully applied in classical complexity theory, and also a quantum extension of results by Nisan about a polynomial relationship between randomized and deterministic decision tree complexity.<|reference_end|> | arxiv | @article{beals1998quantum,
title={Quantum Lower Bounds by Polynomials},
author={Robert Beals (U of Arizona), Harry Buhrman (CWI), Richard Cleve (U of
Calgary), Michele Mosca (U of Oxford), Ronald de Wolf (CWI and U of
Amsterdam)},
journal={arXiv preprint arXiv:quant-ph/9802049},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9802049},
primaryClass={quant-ph cs.CC}
} | beals1998quantum |
arxiv-677417 | quant-ph/9802062 | 1-way quantum finite automata: strengths, weaknesses and generalizations | <|reference_start|>1-way quantum finite automata: strengths, weaknesses and generalizations: We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (over 0.98), then the power of 1-way QFAs is equal to the power of 1-way reversible automata. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. Namely, we construct a 1-way QFA which is exponentially smaller than any equivalent classical (even randomized) finite automaton. This construction may be useful for design of other space-efficient quantum algorithms. Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.<|reference_end|> | arxiv | @article{ambainis19981-way,
title={1-way quantum finite automata: strengths, weaknesses and generalizations},
author={A. Ambainis, R. Freivalds},
journal={arXiv preprint arXiv:quant-ph/9802062},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9802062},
primaryClass={quant-ph cs.CC}
} | ambainis19981-way |
arxiv-677418 | quant-ph/9804043 | Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata | <|reference_start|>Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata: We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that non-trivial quantum encodings exist that have no classical counterparts. On the other hand, we show that quantum encodings cannot be much more succint as compared to classical encodings, and we provide a lower bound on such quantum encodings. Finally, using this lower bound, we prove an exponential lower bound on the size of 1-way quantum finite automata for a family of languages accepted by linear sized deterministic finite automata.<|reference_end|> | arxiv | @article{ambainis1998dense,
title={Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata},
author={Andris Ambainis, Ashwin Nayak, Amnon Ta-Shma, Umesh Vazirani},
journal={arXiv preprint arXiv:quant-ph/9804043},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9804043},
primaryClass={quant-ph cs.CC}
} | ambainis1998dense |
arxiv-677419 | quant-ph/9804066 | The quantum query complexity of approximating the median and related statistics | <|reference_start|>The quantum query complexity of approximating the median and related statistics: Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \epsilon > 0, we say that x_i is an \epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less than (1+\epsilon)n/2. We consider the quantum query complexity of computing an \epsilon-approximate median, given the sequence X as an oracle. We prove a lower bound of \Omega(\min{{1/\epsilon},n}) queries for any quantum algorithm that computes an \epsilon-approximate median with any constant probability greater than 1/2. We also show how an \epsilon-approximate median may be computed with O({1/\epsilon}\log({1\/\epsilon}) \log\log({1/\epsilon})) oracle queries, which represents an improvement over an earlier algorithm due to Grover. Thus, the lower bound we obtain is essentially optimal. The upper and the lower bound both hold in the comparison tree model as well. Our lower bound result is an application of the polynomial paradigm recently introduced to quantum complexity theory by Beals et al. The main ingredient in the proof is a polynomial degree lower bound for real multilinear polynomials that ``approximate'' symmetric partial boolean functions. The degree bound extends a result of Paturi and also immediately yields lower bounds for the problems of approximating the kth-smallest element, approximating the mean of a sequence of numbers, and that of approximately counting the number of ones of a boolean function. All bounds obtained come within polylogarithmic factors of the optimal (as we show by presenting algorithms where no such optimal or near optimal algorithms were known), thus demonstrating the power of the polynomial method.<|reference_end|> | arxiv | @article{nayak1998the,
title={The quantum query complexity of approximating the median and related
statistics},
author={Ashwin Nayak, Felix Wu},
journal={arXiv preprint arXiv:quant-ph/9804066},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9804066},
