Quantum Machine Learning over Infinite Dimensions

Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George; Weedbrook, Christian

doi:10.1103/PhysRevLett.118.080501

Title: Quantum Machine Learning over Infinite Dimensions

Journal Article · Tue Feb 21 00:00:00 EST 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.118.080501· OSTI ID:1435294

Lau, Hoi-Kwan ^[1]; Pooser, Raphael ^[2]; Siopsis, George ^[3]; Weedbrook, Christian ^[4]

Ulm Univ. (Germany)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Univ. of Tennessee, Knoxville, TN (United States)
CipherQ, Toronto, ON (Canada)

Machine learning is a fascinating and exciting eld within computer science. Recently, this ex- citement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the nite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practi- cal, in nite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, we also map out an experi- mental implementation which can be used as a blueprint for future photonic demonstrations.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1435294

Alternate ID(s):: OSTI ID: 1344616

Journal Information:: Physical Review Letters, Vol. 118, Issue 8; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 58 works

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References (72)

Quantum computers Ladd, T. D.; Jelezko, F.; Laflamme, R. Nature, Vol. 464, Issue 7285 https://doi.org/10.1038/nature08812	journal	March 2010
Gaussian quantum information Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl Reviews of Modern Physics, Vol. 84, Issue 2 https://doi.org/10.1103/RevModPhys.84.621	journal	May 2012
Deep learning LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey Nature, Vol. 521, Issue 7553 https://doi.org/10.1038/nature14539	journal	May 2015
Quantum Computation over Continuous Variables Lloyd, Seth; Braunstein, Samuel L. Physical Review Letters, Vol. 82, Issue 8 https://doi.org/10.1103/PhysRevLett.82.1784	journal	February 1999
Temporal-mode continuous-variable cluster states using linear optics Menicucci, Nicolas C. Physical Review A, Vol. 83, Issue 6 https://doi.org/10.1103/PhysRevA.83.062314	journal	June 2011
Experimental Realization of a Quantum Support Vector Machine Li, Zhaokai; Liu, Xiaomei; Xu, Nanyang Physical Review Letters, Vol. 114, Issue 14 https://doi.org/10.1103/PhysRevLett.114.140504	journal	April 2015
Quantum simulation of quantum field theory using continuous variables Marshall, Kevin; Pooser, Raphael; Siopsis, George Physical Review A, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevA.92.063825	journal	December 2015
Experimental Quantum Computing to Solve Systems of Linear Equations Cai, X. -D.; Weedbrook, C.; Su, Z. -E. Physical Review Letters, Vol. 110, Issue 23 https://doi.org/10.1103/PhysRevLett.110.230501	journal	June 2013
Quantum information with continuous variables Braunstein, Samuel L.; van Loock, Peter Reviews of Modern Physics, Vol. 77, Issue 2 https://doi.org/10.1103/RevModPhys.77.513	journal	June 2005
Efficient state preparation for a register of quantum bits Soklakov, Andrei N.; Schack, Rüdiger Physical Review A, Vol. 73, Issue 1 https://doi.org/10.1103/PhysRevA.73.012307	journal	January 2006
Read the fine print Aaronson, Scott Nature Physics, Vol. 11, Issue 4 https://doi.org/10.1038/nphys3272	journal	April 2015
Continuous-variable Gaussian analog of cluster states Zhang, Jing; Braunstein, Samuel L. Physical Review A, Vol. 73, Issue 3 https://doi.org/10.1103/PhysRevA.73.032318	journal	March 2006
Invited Article: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing Yoshikawa, Jun-ichi; Yokoyama, Shota; Kaji, Toshiyuki APL Photonics, Vol. 1, Issue 6 https://doi.org/10.1063/1.4962732	journal	September 2016
Universal Quantum Computation with Continuous-Variable Cluster States Menicucci, Nicolas C.; van Loock, Peter; Gu, Mile Physical Review Letters, Vol. 97, Issue 11 https://doi.org/10.1103/PhysRevLett.97.110501	journal	September 2006
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer Shor, Peter W. SIAM Journal on Computing, Vol. 26, Issue 5 https://doi.org/10.1137/S0097539795293172	journal	October 1997
Quantum secret sharing with continuous-variable cluster states Lau, Hoi-Kwan; Weedbrook, Christian Physical Review A, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevA.88.042313	journal	October 2013
Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency Vahlbruch, Henning; Mehmet, Moritz; Danzmann, Karsten Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.110801	journal	September 2016
Repeat-until-success cubic phase gate for universal continuous-variable quantum computation Marshall, Kevin; Pooser, Raphael; Siopsis, George Physical Review A, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevA.91.032321	journal	March 2015
Noise analysis of single-mode Gaussian operations using continuous-variable cluster states Alexander, Rafael N.; Armstrong, Seiji C.; Ukai, Ryuji Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevA.90.062324	journal	December 2014
Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state Gao, Wei-Bo; Lu, Chao-Yang; Yao, Xing-Can Nature Physics, Vol. 6, Issue 5 https://doi.org/10.1038/nphys1603	journal	March 2010
Experimental realization of a dynamic squeezing gate Miyata, Kazunori; Ogawa, Hisashi; Marek, Petr Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevA.90.060302	journal	December 2014
Quantum principal component analysis Lloyd, Seth; Mohseni, Masoud; Rebentrost, Patrick Nature Physics, Vol. 10, Issue 9 https://doi.org/10.1038/nphys3029	journal	July 2014
Demonstration of a fully tunable entangling gate for continuous-variable one-way quantum computation Yokoyama, Shota; Ukai, Ryuji; Armstrong, Seiji C. Physical Review A, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevA.92.032304	journal	September 2015
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States Menicucci, Nicolas C. Physical Review Letters, Vol. 112, Issue 12 https://doi.org/10.1103/PhysRevLett.112.120504	journal	March 2014
Entanglement-Based Machine Learning on a Quantum Computer Cai, X. -D.; Wu, D.; Su, Z. -E. Physical Review Letters, Vol. 114, Issue 11 https://doi.org/10.1103/PhysRevLett.114.110504	journal	March 2015
Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb Chen, Moran; Menicucci, Nicolas C.; Pfister, Olivier Physical Review Letters, Vol. 112, Issue 12 https://doi.org/10.1103/PhysRevLett.112.120505	journal	March 2014
Ultra-large-scale continuous-variable cluster states multiplexed in the time domain Yokoyama, Shota; Ukai, Ryuji; Armstrong, Seiji C. Nature Photonics, Vol. 7, Issue 12 https://doi.org/10.1038/nphoton.2013.287	journal	November 2013
Quantum Random Access Memory Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Physical Review Letters, Vol. 100, Issue 16 https://doi.org/10.1103/PhysRevLett.100.160501	journal	April 2008
Detecting the degree of macroscopic quantumness using an overlap measurement Jeong, Hyunseok; Noh, Changsuk; Bae, Seunglee Journal of the Optical Society of America B, Vol. 31, Issue 12 https://doi.org/10.1364/JOSAB.31.003057	journal	January 2014
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding Lau, Hoi-Kwan; Plenio, Martin B. Physical Review Letters, Vol. 117, Issue 10 https://doi.org/10.1103/PhysRevLett.117.100501	journal	August 2016
Power of one qumode for quantum computation Liu, Nana; Thompson, Jayne; Weedbrook, Christian Physical Review A, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevA.93.052304	journal	May 2016
Quantum Algorithm for Linear Systems of Equations Harrow, Aram W.; Hassidim, Avinatan; Lloyd, Seth Physical Review Letters, Vol. 103, Issue 15 https://doi.org/10.1103/PhysRevLett.103.150502	journal	October 2009
Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms Dowling, Jonathan P.; Agarwal, G. S.; Schleich, Wolfgang P. Physical Review A, Vol. 49, Issue 5 https://doi.org/10.1103/PhysRevA.49.4101	journal	May 1994
Quantum computing with continuous-variable clusters Gu, Mile; Weedbrook, Christian; Menicucci, Nicolas C. Physical Review A, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevA.79.062318	journal	June 2009
Quantum adiabatic machine learning Pudenz, Kristen L.; Lidar, Daniel A. Quantum Information Processing, Vol. 12, Issue 5 https://doi.org/10.1007/s11128-012-0506-4	journal	November 2012
Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble Kubo, Y.; Grezes, C.; Dewes, A. Physical Review Letters, Vol. 107, Issue 22 https://doi.org/10.1103/PhysRevLett.107.220501	journal	November 2011
Hybrid discrete- and continuous-variable quantum information Andersen, Ulrik L.; Neergaard-Nielsen, Jonas S.; van Loock, Peter Nature Physics, Vol. 11, Issue 9 https://doi.org/10.1038/nphys3410	journal	September 2015
Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing Furusawa, Akira; van Loock, Peter https://doi.org/10.1002/9783527635283	book	January 2011
Overlap and entanglement-witness measurements Filip, Radim Physical Review A, Vol. 65, Issue 6 https://doi.org/10.1103/PhysRevA.65.062320	journal	June 2002
Quantum Support Vector Machine for Big Data Classification Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth Physical Review Letters, Vol. 113, Issue 13 https://doi.org/10.1103/PhysRevLett.113.130503	journal	September 2014
Generation and eight-port homodyne characterization of time-bin qubits for continuous-variable quantum information processing Takeda, Shuntaro; Mizuta, Takahiro; Fuwa, Maria Physical Review A, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevA.87.043803	journal	April 2013
Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states Wang, Pei; Chen, Moran; Menicucci, Nicolas C. Physical Review A, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevA.90.032325	journal	September 2014
Universal Quantum Simulators Lloyd, S. Science, Vol. 273, Issue 5278 https://doi.org/10.1126/science.273.5278.1073	journal	August 1996
A One-Way Quantum Computer Raussendorf, Robert; Briegel, Hans J. Physical Review Letters, Vol. 86, Issue 22 https://doi.org/10.1103/PhysRevLett.86.5188	journal	May 2001
