Quantum Machine Learning over Infinite Dimensions
Abstract
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.
- Authors:
-
- 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)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1435294
- Alternate Identifier(s):
- OSTI ID: 1344616
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 118; Journal Issue: 8; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Lau, Hoi-Kwan, Pooser, Raphael, Siopsis, George, and Weedbrook, Christian. Quantum Machine Learning over Infinite Dimensions. United States: N. p., 2017.
Web. doi:10.1103/PhysRevLett.118.080501.
Lau, Hoi-Kwan, Pooser, Raphael, Siopsis, George, & Weedbrook, Christian. Quantum Machine Learning over Infinite Dimensions. United States. https://doi.org/10.1103/PhysRevLett.118.080501
Lau, Hoi-Kwan, Pooser, Raphael, Siopsis, George, and Weedbrook, Christian. Tue .
"Quantum Machine Learning over Infinite Dimensions". United States. https://doi.org/10.1103/PhysRevLett.118.080501. https://www.osti.gov/servlets/purl/1435294.
@article{osti_1435294,
title = {Quantum Machine Learning over Infinite Dimensions},
author = {Lau, Hoi-Kwan and Pooser, Raphael and Siopsis, George and Weedbrook, Christian},
abstractNote = {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.},
doi = {10.1103/PhysRevLett.118.080501},
journal = {Physical Review Letters},
number = 8,
volume = 118,
place = {United States},
year = {Tue Feb 21 00:00:00 EST 2017},
month = {Tue Feb 21 00:00:00 EST 2017}
}
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Works referenced in this record:
Quantum computers
journal, March 2010
- Ladd, T. D.; Jelezko, F.; Laflamme, R.
- Nature, Vol. 464, Issue 7285
Gaussian quantum information
journal, May 2012
- Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl
- Reviews of Modern Physics, Vol. 84, Issue 2
Deep learning
journal, May 2015
- LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey
- Nature, Vol. 521, Issue 7553
Quantum Computation over Continuous Variables
journal, February 1999
- Lloyd, Seth; Braunstein, Samuel L.
- Physical Review Letters, Vol. 82, Issue 8
Temporal-mode continuous-variable cluster states using linear optics
journal, June 2011
- Menicucci, Nicolas C.
- Physical Review A, Vol. 83, Issue 6
Experimental Realization of a Quantum Support Vector Machine
journal, April 2015
- Li, Zhaokai; Liu, Xiaomei; Xu, Nanyang
- Physical Review Letters, Vol. 114, Issue 14
Quantum simulation of quantum field theory using continuous variables
journal, December 2015
- Marshall, Kevin; Pooser, Raphael; Siopsis, George
- Physical Review A, Vol. 92, Issue 6
Experimental Quantum Computing to Solve Systems of Linear Equations
journal, June 2013
- Cai, X. -D.; Weedbrook, C.; Su, Z. -E.
- Physical Review Letters, Vol. 110, Issue 23
Quantum information with continuous variables
journal, June 2005
- Braunstein, Samuel L.; van Loock, Peter
- Reviews of Modern Physics, Vol. 77, Issue 2
Efficient state preparation for a register of quantum bits
journal, January 2006
- Soklakov, Andrei N.; Schack, Rüdiger
- Physical Review A, Vol. 73, Issue 1
Continuous-variable Gaussian analog of cluster states
journal, March 2006
- Zhang, Jing; Braunstein, Samuel L.
- Physical Review A, Vol. 73, Issue 3
Invited Article: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing
journal, September 2016
- Yoshikawa, Jun-ichi; Yokoyama, Shota; Kaji, Toshiyuki
- APL Photonics, Vol. 1, Issue 6
Universal Quantum Computation with Continuous-Variable Cluster States
journal, September 2006
- Menicucci, Nicolas C.; van Loock, Peter; Gu, Mile
- Physical Review Letters, Vol. 97, Issue 11
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
journal, October 1997
- Shor, Peter W.
