Improving application performance with biased distributions of quantum states

Lohani, Sanjaya; Lukens, Joseph M.; Jones, Daniel E.; Searles, Thomas A.; Glasser, Ryan T.; Kirby, Brian T.

doi:10.1103/PhysRevResearch.3.043145

Title: Improving application performance with biased distributions of quantum states

Abstract

We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert–Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert–Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert–Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert–Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert–Schmidt distributed states for various experimental conditions.

Authors:

;

; Glasser, Ryan T.; Kirby, Brian T.

Publication Date:: Mon Nov 29 00:00:00 EST 2021

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

Sponsoring Org.:: USDOE; US Army Research Office (ARO)

OSTI Identifier:: 1832932

Alternate Identifier(s):: OSTI ID: 1833950

Grant/Contract Number:: AC05-00OR22725; W911NF-19-2-0087; W911NF-20-2-0168

Resource Type:: Published Article

Journal Name:: Physical Review Research

Additional Journal Information:: Journal Name: Physical Review Research Journal Volume: 3 Journal Issue: 4; Journal ID: ISSN 2643-1564

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum computation; quantum information processing

Citation Formats


                    Lohani, Sanjaya, Lukens, Joseph M., Jones, Daniel E., Searles, Thomas A., Glasser, Ryan T., and Kirby, Brian T. Improving application performance with biased distributions of quantum states.  United States: N. p., 2021. 
Web.  doi:10.1103/PhysRevResearch.3.043145.

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                    Lohani, Sanjaya, Lukens, Joseph M., Jones, Daniel E., Searles, Thomas A., Glasser, Ryan T., & Kirby, Brian T. Improving application performance with biased distributions of quantum states.  United States.  https://doi.org/10.1103/PhysRevResearch.3.043145

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                    Lohani, Sanjaya, Lukens, Joseph M., Jones, Daniel E., Searles, Thomas A., Glasser, Ryan T., and Kirby, Brian T. Mon .  
"Improving application performance with biased distributions of quantum states".  United States.  https://doi.org/10.1103/PhysRevResearch.3.043145.

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@article{osti_1832932,

  title        = {Improving application performance with biased distributions of quantum states},

  author       = {Lohani, Sanjaya and Lukens, Joseph M. and Jones, Daniel E. and Searles, Thomas A. and Glasser, Ryan T. and Kirby, Brian T.},

  abstractNote = {We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert–Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert–Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert–Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert–Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert–Schmidt distributed states for various experimental conditions.},

  doi          = {10.1103/PhysRevResearch.3.043145},

  journal      = {Physical Review Research},

  number       = 4,

  volume       = 3,

  place        = {United States},

  year         = {Mon Nov 29 00:00:00 EST 2021},

  month        = {Mon Nov 29 00:00:00 EST 2021}

}

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Title: Improving application performance with biased distributions of quantum states

Abstract

Citation Formats

Classification and reconstruction of optical quantum states with deep neural networks journal, September 2021

Volume of the set of separable states. II journal, November 1999

Quantum discord for general two-qubit states: Analytical progress journal, May 2011

Separability-entanglement classifier via machine learning journal, July 2018

Monte Carlo sampling from the quantum state space. II journal, April 2015

Induced measures in the space of mixed quantum states journal, August 2001

Average fidelity between random quantum states journal, March 2005

Practical Bayesian tomography journal, March 2016

Recovering full coherence in a qubit by measuring half of its environment journal, December 2015

Machine learning meets quantum foundations: A brief survey journal, October 2020

Entanglement swapping of two arbitrarily degraded entangled states journal, July 2016

A Better Bound on the Variance journal, April 2000

Photonic State Tomography book, May 2005

Reconfigurable Quantum Local Area Network Over Deployed Fiber journal, October 2021

Optimal, reliable estimation of quantum states journal, April 2010

A practical and efficient approach for Bayesian quantum state estimation journal, June 2020

A Bayesian analysis of classical shadows journal, July 2021

Optimal measurements to access classical correlations of two-qubit states journal, January 2011

Cryptographic distinguishability measures for quantum-mechanical states journal, May 1999

Entanglement classification via neural network quantum states journal, April 2020

Random quantum states journal, November 1990

On the Experimental Feasibility of Quantum State Reconstruction via Machine Learning journal, January 2021

Adaptive bandwidth management for entanglement distribution in quantum networks journal, January 2021

MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster journal, August 2013

Predicting many properties of a quantum system from very few measurements journal, June 2020

Statistical Ensembles of Complex, Quaternion, and Real Matrices journal, March 1965