primaryClass={quant-ph cs.CC}
} | nayak1998the |
arxiv-677420 | quant-ph/9805006 | Quantum Oracle Interrogation: Getting all information for almost half the price | <|reference_start|>Quantum Oracle Interrogation: Getting all information for almost half the price: Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+sqrt(N) queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2+O(sqrt(N)) oracle queries. In the second part of the article `approximate interrogation' is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio.<|reference_end|> | arxiv | @article{van dam1998quantum,
title={Quantum Oracle Interrogation: Getting all information for almost half
the price},
author={Wim van Dam (U of Oxford, CWI)},
journal={Proceedings of the 39th Annual IEEE Symposium on Foundations of
Computer Science (FOCS), pages 362-367 (1998)},
year={1998},
doi={10.1109/SFCS.1998.743486},
number={CQC-040598},
archivePrefix={arXiv},
eprint={quant-ph/9805006},
primaryClass={quant-ph cs.CC}
} | van dam1998quantum |
arxiv-677421 | quant-ph/9806090 | Two Classical Queries versus One Quantum Query | <|reference_start|>Two Classical Queries versus One Quantum Query: In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such query. It is shown that any decision problem that requires two parallel (non-adaptive) SAT-queries on a classical computer can also be solved exactly by a quantum computer using only one SAT-oracle call, where both computations have polynomial time-complexity. Such a simulation is generally believed to be impossible for a one-query classical computer. The reduction also does not hold if we replace the SAT-oracle by a general black-box. This result gives therefore an example of how a quantum computer is probably more powerful than a classical computer. It also highlights the potential differences between quantum complexity results for general oracles when compared to results for more structured tasks like the SAT-problem.<|reference_end|> | arxiv | @article{van dam1998two,
title={Two Classical Queries versus One Quantum Query},
author={Wim van Dam (U of Oxford, CWI)},
journal={arXiv preprint arXiv:quant-ph/9806090},
year={1998},
number={CQC-2CQ:1QQ},
archivePrefix={arXiv},
eprint={quant-ph/9806090},
primaryClass={quant-ph cs.CC}
} | van dam1998two |
arxiv-677422 | quant-ph/9807064 | Fast Quantum Fourier Transforms for a Class of Non-abelian Groups | <|reference_start|>Fast Quantum Fourier Transforms for a Class of Non-abelian Groups: An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to obtain systematically fast Fourier transforms for solvable groups on a quantum computer. The inherent structure of the Hilbert space imposed by the qubit architecture suggests to consider groups of order 2^n first (where n is the number of qubits). As an example, fast quantum Fourier transforms for all 4 classes of non-abelian 2-groups with cyclic normal subgroup of index 2 are explicitly constructed in terms of quantum circuits. The (quantum) complexity of the Fourier transform for these groups of size 2^n is O(n^2) in all cases.<|reference_end|> | arxiv | @article{pueschel1998fast,
title={Fast Quantum Fourier Transforms for a Class of Non-abelian Groups},
author={Markus Pueschel, Martin Roetteler, and Thomas Beth (Universitaet
Karlsruhe)},
journal={Proceedings 13th International Symposium on Applied Algebra,
Algebraic Algorithms and Error-Correcting Codes (AAECC'99), Honolulu, Hawaii,
Springer LNCS, pp. 148-159, 1999},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9807064},
primaryClass={quant-ph cs.ET}
} | pueschel1998fast |
arxiv-677423 | quant-ph/9809016 | An Introduction to Quantum Computing for Non-Physicists | <|reference_start|>An Introduction to Quantum Computing for Non-Physicists: Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new non-traditional programming techniques. The aim of this paper is to guide computer scientists and other non-physicists through the conceptual and notational barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to harnessing the power of quantum parallelism are explained, including Shor's algorithm, Grover's algorithm, and Hogg's algorithms. We conclude with a discussion of quantum error correction.<|reference_end|> | arxiv | @article{rieffel1998an,
title={An Introduction to Quantum Computing for Non-Physicists},
author={Eleanor G. Rieffel and Wolfgang Polak},
journal={ACM Comput.Surveys 32:300-335,2000},
year={1998},
number={FXPAL-TR-98-044},
archivePrefix={arXiv},
eprint={quant-ph/9809016},
primaryClass={quant-ph cs.GL}
} | rieffel1998an |