- SIAM Journal on Computing, Vol. 26, Issue 5
Quantum secret sharing with continuous-variable cluster states
journal, October 2013
- Lau, Hoi-Kwan; Weedbrook, Christian
- Physical Review A, Vol. 88, Issue 4
Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
journal, September 2016
- Vahlbruch, Henning; Mehmet, Moritz; Danzmann, Karsten
- Physical Review Letters, Vol. 117, Issue 11
Repeat-until-success cubic phase gate for universal continuous-variable quantum computation
journal, March 2015
- Marshall, Kevin; Pooser, Raphael; Siopsis, George
- Physical Review A, Vol. 91, Issue 3
Noise analysis of single-mode Gaussian operations using continuous-variable cluster states
journal, December 2014
- Alexander, Rafael N.; Armstrong, Seiji C.; Ukai, Ryuji
- Physical Review A, Vol. 90, Issue 6
Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state
journal, March 2010
- Gao, Wei-Bo; Lu, Chao-Yang; Yao, Xing-Can
- Nature Physics, Vol. 6, Issue 5
Experimental realization of a dynamic squeezing gate
journal, December 2014
- Miyata, Kazunori; Ogawa, Hisashi; Marek, Petr
- Physical Review A, Vol. 90, Issue 6
Quantum principal component analysis
journal, July 2014
- Lloyd, Seth; Mohseni, Masoud; Rebentrost, Patrick
- Nature Physics, Vol. 10, Issue 9
Demonstration of a fully tunable entangling gate for continuous-variable one-way quantum computation
journal, September 2015
- Yokoyama, Shota; Ukai, Ryuji; Armstrong, Seiji C.
- Physical Review A, Vol. 92, Issue 3
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
journal, March 2014
- Menicucci, Nicolas C.
- Physical Review Letters, Vol. 112, Issue 12
Entanglement-Based Machine Learning on a Quantum Computer
journal, March 2015
- Cai, X. -D.; Wu, D.; Su, Z. -E.
- Physical Review Letters, Vol. 114, Issue 11
Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb
journal, March 2014
- Chen, Moran; Menicucci, Nicolas C.; Pfister, Olivier
- Physical Review Letters, Vol. 112, Issue 12
Ultra-large-scale continuous-variable cluster states multiplexed in the time domain
journal, November 2013
- Yokoyama, Shota; Ukai, Ryuji; Armstrong, Seiji C.
- Nature Photonics, Vol. 7, Issue 12
Quantum Random Access Memory
journal, April 2008
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- Physical Review Letters, Vol. 100, Issue 16
Detecting the degree of macroscopic quantumness using an overlap measurement
journal, January 2014
- Jeong, Hyunseok; Noh, Changsuk; Bae, Seunglee
- Journal of the Optical Society of America B, Vol. 31, Issue 12
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
journal, August 2016
- Lau, Hoi-Kwan; Plenio, Martin B.
- Physical Review Letters, Vol. 117, Issue 10
Power of one qumode for quantum computation
journal, May 2016
- Liu, Nana; Thompson, Jayne; Weedbrook, Christian
- Physical Review A, Vol. 93, Issue 5
Quantum Algorithm for Linear Systems of Equations
journal, October 2009
- Harrow, Aram W.; Hassidim, Avinatan; Lloyd, Seth
- Physical Review Letters, Vol. 103, Issue 15
Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms
journal, May 1994
- Dowling, Jonathan P.; Agarwal, G. S.; Schleich, Wolfgang P.
- Physical Review A, Vol. 49, Issue 5
Quantum computing with continuous-variable clusters
journal, June 2009
- Gu, Mile; Weedbrook, Christian; Menicucci, Nicolas C.
- Physical Review A, Vol. 79, Issue 6
Quantum adiabatic machine learning
journal, November 2012
- Pudenz, Kristen L.; Lidar, Daniel A.
- Quantum Information Processing, Vol. 12, Issue 5
Hybrid Quantum Circuit with a Superconducting Qubit Coupled to a Spin Ensemble
journal, November 2011
- Kubo, Y.; Grezes, C.; Dewes, A.
- Physical Review Letters, Vol. 107, Issue 22
Hybrid discrete- and continuous-variable quantum information
journal, September 2015
- Andersen, Ulrik L.; Neergaard-Nielsen, Jonas S.; van Loock, Peter
- Nature Physics, Vol. 11, Issue 9
Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing
book, January 2011
- Furusawa, Akira; van Loock, Peter
Overlap and entanglement-witness measurements
journal, June 2002
- Filip, Radim
- Physical Review A, Vol. 65, Issue 6
Quantum Support Vector Machine for Big Data Classification
journal, September 2014
- Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth
- Physical Review Letters, Vol. 113, Issue 13
Generation and eight-port homodyne characterization of time-bin qubits for continuous-variable quantum information processing
journal, April 2013
- Takeda, Shuntaro; Mizuta, Takahiro; Fuwa, Maria
- Physical Review A, Vol. 87, Issue 4
Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states
journal, September 2014
- Wang, Pei; Chen, Moran; Menicucci, Nicolas C.
