Quantum Computing and Communication Complexity

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[1]  Lance Fortnow,et al.  Complexity limitations on quantum computation , 1999, J. Comput. Syst. Sci..

[2]  Noam Nisan,et al.  CREW PRAMS and decision trees , 1989, STOC '89.

[3]  Edith Hemaspaandra,et al.  Almost-Everywhere Superiority for Quantum Polynomial Time , 2002, Inf. Comput..

[4]  T. J. Rivlin,et al.  The growth of polynomials bounded at equally spaced points , 1992 .

[5]  Harry Buhrman,et al.  Quantum Entanglement and Communication Complexity , 2000, SIAM J. Comput..

[6]  Ronald de Wolf,et al.  Lower Bounds for Quantum Search and Derandomization , 1998, ArXiv.

[7]  R. M. deWolf.  Quantum Computing and Communication Complexity , 2001 .

[8]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

[9]  László Babai,et al.  Randomized simultaneous messages: solution of a problem of Yao in communication complexity , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[10]  Sean Hallgren,et al.  Quantum Fourier sampling simplified , 1999, STOC '99.

[11]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[12]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[13]  Karl Zeller,et al.  Schwankung von Polynomen zwischen Gitterpunkten , 1964 .

[14]  Peter W. Shor,et al.  Algorithms for Quantum Computation: Discrete Log and Factoring (Extended Abstract) , 1994, FOCS 1994.

[15]  Ronald de Wolf,et al.  Bounds for small-error and zero-error quantum algorithms , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[16]  Michael E. Saks,et al.  Super-linear time-space tradeoff lower bounds for randomized computation , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[17]  Andrew Chi-Chih Yao.  Monotone Bipartite Graph Properties are Evasive , 1988, SIAM J. Comput..

[18]  Jørn Justesen,et al.  Class of constructive asymptotically good algebraic codes , 1972, IEEE Trans. Inf. Theory.

[19]  Andris Ambainis,et al.  A better lower bound for quantum algorithms searching an ordered list , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[20]  D. Coppersmith.  An approximate Fourier transform useful in quantum factoring , 2002, quant-ph/0201067.

[21]  Ramamohan Paturi,et al.  On the degree of polynomials that approximate symmetric Boolean functions (preliminary version) , 1992, STOC '92.

[22]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[23]  Michael E. Saks,et al.  Communication Complexity and Combinatorial Lattice Theory , 1993, J. Comput. Syst. Sci..

[24]  L M Vandersypen,et al.  Experimental realization of an order-finding algorithm with an NMR quantum computer. , 2000, Physical review letters.

[25]  S. Lloyd.  Quantum-Mechanical Computers , 1995 .

[26]  Ashwin Nayak,et al.  Optimal lower bounds for quantum automata and random access codes , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[27]  Ran Canetti,et al.  Bounds on tradeoffs between randomness and communication complexity , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[28]  Gilles Brassard,et al.  An exact quantum polynomial-time algorithm for Simon's problem , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[29]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[30]  Richard Cleve,et al.  The query complexity of order-finding , 1999, Proceedings 15th Annual IEEE Conference on Computational Complexity.

[31]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[32]  Gilles Brassard,et al.  Cost of Exactly Simulating Quantum Entanglement with Classical Communication , 1999 .

[33]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[34]  Noga Alon,et al.  Construction Of Asymptotically Good Low-rate Error-correcting Codes Through Pseudo-random Graphs , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[35]  M. Sipser,et al.  A Limit on the Speed of Quantum Computation for Insertion into an Ordered List , 1998 .

[36]  Donald E. Knuth.  The Sandwich Theorem , 1994, Electron. J. Comb..

[37]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[38]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[39]  Kurt Mehlhorn,et al.  Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity , 1990 .

[40]  Richard Beigel,et al.  The polynomial method in circuit complexity , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[41]  Leonid A. Levin,et al.  Average Case Complete Problems , 1986, SIAM J. Comput..

[42]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[43]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[44]  W. L. Nicholson,et al.  On the Normal Approximation to the Hypergeometric Distribution , 1956 .

[45]  Michael E. Saks,et al.  Probabilistic Boolean decision trees and the complexity of evaluating game trees , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[46]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[47]  Carl Pomerance,et al.  The Development of the Number Field Sieve , 1994 .