arxiv-677424 | quant-ph/9809081 | Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes | <|reference_start|>Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes: An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFSs are the class of quantum error correcting codes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against collective decoherence perturbed by independent decoherence. The code yields an error threshold which depends only on the perturbing independent decoherence rate.<|reference_end|> | arxiv | @article{lidar1998concatenating,
title={Concatenating Decoherence Free Subspaces with Quantum Error Correcting
Codes},
author={D.A. Lidar, D. Bacon and K.B. Whaley (UC Berkeley)},
journal={Phys.Rev.Lett. 82 (1999) 4556-4559},
year={1998},
doi={10.1103/PhysRevLett.82.4556},
archivePrefix={arXiv},
eprint={quant-ph/9809081},
primaryClass={quant-ph cs.IT math-ph math.IT math.MP}
} | lidar1998concatenating |
arxiv-677425 | quant-ph/9810067 | Coin Tossing is Strictly Weaker Than Bit Commitment | <|reference_start|>Coin Tossing is Strictly Weaker Than Bit Commitment: We define cryptographic assumptions applicable to two mistrustful parties who each control two or more separate secure sites between which special relativity guarantees a time lapse in communication. We show that, under these assumptions, unconditionally secure coin tossing can be carried out by exchanges of classical information. We show also, following Mayers, Lo and Chau, that unconditionally secure bit commitment cannot be carried out by finitely many exchanges of classical or quantum information. Finally we show that, under standard cryptographic assumptions, coin tossing is strictly weaker than bit commitment. That is, no secure classical or quantum bit commitment protocol can be built from a finite number of invocations of a secure coin tossing black box together with finitely many additional information exchanges.<|reference_end|> | arxiv | @article{kent1998coin,
title={Coin Tossing is Strictly Weaker Than Bit Commitment},
author={Adrian Kent},
journal={Phys.Rev.Lett. 83 (1999) 5382-5384},
year={1998},
doi={10.1103/PhysRevLett.83.5382},
number={DAMTP-1998-123},
archivePrefix={arXiv},
eprint={quant-ph/9810067},
primaryClass={quant-ph cs.CR}
} | kent1998coin |
arxiv-677426 | quant-ph/9810068 | Unconditionally Secure Bit Commitment | <|reference_start|>Unconditionally Secure Bit Commitment: We describe a new classical bit commitment protocol based on cryptographic constraints imposed by special relativity. The protocol is unconditionally secure against classical or quantum attacks. It evades the no-go results of Mayers, Lo and Chau by requiring from Alice a sequence of communications, including a post-revelation verification, each of which is guaranteed to be independent of its predecessor.<|reference_end|> | arxiv | @article{kent1998unconditionally,
title={Unconditionally Secure Bit Commitment},
author={Adrian Kent},
journal={Phys.Rev.Lett. 83 (1999) 1447-1450},
year={1998},
doi={10.1103/PhysRevLett.83.1447},
number={DAMTP-1997-135},
archivePrefix={arXiv},
eprint={quant-ph/9810068},
primaryClass={quant-ph cs.CR}
} | kent1998unconditionally |
arxiv-677427 | quant-ph/9811046 | Lower Bounds for Quantum Search and Derandomization | <|reference_start|>Lower Bounds for Quantum Search and Derandomization: We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a constant. If we want error <1/2^N then we need T=Omega(N) queries. We apply this to show that a quantum computer cannot do much better than a classical computer when amplifying the success probability of an RP-machine. A classical computer can achieve error <=1/2^k using k applications of the RP-machine, a quantum computer still needs at least ck applications for this (when treating the machine as a black-box), where c>0 is a constant independent of k. Furthermore, we prove a lower bound of Omega(sqrt{log N}/loglog N) queries for quantum bounded-error search of an ordered list of N items.<|reference_end|> | arxiv | @article{buhrman1998lower,
title={Lower Bounds for Quantum Search and Derandomization},
author={Harry Buhrman (CWI) and Ronald de Wolf (CWI and U Amsterdam)},
journal={arXiv preprint arXiv:quant-ph/9811046},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9811046},
primaryClass={quant-ph cs.CC}
} | buhrman1998lower |
arxiv-677428 | quant-ph/9811056 | A Quick Glance at Quantum Cryptography | <|reference_start|>A Quick Glance at Quantum Cryptography: The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication. As a result of these new developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a guarantee of no eavesdropping should it not occur. CONTENTS P3. Cryptographic systems before quantum cryptography P7. Preamble to quantum cryptography P10. The BB84 quantum cryptographic protocol without noise P16. The BB84 quantum cryptographic protocol with noise P19..The B92 quantum cryptographic protocol P21. EPR quantum cryptographic protocols P25. Other protocols P25. Eavesdropping stategies and counter measures P26. Conclusion P29. Appendix A. The no cloning theorem P30. Appendix B. Proof that an undetectable eavesdropper can obtain no information from the B92 protocol P31. Appendix C. Part of a Rosetta stone for quantum mechanics P44. References<|reference_end|> | arxiv | @article{lomonaco1998a,