- Physical Review A, Vol. 90, Issue 3
A One-Way Quantum Computer
journal, May 2001
- Raussendorf, Robert; Briegel, Hans J.
- Physical Review Letters, Vol. 86, Issue 22
Parallel Generation of Quadripartite Cluster Entanglement in the Optical Frequency Comb
journal, July 2011
- Pysher, Matthew; Miwa, Yoshichika; Shahrokhshahi, Reihaneh
- Physical Review Letters, Vol. 107, Issue 3
Building Gaussian cluster states by linear optics
journal, September 2007
- van Loock, Peter; Weedbrook, Christian; Gu, Mile
- Physical Review A, Vol. 76, Issue 3
Holographic Quantum Computing
journal, July 2008
- Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus
- Physical Review Letters, Vol. 101, Issue 4
A two-qubit photonic quantum processor and its application to solving systems of linear equations
journal, August 2014
- Barz, Stefanie; Kassal, Ivan; Ringbauer, Martin
- Scientific Reports, Vol. 4, Issue 1
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
journal, August 2014
- Demarie, Tommaso F.; Linjordet, Trond; Menicucci, Nicolas C.
- New Journal of Physics, Vol. 16, Issue 8
A One-Way Quantum Computer
text, January 2001
- Briegel, Hans J.; Raussendorf, Robert
- The American Physical Society
Quantum random access memory
text, January 2007
- Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo
- arXiv
Holographic quantum computing
text, January 2008
- Tordrup, Karl; Negretti, Antonio; Molmer, Klaus
- arXiv
Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble
text, January 2011
- Kubo, Y.; Grezes, C.; Dewes, A.
- arXiv
Generation and Eight-port Homodyne Characterization of Time-bin Qubits for Continuous-variable Quantum Information Processing
text, January 2012
- Takeda, Shuntaro; Mizuta, Takahiro; Fuwa, Maria
- arXiv
Experimental Quantum Computing to Solve Systems of Linear Equations
text, January 2013
- Cai, X. -D.; Weedbrook, Christian; Su, Z. -E.
- arXiv
Quantum principal component analysis
text, January 2013
- Lloyd, Seth; Mohseni, Masoud; Rebentrost, Patrick
- arXiv
Quantum support vector machine for big data classification
text, January 2013
- Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth
- arXiv
Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states
text, January 2013
- Wang, Pei; Chen, Moran; Menicucci, Nicolas C.
- arXiv
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
text, January 2013
- Menicucci, Nicolas C.
- arXiv
Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb
text, January 2013
- Chen, Moran; Menicucci, Nicolas C.; Pfister, Olivier
- arXiv
Noise analysis of single-qumode Gaussian operations using continuous-variable cluster states
text, January 2013
- Alexander, Rafael N.; Armstrong, Seiji C.; Ukai, Ryuji
- arXiv
Experimental realization of a dynamic squeezing gate
text, January 2014
- Miyata, Kazunori; Ogawa, Hisashi; Marek, Petr
- arXiv
Demonstration of a fully tuneable entangling gate for continuous-variable one-way quantum computation
text, January 2014
- Yokoyama, Shota; Ukai, Ryuji; Armstrong, Seiji C.
- arXiv
Quantum simulation of quantum field theory using continuous variables
text, January 2015
- Marshall, Kevin; Pooser, Raphael; Siopsis, George
- arXiv
The power of one qumode for quantum computation
text, January 2015
- Liu, Nana; Thompson, Jayne; Weedbrook, Christian
- arXiv
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
text, January 2016
- Lau, Hoi-Kwan; Plenio, Martin B.
- arXiv
Quantum information with continuous variables
text, January 2004
- Braunstein, Samuel L.; van Loock, Peter
- arXiv
Universal Quantum Computation with Continuous-Variable Cluster States
text, January 2006
- Menicucci, Nicolas C.; van Loock, Peter; Gu, Mile
- arXiv
Building Gaussian Cluster States by Linear Optics
text, January 2006
- van Loock, Peter; Weedbrook, Christian; Gu, Mile
- arXiv
Quantum computation over continuous variables
text, January 1998
- Lloyd, Seth; Braunstein, Samuel L.