Quantum state estimation when qubits are lost: a no-data-left-behind approach journal, April 2017

Active learning machine learns to create new quantum experiments journal, January 2018

Fully Arbitrary Control of Frequency-Bin Qubits journal, September 2020

Quantum Entanglement in Random Physical States journal, July 2012

Statistical properties of random density matrices journal, August 2004

Pseudo-Bayesian quantum tomography with rank-adaptation journal, May 2017

Direct Estimations of Linear and Nonlinear Functionals of a Quantum State journal, May 2002

Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal journal, January 2009

1-Bit matrix completion: PAC-Bayesian analysis of a variational approximation journal, September 2017

All-fiber photon-pair source for quantum communications journal, July 2002

Machine learning assisted quantum state estimation journal, July 2020

Random Bures mixed states and the distribution of their purity journal, January 2010

A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution journal, January 2015

Thermalization of strongly interacting bosons after spontaneous emissions in optical lattices journal, January 2015

Bures volume of the set of mixed quantum states journal, September 2003

Bipartite entanglement of quantum states in a pair basis journal, December 2014

On the Distinguishability of Random Quantum States journal, March 2007

Efficient Method for Computing the Maximum-Likelihood Quantum State from Measurements with Additive Gaussian Noise journal, February 2012

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence journal, August 2012

Machine learning pipeline for quantum state estimation with incomplete measurements journal, May 2021

Classification and reconstruction of optical quantum states with deep neural networks
journal, September 2021

Volume of the set of separable states. II
journal, November 1999

Quantum discord for general two-qubit states: Analytical progress
journal, May 2011

Separability-entanglement classifier via machine learning
journal, July 2018

Monte Carlo sampling from the quantum state space. II
journal, April 2015

Induced measures in the space of mixed quantum states
journal, August 2001

Average fidelity between random quantum states
journal, March 2005

Practical Bayesian tomography
journal, March 2016

Recovering full coherence in a qubit by measuring half of its environment
journal, December 2015

Machine learning meets quantum foundations: A brief survey
journal, October 2020

Entanglement swapping of two arbitrarily degraded entangled states
journal, July 2016

A Better Bound on the Variance
journal, April 2000

Photonic State Tomography
book, May 2005

Reconfigurable Quantum Local Area Network Over Deployed Fiber
journal, October 2021

Optimal, reliable estimation of quantum states
journal, April 2010

A practical and efficient approach for Bayesian quantum state estimation
journal, June 2020

A Bayesian analysis of classical shadows
journal, July 2021

Optimal measurements to access classical correlations of two-qubit states
journal, January 2011

Cryptographic distinguishability measures for quantum-mechanical states
journal, May 1999

Entanglement classification via neural network quantum states
journal, April 2020

Random quantum states
journal, November 1990

On the Experimental Feasibility of Quantum State Reconstruction via Machine Learning
journal, January 2021

Adaptive bandwidth management for entanglement distribution in quantum networks
journal, January 2021

MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster
journal, August 2013

Predicting many properties of a quantum system from very few measurements
journal, June 2020

Statistical Ensembles of Complex, Quaternion, and Real Matrices
journal, March 1965

Quantum state estimation when qubits are lost: a no-data-left-behind approach
journal, April 2017

Active learning machine learns to create new quantum experiments
journal, January 2018

Fully Arbitrary Control of Frequency-Bin Qubits
journal, September 2020

Quantum Entanglement in Random Physical States
journal, July 2012

Statistical properties of random density matrices
journal, August 2004

Pseudo-Bayesian quantum tomography with rank-adaptation
journal, May 2017

Direct Estimations of Linear and Nonlinear Functionals of a Quantum State
journal, May 2002

Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal
journal, January 2009

1-Bit matrix completion: PAC-Bayesian analysis of a variational approximation
journal, September 2017

All-fiber photon-pair source for quantum communications
journal, July 2002

Machine learning assisted quantum state estimation
journal, July 2020

Random Bures mixed states and the distribution of their purity
journal, January 2010

A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution
journal, January 2015

Thermalization of strongly interacting bosons after spontaneous emissions in optical lattices
journal, January 2015

Bures volume of the set of mixed quantum states
journal, September 2003

Bipartite entanglement of quantum states in a pair basis
journal, December 2014

On the Distinguishability of Random Quantum States
journal, March 2007

Efficient Method for Computing the Maximum-Likelihood Quantum State from Measurements with Additive Gaussian Noise
journal, February 2012

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence
journal, August 2012

Machine learning pipeline for quantum state estimation with incomplete measurements
journal, May 2021