[48]  Andrew Chi-Chih Yao.  Near-Optimal Time-Space Tradeoff for Element Distinctness , 1994, SIAM J. Comput..

[49]  M. Mosca.  Quantum Searching Counting and Amplitude Ampli cation by Eigenvector Analysis , 1998 .

[50]  László Lovász,et al.  Lecture Notes on Evasiveness of Graph Properties , 2002, ArXiv.

[51]  Miklós Ajtai,et al.  Determinism versus non-determinism for linear time RAMs (extended abstract) , 1999, STOC '99.

[52]  G. Brassard,et al.  Quantum Amplitude Amplification and Estimation , 2000, quant-ph/0005055.

[53]  Andris Ambainis,et al.  Average-Case Quantum Query Complexity , 2000, STACS.

[54]  H. Buhrman,et al.  Complexity measures and decision tree complexity: a survey , 2002, Theor. Comput. Sci..

[55]  Hartmut Klauck,et al.  Interaction in quantum communication and the complexity of set disjointness , 2001, STOC '01.

[56]  Umesh V. Vazirani,et al.  Quantum complexity theory , 1993, STOC.

[57]  Noam Nisan,et al.  On the degree of boolean functions as real polynomials , 1992, STOC '92.

[58]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[59]  T. J. Rivlin.  Chebyshev polynomials : from approximation theory to algebra and number theory , 1990 .

[60]  Andris Ambainis,et al.  Private quantum channels , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[61]  Carl W. Helstrom,et al.  Detection Theory and Quantum Mechanics , 1967, Inf. Control..

[62]  Hartmut Klauck,et al.  On quantum and probabilistic communication: Las Vegas and one-way protocols , 2000, STOC '00.

[63]  Michael Werman,et al.  On computing majority by comparisons , 1991, Comb..

[64]  N. Bohr.  II - Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , 1935 .

[65]  Ronald de Wolf,et al.  Quantum communication and complexity , 2002, Theor. Comput. Sci..

[66]  Elliott Ward Cheney,et al.  A Comparison of Uniform Approximations on an Interval and a Finite Subset Thereof , 1966 .

[67]  Ran Raz,et al.  Exponential separation of quantum and classical communication complexity , 1999, STOC '99.

[68]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[69]  Dave Bacon,et al.  Classical simulation of quantum entanglement without local hidden variables , 2001 .

[70]  H. Lo.  Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity , 1999, quant-ph/9912009.

[71]  Avi Wigderson,et al.  On Read-Once Threshold Formulae and Their Randomized Decision in Tree Complexity , 1993, Theor. Comput. Sci..

[72]  Bala Kalyanasundaram,et al.  The Probabilistic Communication Complexity of Set Intersection , 1992, SIAM J. Discret. Math..

[73]  R. Schumann.  Quantum Information Theory , 2000, quant-ph/0010060.

[74]  Ronald de Wolf,et al.  A Lower Bound for Quantum Search of an Ordered List , 1999, Inf. Process. Lett..

[75]  András Rácz,et al.  A Lower Bound for the Integer Element Distinctness Problem , 1991, Inf. Comput..

[76]  Valerie King.  An Ω(n5/4) lower bound on the randomized complexity of graph properties , 1991, Comb..

[77]  Ronald de Wolf,et al.  Characterization of Non-Deterministic Quantum Query and Quantum Communication Complexity , 2000, CCC.

[78]  Stuart A. Kurtz,et al.  On oracle builder's toolkit , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[79]  Jürgen Bierbrauer,et al.  Almost Independent and Weakly Biased Arrays: Efficient Constructions and Cryptologic Applications , 2000, CRYPTO.

[80]  A. Wehrl.  General properties of entropy , 1978 .

[81]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[82]  P. Benioff.  Quantum mechanical hamiltonian models of turing machines , 1982 .

[83]  Stephen A. Fenner,et al.  Determining acceptance possibility for a quantum computation is hard for the polynomial hierarchy , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[84]  Andris Ambainis,et al.  A Note on Quantum Black-Box Complexity of Almost all Boolean Functions , 1998, Inf. Process. Lett..