- arXiv
Works referencing / citing this record:
A quantum walk-assisted approximate algorithm for bounded NP optimisation problems
journal, January 2019
- Marsh, S.; Wang, J. B.
- Quantum Information Processing, Vol. 18, Issue 3
Quantum machine learning
journal, September 2017
- Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola
- Nature, Vol. 549, Issue 7671
Entanglement of bosonic modes through an engineered exchange interaction
journal, February 2019
- Gao, Yvonne Y.; Lester, Brian J.; Chou, Kevin S.
- Nature, Vol. 566, Issue 7745
Implementation of SWAP test for two unknown states in photons via cross-Kerr nonlinearities under decoherence effect
journal, April 2019
- Kang, Min-Sung; Heo, Jino; Choi, Seong-Gon
- Scientific Reports, Vol. 9, Issue 1
Pedagogical introduction to the entropy of entanglement for Gaussian states
journal, March 2018
- Demarie, Tommaso F.
- European Journal of Physics, Vol. 39, Issue 3
Machine learning & artificial intelligence in the quantum domain: a review of recent progress
journal, June 2018
- Dunjko, Vedran; Briegel, Hans J.
- Reports on Progress in Physics, Vol. 81, Issue 7
Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
journal, August 2017
- Sobrino-Coll, N.; Puertas-Centeno, D.; Toranzo, I. V.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 8
Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
journal, June 2018
- Perdomo-Ortiz, Alejandro; Benedetti, Marcello; Realpe-Gómez, John
- Quantum Science and Technology, Vol. 3, Issue 3
Quantum-assisted Helmholtz machines: A quantum–classical deep learning framework for industrial datasets in near-term devices
journal, May 2018
- Benedetti, Marcello; Realpe-Gómez, John; Perdomo-Ortiz, Alejandro
- Quantum Science and Technology, Vol. 3, Issue 3
Machine learning method for state preparation and gate synthesis on photonic quantum computers
journal, January 2019
- Arrazola, Juan Miguel; Bromley, Thomas R.; Izaac, Josh
- Quantum Science and Technology, Vol. 4, Issue 2
Production of photonic universal quantum gates enhanced by machine learning
journal, July 2019
- Sabapathy, Krishna Kumar; Qi, Haoyu; Izaac, Josh
- Physical Review A, Vol. 100, Issue 1
Client-friendly continuous-variable blind and verifiable quantum computing
journal, December 2019
- Liu, Nana; Demarie, Tommaso F.; Tan, Si-Hui
- Physical Review A, Vol. 100, Issue 6
Analytic continuation via domain knowledge free machine learning
journal, December 2018
- Yoon, Hongkee; Sim, Jae-Hoon; Han, Myung Joon
- Physical Review B, Vol. 98, Issue 24
Machine Learning Based Localization and Classification with Atomic Magnetometers
journal, January 2018
- Deans, Cameron; Griffin, Lewis D.; Marmugi, Luca
- Physical Review Letters, Vol. 120, Issue 3
Characterizing the performance of continuous-variable Gaussian quantum gates
journal, February 2020
- Sharma, Kunal; Wilde, Mark M.
- Physical Review Research, Vol. 2, Issue 1
Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
text, January 2017
- Perdomo-Ortiz, Alejandro; Benedetti, Marcello; Realpe-Gómez, John
- arXiv
Quantum-assisted Helmholtz machines: A quantum-classical deep learning framework for industrial datasets in near-term devices
text, January 2017
- Benedetti, Marcello; Realpe-Gómez, John; Perdomo-Ortiz, Alejandro
- arXiv
Machine learning based localization and classification with atomic magnetometers
text, January 2017
- Deans, Cameron; Griffin, Lewis D.; Marmugi, Luca
- arXiv
Machine learning method for state preparation and gate synthesis on photonic quantum computers
text, January 2018
- Arrazola, Juan Miguel; Bromley, Thomas R.; Izaac, Josh
- arXiv
Characterizing the performance of continuous-variable Gaussian quantum gates
text, January 2018
- Sharma, Kunal; Wilde, Mark M.
- arXiv