The Road to Quantum Computational Supremacy

We present an idiosyncratic view of the race for quantum computational supremacy. Google's approach and IBM challenge are examined. An unexpected side-effect of the race is the significant progress in designing fast classical algorithms. Quantum supremacy, if achieved, won't make classical computing obsolete.

[1]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[2]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[3]  Scott Aaronson,et al.  The limits of quantum computers. , 2008 .

[4]  Cristian S. Calude DE-QUANTIZING THE SOLUTION OF DEUTSCH'S PROBLEM , 2006, quant-ph/0610220.

[5]  I. Lakatos Falsification and the Methodology of Scientific Research Programmes , 1976 .

[6]  H. Neven,et al.  Simulation of low-depth quantum circuits as complex undirected graphical models , 2017, 1712.05384.

[7]  Anne Broadbent,et al.  How to Verify a Quantum Computation , 2015, Theory Comput..

[8]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[9]  Cristian S. Calude Super-Exponentials Nonprimitive Recursive, but Rudimentary , 1987, Inf. Process. Lett..

[10]  W. Ackermann Zum Hilbertschen Aufbau der reellen Zahlen , 1928 .

[11]  Robert König,et al.  Quantum advantage with shallow circuits , 2017, Science.

[12]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[13]  Ewin Tang,et al.  A quantum-inspired classical algorithm for recommendation systems , 2018, Electron. Colloquium Comput. Complex..

[14]  Jeffrey K. Uhlmann,et al.  Hybrid quantum-classical computing with applications to computer graphics , 2005, SIGGRAPH Courses.

[15]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  Daniel J. Bernstein,et al.  Post-quantum RSA , 2017, PQCrypto.

[17]  Ashley Montanaro,et al.  Quantum algorithms: an overview , 2015, npj Quantum Information.

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

[19]  Ryan O'Donnell,et al.  Special Issue: CCC 2017: Guest Editor's Foreword , 2018, Theory of Computing.

[20]  Cristian S. Calude,et al.  Guest Column: Adiabatic Quantum Computing Challenges , 2015, SIGA.

[21]  Raphaël Clifford,et al.  Classical boson sampling algorithms with superior performance to near-term experiments , 2017, Nature Physics.

[22]  Alastair A. Abbott The Deutsch–Jozsa problem: de-quantisation and entanglement , 2011, Natural Computing.

[23]  N. David Mermin,et al.  What's Wrong with these Equations? , 1989 .

[24]  Adam Becker,et al.  What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics , 2018 .

[25]  Karl Svozil,et al.  Quantum Hocus Pocus , 2016, 1605.08569.

[26]  John Preskill,et al.  Quantum computing and the entanglement frontier , 2012, 1203.5813.

[27]  Martin Fürer Solving NP-Complete Problems with Quantum Search , 2008, LATIN.

[28]  Cristian S. Calude,et al.  Experimental Evidence of Quantum Randomness Incomputability , 2010, ArXiv.

[29]  Vincenzo Tamma,et al.  Analogue algorithm for parallel factorization of an exponential number of large integers: II—optical implementation , 2015, Quantum Inf. Process..

[30]  E. Campbell Random Compiler for Fast Hamiltonian Simulation. , 2018, Physical review letters.

[31]  D. Browne Efficient classical simulation of the quantum Fourier transform , 2006, quant-ph/0612021.

[32]  Renato Renner,et al.  An intuitive proof of the data processing inequality , 2011, Quantum Inf. Comput..

[33]  Gilles Brassard,et al.  Oracle Quantum Computing , 1994 .

[34]  M. Lukin,et al.  Probing many-body dynamics on a 51-atom quantum simulator , 2017, Nature.

[35]  Gil Kalai,et al.  How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation , 2011, ArXiv.

[36]  Adi Shamir,et al.  Factoring Numbers in O(log n) Arithmetic Steps , 1979, Inf. Process. Lett..

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

[38]  Alastair A. Abbott,et al.  De-quantisation of the quantum Fourier transform , 2010, Appl. Math. Comput..

[39]  Iordanis Kerenidis,et al.  Quantum Recommendation System , 2017 .

[40]  Shuntaro Takeda,et al.  Universal Quantum Computing with Measurement-Induced Continuous-Variable Gate Sequence in a Loop-Based Architecture. , 2017, Physical review letters.

[41]  N. David Mermin,et al.  What's Wrong with this Pillow? , 1989 .

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

[43]  H Neven,et al.  A blueprint for demonstrating quantum supremacy with superconducting qubits , 2017, Science.

[44]  Griffiths,et al.  Semiclassical Fourier transform for quantum computation. , 1995, Physical review letters.

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

[46]  Cristian S. Calude,et al.  A Hybrid Quantum-Classical Paradigm to Mitigate Embedding Costs in Quantum Annealing , 2018, PC@UCNC.

[47]  K. Wiesner The careless use of language in quantum information , 2017 .

[48]  Niklas Johansson,et al.  Efficient classical simulation of the Deutsch–Jozsa and Simon’s algorithms , 2015, Quantum Information Processing.

[49]  Cristian S. Calude,et al.  QUBO formulations for the graph isomorphism problem and related problems , 2017, Theor. Comput. Sci..

[50]  Elad Eban,et al.  Interactive Proofs For Quantum Computations , 2017, 1704.04487.

[51]  C. Monroe,et al.  Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator , 2017, Nature.

[52]  Joseph W. Haus,et al.  A brief review of theoretical results for photonic band structures , 1994 .

[53]  J. Schwartz,et al.  A note on monte carlo primality tests and algorithmic information theory , 1978 .

[54]  A Pritchard,et al.  The defeat of reason. , 1997, Health care analysis : HCA : journal of health philosophy and policy.

[55]  John A. Gunnels,et al.  Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits , 2017, 1710.05867.

[56]  Cristian S. Calude,et al.  Understanding the Quantum Computational Speed-up via De-quantisation , 2010, DCM.

[57]  Aram W. Harrow,et al.  Quantum computational supremacy , 2017, Nature.

[58]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[59]  Umesh V. Vazirani,et al.  Quantum Complexity Theory , 1997, SIAM J. Comput..

[60]  Peter W. Shor,et al.  Why haven't more quantum algorithms been found? , 2003, JACM.

[61]  W. Munro,et al.  Quantum analogue computing , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[62]  Daniel R. Simon On the Power of Quantum Computation , 1997, SIAM J. Comput..

[63]  Scott Aaronson,et al.  Complexity-Theoretic Foundations of Quantum Supremacy Experiments , 2016, CCC.

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

[65]  Andrew Chi-Chih Yao,et al.  Classical physics and the Church--Turing Thesis , 2003, JACM.

[66]  Cristian S. Calude,et al.  Quassical Computing , 2018, Int. J. Unconv. Comput..

[67]  Iordanis Kerenidis,et al.  Quantum Recommendation Systems , 2016, ITCS.

[68]  Manisha J. Nene,et al.  Shor’s Algorithm for Quantum Factoring , 2016 .

[69]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

[70]  Masoud Mohseni,et al.  Commercialize quantum technologies in five years , 2017, Nature.

[71]  Jozef Gruska,et al.  Quantum Computing , 2008, Wiley Encyclopedia of Computer Science and Engineering.

[72]  H. Neven,et al.  Characterizing quantum supremacy in near-term devices , 2016, Nature Physics.

[73]  Jozef Gruska,et al.  Quantum Computing Challenges , 2001 .