title={A Quick Glance at Quantum Cryptography},
author={Samuel J. Lomonaco},
journal={arXiv preprint arXiv:quant-ph/9811056},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9811056},
primaryClass={quant-ph cs.CR}
} | lomonaco1998a |
arxiv-677429 | quant-ph/9811080 | A note on quantum black-box complexity of almost all Boolean functions | <|reference_start|>A note on quantum black-box complexity of almost all Boolean functions: We show that, for almost all N-variable Boolean functions f, at least N/4-O(\sqrt{N} log N) queries are required to compute f in quantum black-box model with bounded error.<|reference_end|> | arxiv | @article{ambainis1998a,
title={A note on quantum black-box complexity of almost all Boolean functions},
author={Andris Ambainis},
journal={Inform.Proc.Lett. 71 (1999) 5-7},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9811080},
primaryClass={quant-ph cs.CC}
} | ambainis1998a |
arxiv-677430 | quant-ph/9812032 | NQP_C = co-C_=P | <|reference_start|>NQP_C = co-C_=P: Adleman, DeMarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. Fortnow and Rogers implicitly showed that, when the amplitudes are rational numbers, NQP is contained in the complement of C_{=}P. Fenner, Green, Homer, and Pruim improved this result by showing that, when the amplitudes are arbitrary algebraic numbers, NQP coincides with co-C_{=}P. In this paper we prove that, even when the amplitudes are arbitrary complex numbers, NQP still remains identical to co-C_{=}P. As an immediate corollary, BQP differs from NQP when the amplitudes are unrestricted.<|reference_end|> | arxiv | @article{yamakami1998nqp_{c},
title={NQP_{C} = co-C_{=}P},
author={Tomoyuki Yamakami and Andrew C. Yao},
journal={Inform.Proc.Lett. 71 (1999) 63-69},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9812032},
primaryClass={quant-ph cs.CC}
} | yamakami1998nqp_{c} |
arxiv-677431 | quant-ph/9812070 | Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups | <|reference_start|>Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups: We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer.<|reference_end|> | arxiv | @article{roetteler1998polynomial-time,
title={Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of
non-abelian Groups},
author={Martin Roetteler, and Thomas Beth},
journal={arXiv preprint arXiv:quant-ph/9812070},
year={1998},
archivePrefix={arXiv},
eprint={quant-ph/9812070},
primaryClass={quant-ph cs.ET}
} | roetteler1998polynomial-time |
arxiv-677432 | quant-ph/9902053 | A better lower bound for quantum algorithms searching an ordered list | <|reference_start|>A better lower bound for quantum algorithms searching an ordered list: We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only a constant speedup for this problem. Our result improves lower bounds of Buhrman and de Wolf(quant-ph/9811046) and Farhi, Goldstone, Gutmann and Sipser (quant-ph/9812057).<|reference_end|> | arxiv | @article{ambainis1999a,
title={A better lower bound for quantum algorithms searching an ordered list},
author={Andris Ambainis},
journal={arXiv preprint arXiv:quant-ph/9902053},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9902053},
primaryClass={quant-ph cs.CC cs.DS}
} | ambainis1999a |
arxiv-677433 | quant-ph/9903035 | Quantum Bounded Query Complexity | <|reference_start|>Quantum Bounded Query Complexity: We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function classes. For decision problems and function classes we obtain the following results: o P_||^NP[2k] is included in EQP_||^NP[k] o P_||^NP[2^(k+1)-2] is included in EQP^NP[k] o FP_||^NP[2^(k+1)-2] is included in FEQP^NP[2k] o FP_||^NP is included in FEQP^NP[O(log n)] For sets A that are many-one complete for PSPACE or EXP we show that FP^A is included in FEQP^A[1]. Sets A that are many-one complete for PP have the property that FP_||^A is included in FEQP^A[1]. In general we prove that for any set A there is a set X such that FP^A is included in FEQP^X[1], establishing that no set is superterse in the quantum setting.<|reference_end|> | arxiv | @article{buhrman1999quantum,
title={Quantum Bounded Query Complexity},
author={Harry Buhrman (CWI) and Wim van Dam (CQC and CWI)},
journal={Proceedings of the 14th Annual IEEE Conference on Computational
Complexity, pp. 149-156 (1999)},