Parallel Generation of Quadripartite Cluster Entanglement in the Optical Frequency Comb Pysher, Matthew; Miwa, Yoshichika; Shahrokhshahi, Reihaneh Physical Review Letters, Vol. 107, Issue 3 https://doi.org/10.1103/PhysRevLett.107.030505	journal	July 2011
Building Gaussian cluster states by linear optics van Loock, Peter; Weedbrook, Christian; Gu, Mile Physical Review A, Vol. 76, Issue 3 https://doi.org/10.1103/PhysRevA.76.032321	journal	September 2007
Holographic Quantum Computing Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus Physical Review Letters, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevLett.101.040501	journal	July 2008
A two-qubit photonic quantum processor and its application to solving systems of linear equations Barz, Stefanie; Kassal, Ivan; Ringbauer, Martin Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06115	journal	August 2014
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators Demarie, Tommaso F.; Linjordet, Trond; Menicucci, Nicolas C. New Journal of Physics, Vol. 16, Issue 8 https://doi.org/10.1088/1367-2630/16/8/085011	journal	August 2014
Quantum computers Amiri, P. K. IEEE Potentials, Vol. 21, Issue 5 https://doi.org/10.1109/mp.2002.1166617	journal	December 2002
A One-Way Quantum Computer Briegel, Hans J.; Raussendorf, Robert The American Physical Society https://doi.org/10.17877/de290r-1703	text	January 2001
Deep Learning Ganatra, Sanket Zenodo https://doi.org/10.5281/zenodo.1189359	text	January 2018
Quantum random access memory Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo arXiv https://doi.org/10.48550/arxiv.0708.1879	text	January 2007
Holographic quantum computing Tordrup, Karl; Negretti, Antonio; Molmer, Klaus arXiv https://doi.org/10.48550/arxiv.0802.4406	text	January 2008
Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble Kubo, Y.; Grezes, C.; Dewes, A. arXiv https://doi.org/10.48550/arxiv.1110.2978	text	January 2011
Generation and Eight-port Homodyne Characterization of Time-bin Qubits for Continuous-variable Quantum Information Processing Takeda, Shuntaro; Mizuta, Takahiro; Fuwa, Maria arXiv https://doi.org/10.48550/arxiv.1205.4862	text	January 2012
Experimental Quantum Computing to Solve Systems of Linear Equations Cai, X. -D.; Weedbrook, Christian; Su, Z. -E. arXiv https://doi.org/10.48550/arxiv.1302.4310	text	January 2013
Quantum principal component analysis Lloyd, Seth; Mohseni, Masoud; Rebentrost, Patrick arXiv https://doi.org/10.48550/arxiv.1307.0401	text	January 2013
Quantum support vector machine for big data classification Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth arXiv https://doi.org/10.48550/arxiv.1307.0471	text	January 2013
Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states Wang, Pei; Chen, Moran; Menicucci, Nicolas C. arXiv https://doi.org/10.48550/arxiv.1309.4105	text	January 2013
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States Menicucci, Nicolas C. arXiv https://doi.org/10.48550/arxiv.1310.7596	text	January 2013
Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb Chen, Moran; Menicucci, Nicolas C.; Pfister, Olivier arXiv https://doi.org/10.48550/arxiv.1311.2957	text	January 2013
Noise analysis of single-qumode Gaussian operations using continuous-variable cluster states Alexander, Rafael N.; Armstrong, Seiji C.; Ukai, Ryuji arXiv https://doi.org/10.48550/arxiv.1311.3538	text	January 2013
Experimental realization of a dynamic squeezing gate Miyata, Kazunori; Ogawa, Hisashi; Marek, Petr arXiv https://doi.org/10.48550/arxiv.1409.3754	text	January 2014
Demonstration of a fully tuneable entangling gate for continuous-variable one-way quantum computation Yokoyama, Shota; Ukai, Ryuji; Armstrong, Seiji C. arXiv https://doi.org/10.48550/arxiv.1410.0472	text	January 2014
Quantum simulation of quantum field theory using continuous variables Marshall, Kevin; Pooser, Raphael; Siopsis, George arXiv https://doi.org/10.48550/arxiv.1503.08121	text	January 2015
The power of one qumode for quantum computation Liu, Nana; Thompson, Jayne; Weedbrook, Christian arXiv https://doi.org/10.48550/arxiv.1510.04758	text	January 2015
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding Lau, Hoi-Kwan; Plenio, Martin B. arXiv https://doi.org/10.48550/arxiv.1605.09278	text	January 2016
Quantum information with continuous variables Braunstein, Samuel L.; van Loock, Peter arXiv https://doi.org/10.48550/arxiv.quant-ph/0410100	text	January 2004
Universal Quantum Computation with Continuous-Variable Cluster States Menicucci, Nicolas C.; van Loock, Peter; Gu, Mile arXiv https://doi.org/10.48550/arxiv.quant-ph/0605198	text	January 2006
Building Gaussian Cluster States by Linear Optics van Loock, Peter; Weedbrook, Christian; Gu, Mile arXiv https://doi.org/10.48550/arxiv.quant-ph/0610119	text	January 2006
Quantum computation over continuous variables Lloyd, Seth; Braunstein, Samuel L. arXiv https://doi.org/10.48550/arxiv.quant-ph/9810082	text	January 1998

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