[85]  Ilan Newman,et al.  Private vs. Common Random Bits in Communication Complexity , 1991, Inf. Process. Lett..

[86]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[87]  Christoph Dürr,et al.  A Quantum Algorithm for Finding the Minimum , 1996, ArXiv.

[88]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[89]  Ronald de Wolf,et al.  Quantum lower bounds by polynomials , 2001, JACM.

[90]  Gilles Brassard,et al.  Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..

[91]  Thomas P. Hayes,et al.  On the Quantum Complexity of Majority , 1998 .

[92]  Alexei Y. Kitaev,et al.  Parallelization, amplification, and exponential time simulation of quantum interactive proof systems , 2000, STOC '00.

[93]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[94]  Valerie King.  Lower bounds on the complexity of graph properties , 1988, STOC '88.

[95]  J. G. Pierce,et al.  Geometric Algorithms and Combinatorial Optimization , 2016 .

[96]  Peter Frankl,et al.  Complexity classes in communication complexity theory , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[97]  Avi Wigderson,et al.  Quantum vs. classical communication and computation , 1998, STOC '98.

[98]  Michele Mosca,et al.  The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer , 1998, QCQC.

[99]  Wim van Dam,et al.  Quantum Oracle Interrogation: Getting All Information for Almost Half the Price , 1999 .

[100]  Gilles Brassard,et al.  Quantum Counting , 1998, ICALP.

[101]  C. Fuchs.  Distinguishability and Accessible Information in Quantum Theory , 1996, quant-ph/9601020.

[102]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[103]  A. Holevo.  Bounds for the quantity of information transmitted by a quantum communication channel , 1973 .

[104]  Jan Neerbek,et al.  Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness , 2002, Algorithmica.

[105]  R. Werner.  All teleportation and dense coding schemes , 2000, quant-ph/0003070.

[106]  Andrew M. Steane,et al.  Physicists triumph at 'Guess My Number' , 2000 .

[107]  Ronald L. Rivest,et al.  On Recognizing Graph Properties from Adjacency Matrices , 1976, Theor. Comput. Sci..

[108]  Dima Grigoriev,et al.  Randomized complexity lower bounds , 1998, STOC '98.

[109]  Ronald de Wolf,et al.  Communication complexity lower bounds by polynomials , 1999, Proceedings 16th Annual IEEE Conference on Computational Complexity.

[110]  H. Lenstra,et al.  A rigorous time bound for factoring integers , 1992 .

[111]  Kurt Mehlhorn,et al.  Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract) , 1982, STOC '82.

[112]  René Schott,et al.  The Average-Case Complexity of Determining the Majority , 1997, SIAM J. Comput..

[113]  Edward M. Reingold,et al.  Determining the Majority , 1993, Inf. Process. Lett..

[114]  M. Sipser,et al.  Limit on the Speed of Quantum Computation in Determining Parity , 1998, quant-ph/9802045.

[115]  M. Sipser,et al.  Invariant quantum algorithms for insertion into an ordered list , 1999, quant-ph/9901059.

[116]  Andrew Chi-Chih Yao,et al.  Quantum Circuit Complexity , 1993, FOCS.

[117]  Leonard M. Adleman,et al.  Quantum Computability , 1997, SIAM J. Comput..

[118]  Harold Abelson,et al.  Lower bounds on information transfer in distributed computations , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[119]  R. Feynman.  Simulating physics with computers , 1999 .

[120]  Sanjeev Khanna,et al.  Space Time Tradeoffs for Graph Properties , 1999, ICALP.

[121]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[122]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[123]  Alexander A. Razborov,et al.  On the Distributional Complexity of Disjointness , 1992, Theor. Comput. Sci..

[124]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[125]  R. Cleve,et al.  SUBSTITUTING QUANTUM ENTANGLEMENT FOR COMMUNICATION , 1997, quant-ph/9704026.

[126]  Richard Cleve,et al.  Fast parallel circuits for the quantum Fourier transform , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[127]  Daniel R. Simon,et al.  On the power of quantum computation , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[128]  Amnon Ta-Shma,et al.  Classical versus quantum communication complexity , 1999, SIGA.

[129]  Peter Hoyer,et al.  Multiparty quantum communication complexity. , 1997 .