year={1999},
doi={10.1109/CCC.1999.766273},
archivePrefix={arXiv},
eprint={quant-ph/9903035},
primaryClass={quant-ph cs.CC}
} | buhrman1999quantum |
arxiv-677434 | quant-ph/9903042 | An Almost-Quadratic Lower Bound for Quantum Formula Size | <|reference_start|>An Almost-Quadratic Lower Bound for Quantum Formula Size: We show that Nechiporuk's method for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an n^2 / log^2 n lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas (by Yao) states that the majority function does not have a linear-size quantum formula.<|reference_end|> | arxiv | @article{roychowdhury1999an,
title={An Almost-Quadratic Lower Bound for Quantum Formula Size},
author={Vwani P. Roychowdhury and Farrokh Vatan},
journal={arXiv preprint arXiv:quant-ph/9903042},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9903042},
primaryClass={quant-ph cs.CC}
} | roychowdhury1999an |
arxiv-677435 | quant-ph/9904050 | A Computer Scientist's View of Life, the Universe, and Everything | <|reference_start|>A Computer Scientist's View of Life, the Universe, and Everything: Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of Kolmogorov complexity theory to the set of possible universes, and chat about perceived and true randomness, life, generalization, and learning in a given universe.<|reference_end|> | arxiv | @article{schmidhuber1999a,
title={A Computer Scientist's View of Life, the Universe, and Everything},
author={Juergen Schmidhuber},
journal={In C. Freksa, ed., Foundations of Computer Science: Potential -
Theory - Cognition, Lecture Notes in Computer Science, pp. 201-208, Springer,
1997},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9904050},
primaryClass={quant-ph cs.CC cs.CY physics.comp-ph physics.pop-ph}
} | schmidhuber1999a |
arxiv-677436 | quant-ph/9904066 | Probabilities to accept languages by quantum finite automata | <|reference_start|>Probabilities to accept languages by quantum finite automata: We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.<|reference_end|> | arxiv | @article{ambainis1999probabilities,
title={Probabilities to accept languages by quantum finite automata},
author={Andris Ambainis, Richard Bonner, Rusins Freivalds, Arnolds Kikusts},
journal={arXiv preprint arXiv:quant-ph/9904066},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9904066},
primaryClass={quant-ph cs.CC}
} | ambainis1999probabilities |
arxiv-677437 | quant-ph/9904079 | Average-Case Quantum Query Complexity | <|reference_start|>Average-Case Quantum Query Complexity: We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-exponential. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.<|reference_end|> | arxiv | @article{ambainis1999average-case,
title={Average-Case Quantum Query Complexity},
author={Andris Ambainis (UC Berkeley) and Ronald de Wolf (CWI and U of
Amsterdam)},
journal={arXiv preprint arXiv:quant-ph/9904079},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9904079},
primaryClass={quant-ph cs.CC}
} | ambainis1999average-case |
arxiv-677438 | quant-ph/9904091 | A simple proof of the unconditional security of quantum key distribution | <|reference_start|>A simple proof of the unconditional security of quantum key distribution: Quantum key distribution is the most well-known application of quantum cryptography. Previous proposed proofs of security of quantum key distribution contain various technical subtleties. Here, a conceptually simpler proof of security of quantum key distribution is presented. The new insight is the invariance of the error rate of a teleportation channel: We show that the error rate of a teleportation channel is independent of the signals being transmitted. This is because the non-trivial error patterns are permuted under teleportation. This new insight is combined with the recently proposed quantum to classical reduction theorem. Our result shows that assuming that Alice and Bob have fault-tolerant quantum computers, quantum key distribution can be made unconditionally secure over arbitrarily long distances even against the most general type of eavesdropping attacks and in the presence of all types of noises.<|reference_end|> | arxiv | @article{lo1999a,
title={A simple proof of the unconditional security of quantum key distribution},
author={Hoi-Kwong Lo (Hewlett-Packard Labs, Bristol)},
journal={J.Phys.A34:6957-6968,2001},
year={1999},
doi={10.1088/0305-4470/34/35/321},
archivePrefix={arXiv},
eprint={quant-ph/9904091},
primaryClass={quant-ph cs.CR}
} | lo1999a |
