Models of optical quantum computing

Abstract I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

[1]  Umesh V. Vazirani,et al.  Quantum mechanical algorithms for the nonabelian hidden subgroup problem , 2001, STOC '01.

[2]  Hoi-Kwong Lo,et al.  All-photonic quantum repeaters , 2013, Nature Communications.

[3]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[4]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[5]  H. Bechmann-Pasquinucci,et al.  Quantum cryptography , 2001, quant-ph/0101098.

[6]  T. Ralph,et al.  Demonstration of an all-optical quantum controlled-NOT gate , 2003, Nature.

[7]  A. Crespi,et al.  Integrated multimode interferometers with arbitrary designs for photonic boson sampling , 2013, Nature Photonics.

[8]  Ashley Montanaro,et al.  Quantum algorithms and the finite element method , 2015, 1512.05903.

[9]  J. D. Franson,et al.  Probabilistic quantum logic operations using polarizing beam splitters , 2001, quant-ph/0107091.

[10]  Jérémie Roland,et al.  Anderson localization makes adiabatic quantum optimization fail , 2009, Proceedings of the National Academy of Sciences.

[11]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[12]  Philip Walther,et al.  Experimental boson sampling , 2012, Nature Photonics.

[13]  Martin Rötteler,et al.  An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups , 2008, MMICS.

[14]  Christoph Simon,et al.  Practical quantum repeaters with parametric down-conversion sources , 2015, 1505.03470.

[15]  S. Braunstein.  Squeezing as an irreducible resource , 1999, quant-ph/9904002.

[16]  A. Harrow,et al.  Quantum Supremacy through the Quantum Approximate Optimization Algorithm , 2016, 1602.07674.

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

[18]  Chuang,et al.  Simple quantum computer. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[19]  Dave Bacon,et al.  From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[20]  A Laing,et al.  Boson sampling from a Gaussian state. , 2014, Physical review letters.

[21]  R. Byer,et al.  Network of time-multiplexed optical parametric oscillators as a coherent Ising machine , 2014, Nature Photonics.

[22]  M. Tsang,et al.  Metaphoric optical computing of fluid dynamics , 2005, 2005 Quantum Electronics and Laser Science Conference.

[23]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[24]  N. J. Cerf,et al.  Optical simulation of quantum logic , 1998 .

[25]  Seth Lloyd,et al.  Adiabatic quantum computation is equivalent to standard quantum computation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[26]  Bahram Jalali,et al.  Analog optical computing , 2015, Nature Photonics.

[27]  J. Preskill,et al.  Encoding a qubit in an oscillator , 2000, quant-ph/0008040.

[28]  Óscar Promio Muñoz.  Quantum Annealing in the transverse Ising Model , 2018 .

[29]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[30]  J. O'Brien,et al.  On the experimental verification of quantum complexity in linear optics , 2013, Nature Photonics.

[31]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[32]  Gregory R. Steinbrecher,et al.  High-fidelity quantum state evolution in imperfect photonic integrated circuits , 2015 .

[33]  M. A. Rowe,et al.  A Decoherence-Free Quantum Memory Using Trapped Ions , 2001, Science.

[34]  B. Jack Copeland.  The Modern History of Computing , 2006 .

[35]  Nicolas Gisin,et al.  Mapping multiple photonic qubits into and out of one solid-state atomic ensemble. , 2010, Nature communications.

[36]  M. Dušek,et al.  Experimental investigation of a four-qubit linear-optical quantum logic circuit , 2016, Scientific Reports.

[37]  Alexander Russell,et al.  Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups , 2012, ArXiv.

[38]  Jeffrey H. Shapiro,et al.  Single-photon Kerr nonlinearities do not help quantum computation , 2006 .

[39]  M. J. Fitch,et al.  Experimental controlled-NOT logic gate for single photons in the coincidence basis , 2003, quant-ph/0303095.

[40]  Maris Ozols,et al.  Quantum Walks Can Find a Marked Element on Any Graph , 2010, Algorithmica.

[41]  B. J. Metcalf,et al.  Boson Sampling on a Photonic Chip , 2012, Science.

[42]  Yoshihisa Yamamoto,et al.  Mapping of Ising models onto injection-locked laser systems. , 2011, Optics express.

[43]  S. Braunstein,et al.  Quantum computation over continuous variables , 1998 .

[44]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[45]  Nicolò Spagnolo,et al.  Experimental scattershot boson sampling , 2015, Science Advances.

[46]  Félix Bussières,et al.  Broadband waveguide quantum memory for entangled photons , 2011, SUM 2011.

[47]  Barry C. Sanders,et al.  Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps , 2006, quant-ph/0606026.

[48]  H. Krovi,et al.  Adiabatic condition and the quantum hitting time of Markov chains , 2010, 1004.2721.

[49]  Michael Huber.  Steiner t-designs for large t , 2008, 0809.3117.

[50]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[51]  J. Franson,et al.  Demonstration of nondeterministic quantum logic operations using linear optical elements. , 2001, Physical review letters.

[52]  G. Milburn,et al.  Quantum computation with optical coherent states , 2002, QELS 2002.

[53]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[54]  Ashley Montanaro,et al.  Quantum walk speedup of backtracking algorithms , 2015, Theory Comput..

[55]  Nicolò Spagnolo,et al.  Experimental validation of photonic boson sampling , 2014, Nature Photonics.

[56]  Andrew M. Childs,et al.  Exponential improvement in precision for simulating sparse Hamiltonians , 2013, Forum of Mathematics, Sigma.

[57]  S. Guha,et al.  Optimal measurements for symmetric quantum states with applications to optical communication , 2015, 1507.04737.

[58]  John Preskill,et al.  Quantum Algorithms for Quantum Field Theories , 2011, Science.

[59]  Experimental Characterization of a Telecommunications-Band Quantum Controlled- not Gate , 2009, IEEE Journal of Selected Topics in Quantum Electronics.

[60]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.