arxiv-677439 | quant-ph/9904093 | Optimal lower bounds for quantum automata and random access codes | <|reference_start|>Optimal lower bounds for quantum automata and random access codes: Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum finite automaton (QFA) for it has size 2^{Omega(n/log n)}. This was based on the fact that the evolution of a QFA is required to be reversible. When arbitrary intermediate measurements are allowed, this intuition breaks down. Nonetheless, we show a 2^{Omega(n)} lower bound for such QFA for L_n, thus also improving the previous bound. The improved bound is obtained by simple entropy arguments based on Holevo's theorem. This method also allows us to obtain an asymptotically optimal (1-H(p))n bound for the dense quantum codes (random access codes) introduced by Ambainis et al. We then turn to Holevo's theorem, and show that in typical situations, it may be replaced by a tighter and more transparent in-probability bound.<|reference_end|> | arxiv | @article{nayak1999optimal,
title={Optimal lower bounds for quantum automata and random access codes},
author={Ashwin Nayak},
journal={arXiv preprint arXiv:quant-ph/9904093},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9904093},
primaryClass={quant-ph cs.CC}
} | nayak1999optimal |
arxiv-677440 | quant-ph/9904108 | Self-Testing of Universal and Fault-Tolerant Sets of Quantum Gates | <|reference_start|>Self-Testing of Universal and Fault-Tolerant Sets of Quantum Gates: We consider the design of self-testers for quantum gates. A self-tester for the gates F_1,...,F_m is a classical procedure that, given any gates G_1,...,G_m, decides with high probability if each G_i is close to F_i. This decision has to rely only on measuring in the computational basis the effect of iterating the gates on the classical states. It turns out that instead of individual gates, we can only design procedures for families of gates. To achieve our goal we borrow some elegant ideas of the theory of program testing: we characterize the gate families by specific properties, we develop a theory of robustness for them, and show that they lead to self-testers. In particular we prove that the universal and fault-tolerant set of gates consisting of a Hadamard gate, a c-NOT gate, and a phase rotation gate of angle pi/4 is self-testable.<|reference_end|> | arxiv | @article{van dam1999self-testing,
title={Self-Testing of Universal and Fault-Tolerant Sets of Quantum Gates},
author={Wim van Dam (1,2) and Frederic Magniez (3) and Michele Mosca (2,4) and
Miklos Santha (3,5) ((1) CWI Amsterdam (2) CQC Oxford (3) LRI Paris Sud (4) U
of Waterloo (5) CNRS)},
journal={Proceedings of the 32nd Annual ACM Symposium on Theory of
Computing (STOC2000), pages 688-696},
year={1999},
doi={10.1145/335305.335402},
archivePrefix={arXiv},
eprint={quant-ph/9904108},
primaryClass={quant-ph cs.OH}
} | van dam1999self-testing |
arxiv-677441 | quant-ph/9905026 | Quantum finite multitape automata | <|reference_start|>Quantum finite multitape automata: Quantum finite automata were introduced by C.Moore, J.P. Crutchfield, and by A.Kondacs and J.Watrous. This notion is not a generalization of the deterministic finite automata. Moreover, it was proved that not all regular languages can be recognized by quantum finite automata. A.Ambainis and R.Freivalds proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by a deterministic or probabilistic finite automata. This is the first result on a problem which can be solved by a quantum computer but not by a deterministic or probabilistic computer. Additionally we discover unexpected probabilistic automata recognizing complicated languages.<|reference_end|> | arxiv | @article{ambainis1999quantum,
title={Quantum finite multitape automata},
author={Andris Ambainis, Richard Bonner, Rusins Freivalds, Marats Golovkins,
Marek Karpinski},
journal={arXiv preprint arXiv:quant-ph/9905026},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9905026},
primaryClass={quant-ph cs.CC cs.FL}
} | ambainis1999quantum |
arxiv-677442 | quant-ph/9905043 | Operation of universal gates in a DXD superconducting solid state quantum computer | <|reference_start|>Operation of universal gates in a DXD superconducting solid state quantum computer: We demonstrate that complete set of gates can be realized in a DXD superconducting solid state quantum computer (quamputer), thereby proving its universality.<|reference_end|> | arxiv | @article{blais1999operation,
title={Operation of universal gates in a DXD superconducting solid state
quantum computer},
author={Alexandre Blais and Alexandre M. Zagoskin},
journal={Physical Review A, v.61, 042308 (2000)},
year={1999},
doi={10.1103/PhysRevA.61.042308},
archivePrefix={arXiv},
eprint={quant-ph/9905043},
primaryClass={quant-ph cond-mat.mes-hall cond-mat.other cond-mat.supr-con cs.GL}
} | blais1999operation |
arxiv-677443 | quant-ph/9906084 | A Foundation of Programming a Multi-Tape Quantum Turing machine | <|reference_start|>A Foundation of Programming a Multi-Tape Quantum Turing machine: The notion of quantum Turing machines is a basis of quantum complexity theory. We discuss a general model of multi-tape, multi-head Quantum Turing machines with multi final states that also allow tape heads to stay still.<|reference_end|> | arxiv | @article{yamakami1999a,
title={A Foundation of Programming a Multi-Tape Quantum Turing machine},
author={Tomoyuki Yamakami},
journal={arXiv preprint arXiv:quant-ph/9906084},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9906084},
primaryClass={quant-ph cs.CC}
} | yamakami1999a |
arxiv-677444 | quant-ph/9906103 | Secure Classical Bit Commitment using Fixed Capacity Communication Channels | <|reference_start|>Secure Classical Bit Commitment using Fixed Capacity Communication Channels: If mutually mistrustful parties A and B control two or more appropriately located sites, special relativity can be used to guarantee that a pair of messages exchanged by A and B are independent. In earlier work, we used this fact to define a relativistic bit commitment protocol, RBC1, in which security is maintained by exchanging a sequence of messages whose transmission rate increases exponentially in time. We define here a new relativistic protocol, RBC2, which requires only a constant transmission rate and could be practically implemented. We prove that RBC2 allows a bit commitment to be indefinitely maintained with unconditional security against all classical attacks. We examine its security against quantum attacks, and show that it is immune from the class of attacks shown by Mayers and Lo-Chau to render non-relativistic quantum bit commitment protocols insecure.<|reference_end|> | arxiv | @article{kent1999secure,
title={Secure Classical Bit Commitment using Fixed Capacity Communication
Channels},
author={Adrian Kent (Centre for Quantum Computation, University of Cambridge)},
journal={J.Cryptolog. 18 (2005) 313-335},
year={1999},
number={DAMTP-1999-47},
archivePrefix={arXiv},
eprint={quant-ph/9906103},
primaryClass={quant-ph cs.CR}
} | kent1999secure |
arxiv-677445 | quant-ph/9907009 | The importance of quantum decoherence in brain processes | <|reference_start|>The importance of quantum decoherence in brain processes: Based on a calculation of neural decoherence rates, we argue that that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence timescales ~10^{-13}-10^{-20} seconds are typically much shorter than the relevant dynamical timescales (~0.001-0.1 seconds), both for regular neuron firing and for kink-like polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.<|reference_end|> | arxiv | @article{tegmark1999the,
title={The importance of quantum decoherence in brain processes},
author={Max Tegmark},
journal={Phys.Rev.E61:4194-4206,2000},
year={1999},
doi={10.1103/PhysRevE.61.4194},
archivePrefix={arXiv},
eprint={quant-ph/9907009},
primaryClass={quant-ph cond-mat.dis-nn cs.NE physics.bio-ph q-bio}
} | tegmark1999the |
arxiv-677446 | quant-ph/9909012 | Analysis of Quantum Functions | <|reference_start|>Analysis of Quantum Functions: This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are classical bit strings. We prove complexity-theoretical properties and unique characteristics of these quantum functions by recent techniques developed for the analysis of quantum computations. We also discuss relativized quantum functions that make adaptive and nonadaptive oracle queries.<|reference_end|> | arxiv | @article{yamakami1999analysis,
title={Analysis of Quantum Functions},
author={Tomoyuki Yamakami},
journal={International Journal of Foundations of Computer Science,
Vol.14(5), pp.815-852, October 2003.},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9909012},
primaryClass={quant-ph cs.CC}
} | yamakami1999analysis |
arxiv-677447 | quant-ph/9909094 | Quantum Computation and Quadratically Signed Weight Enumerators | <|reference_start|>Quantum Computation and Quadratically Signed Weight Enumerators: We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be cast in terms of promise problems and has two interesting variants. An oracle for the unconstrained variant may be more powerful than quantum computation, while an oracle for a more constrained variant is efficiently solvable in the one-bit model of quantum computation. Thus, problems involving estimation of quadratically signed weight enumerators yield problems in BQP (bounded error quantum polynomial time) that are distinct from the ones studied so far, include a canonical BQP complete problem, and can be used to define and study complexity classes and their relationships to quantum computation.<|reference_end|> | arxiv | @article{knill1999quantum,
title={Quantum Computation and Quadratically Signed Weight Enumerators},
author={E. Knill, R. Laflamme},
journal={arXiv preprint arXiv:quant-ph/9909094},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9909094},
primaryClass={quant-ph cs.CC}
} | knill1999quantum |
arxiv-677448 | quant-ph/9910033 | Almost-Everywhere Superiority for Quantum Computing | <|reference_start|>Almost-Everywhere Superiority for Quantum Computing: Simon as extended by Brassard and H{\o}yer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine almost everywhere.<|reference_end|> | arxiv | @article{hemaspaandra1999almost-everywhere,
title={Almost-Everywhere Superiority for Quantum Computing},
author={Edith Hemaspaandra (RIT), Lane A. Hemaspaandra (University of
Rochester), Marius Zimand (Towson University)},
journal={arXiv preprint arXiv:quant-ph/9910033},
year={1999},
number={Revised version of URCS-TR-99-720},
archivePrefix={arXiv},
eprint={quant-ph/9910033},
primaryClass={quant-ph cs.CC}
} | hemaspaandra1999almost-everywhere |
arxiv-677449 | quant-ph/9910087 | Unconditionally Secure Commitment of a Certified Classical Bit is Impossible | <|reference_start|>Unconditionally Secure Commitment of a Certified Classical Bit is Impossible: In a secure bit commitment protocol involving only classical physics, A commits either a 0 or a 1 to B. If quantum information is used in the protocol, A may be able to commit a state of the form $\alpha \ket{0} + \beta \ket{1}$. If so, she can also commit mixed states in which the committed bit is entangled with other quantum states under her control. We introduce here a quantum cryptographic primitive, {\it bit commitment with a certificate of classicality} (BCCC), which differs from standard bit commitment in that it guarantees that the committed state has a fixed classical value. We show that no unconditionally secure BCCC protocol based on special relativity and quantum theory exists. We also propose complete definitions of security for quantum and relativistic bit commitment.<|reference_end|> | arxiv | @article{kent1999unconditionally,
title={Unconditionally Secure Commitment of a Certified Classical Bit is
Impossible},
author={Adrian Kent (DAMTP, University of Cambridge)},
journal={Phys. Rev. A 61, 042301 (2000)},
year={1999},
doi={10.1103/PhysRevA.61.042301},
number={DAMTP-1999-51},
archivePrefix={arXiv},
eprint={quant-ph/9910087},
primaryClass={quant-ph cs.CR}
} | kent1999unconditionally |
arxiv-677450 | quant-ph/9911043 | Cheat Sensitive Quantum Bit Commitment | <|reference_start|>Cheat Sensitive Quantum Bit Commitment: We define cheat sensitive cryptographic protocols between mistrustful parties as protocols which guarantee that, if either cheats, the other has some nonzero probability of detecting the cheating. We give an example of an unconditionally secure cheat sensitive non-relativistic bit commitment protocol which uses quantum information to implement a task which is classically impossible; we also describe a simple relativistic protocol.<|reference_end|> | arxiv | @article{hardy1999cheat,
title={Cheat Sensitive Quantum Bit Commitment},
author={Lucien Hardy (The Perimeter Institute) and Adrian Kent (Centre for
Quantum Computation, University of Cambridge)},
journal={Phys. Rev. Lett. 92, 157901 (2004).},
year={1999},
doi={10.1103/PhysRevLett.92.157901},
archivePrefix={arXiv},
eprint={quant-ph/9911043},
primaryClass={quant-ph cs.CR}
} | hardy1999cheat |
arxiv-677451 | quant-ph/9912100 | Quantum Computing, NP-complete Problems and Chaotic Dynamics | <|reference_start|>Quantum Computing, NP-complete Problems and Chaotic Dynamics: An approach to the solution of NP-complete problems based on quantum computing and chaotic dynamics is proposed. We consider the satisfiability problem and argue that the problem, in principle, can be solved in polynomial time if we combine the quantum computer with the chaotic dynamics amplifier based on the logistic map. We discuss a possible implementation of such a chaotic quantum computation by using the atomic quantum computer with quantum gates described by the Hartree-Fock equations. In this case, in principle, one can build not only standard linear quantum gates but also nonlinear gates and moreover they obey to Fermi statistics. This new type of entaglement related with Fermi statistics can be interesting also for quantum communication theory.<|reference_end|> | arxiv | @article{ohya1999quantum,
title={Quantum Computing, NP-complete Problems and Chaotic Dynamics},
author={Masanori Ohya and Igor V. Volovich},
journal={arXiv preprint arXiv:quant-ph/9912100},
year={1999},
archivePrefix={arXiv},
eprint={quant-ph/9912100},
primaryClass={quant-ph chao-dyn cond-mat.mes-hall cs.CC nlin.CD physics.atom-ph}
} | ohya1999quantum |