QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

Guerreschi, Gian Giacomo; Matsuura, A. Y.

doi:10.1038/s41598-019-43176-9

Title: QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

Abstract

Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to facilitate solutions to practical problems. In contrast, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.

Authors:

^[1]; Matsuura, A. Y. ^[1]

Intel Corp., Santa Clara, CA (United States)

Publication Date:: Mon May 06 00:00:00 EDT 2019

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division

OSTI Identifier:: 1527339

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Scientific Reports

Additional Journal Information:: Journal Volume: 9; Journal Issue: 1; Journal ID: ISSN 2045-2322

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Guerreschi, Gian Giacomo, and Matsuura, A. Y. QAOA for Max-Cut requires hundreds of qubits for quantum speed-up.  United States: N. p., 2019. 
Web.  doi:10.1038/s41598-019-43176-9.

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                    Guerreschi, Gian Giacomo, & Matsuura, A. Y. QAOA for Max-Cut requires hundreds of qubits for quantum speed-up.  United States.  https://doi.org/10.1038/s41598-019-43176-9

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                    Guerreschi, Gian Giacomo, and Matsuura, A. Y. Mon .  
"QAOA for Max-Cut requires hundreds of qubits for quantum speed-up".  United States.  https://doi.org/10.1038/s41598-019-43176-9.  https://www.osti.gov/servlets/purl/1527339.

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@article{osti_1527339,

  title        = {QAOA for Max-Cut requires hundreds of qubits for quantum speed-up},

  author       = {Guerreschi, Gian Giacomo and Matsuura, A. Y.},

  abstractNote = {Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to facilitate solutions to practical problems. In contrast, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.},

  doi          = {10.1038/s41598-019-43176-9},

  journal      = {Scientific Reports},

  number       = 1,

  volume       = 9,

  place        = {United States},

  year         = {Mon May 06 00:00:00 EDT 2019},

  month        = {Mon May 06 00:00:00 EDT 2019}

}

Copy to clipboard

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https://doi.org/10.1038/s41598-019-43176-9

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Cited by: 104 works

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Figure 1: Schematic diagram of the QAOA algorithm and auxiliary tasks to solve a single Max-Cut instance. The two branches, labelled “simulation” and “experiment” respectively, distinguish between the operations to simulate the variational algorithm with classical computers and those to perform it experimentally with quantum devices. In our study, 10000more »

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Works referenced in this record:

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Figure 2 (p. 4)

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Title: QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

Abstract

Citation Formats

Figures / Tables:

Compiling quantum circuits to realistic hardware architectures using temporal planners journal, February 2018

Max 2-SAT with up to 108 qubits journal, April 2014

Characterizing quantum supremacy in near-term devices journal, April 2018

Numerical Optimization book, January 1999

Restless Tuneup of High-Fidelity Qubit Gates journal, April 2017

0-1 Quadratic programming approach for optimum solutions of two scheduling problems journal, February 1994

Evidence for quantum annealing with more than one hundred qubits journal, February 2014

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz journal, February 2019

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation journal, June 2016

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Two-step approach to scheduling quantum circuits journal, July 2018

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming journal, November 1995

Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3 journal, September 2008

MAX CUT in cubic graphs journal, November 2004

Applications of cut polyhedra — I journal, November 1994

Quantum Computing in the NISQ era and beyond journal, August 2018

Quantum Mechanics Helps in Searching for a Needle in a Haystack journal, July 1997

Noise gates for decoherent quantum circuits journal, March 2008

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz journal, October 2018

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets journal, September 2017

Superconducting Circuits for Quantum Information: An Outlook journal, March 2013

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer journal, January 1999

Quantum approximate optimization algorithm for MaxCut: A fermionic view journal, February 2018

A blueprint for demonstrating quantum supremacy with superconducting qubits journal, April 2018

Scalable Quantum Simulation of Molecular Energies journal, July 2016

Numerical Optimization book, January 2006

Scalable Quantum Simulation of Molecular Energies text, January 2015

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation preprint, January 2016

Characterizing Quantum Supremacy in Near-Term Devices text, January 2016

Restless Tuneup of High-Fidelity Qubit Gates text, January 2016

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz preprint, January 2017

Compiling quantum circuits to realistic hardware architectures using temporal planners text, January 2017

Two-step approach to scheduling quantum circuits text, January 2017

A blueprint for demonstrating quantum supremacy with superconducting qubits text, January 2017

Quantum Computing in the NISQ era and beyond text, January 2018

MAX CUT in cubic graphs journal, November 2004

Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3 journal, September 2008

Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT journal, August 2003

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation journal, June 2016

Superconducting quantum circuits at the surface code threshold for fault tolerance journal, April 2014

Evidence for quantum annealing with more than one hundred qubits journal, February 2014

0-1 Quadratic programming approach for optimum solutions of two scheduling problems journal, February 1994

Superconducting Circuits for Quantum Information: An Outlook journal, March 2013

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming journal, November 1995

VQE method: a short survey and recent developments journal, January 2022

Quantum computing and the entanglement frontier preprint, January 2012

Characterizing Quantum Supremacy in Near-Term Devices text, January 2016

Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets text, January 2017

Compiling quantum circuits to realistic hardware architectures using temporal planners text, January 2017

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz text, January 2017

A blueprint for demonstrating quantum supremacy with superconducting qubits text, January 2017

Quantum Computing in the NISQ era and beyond text, January 2018

Parameterized quantum circuits as machine learning models journal, October 2019

Methods for classically simulating noisy networked quantum architectures journal, November 2019

Benchmarking the quantum approximate optimization algorithm text, January 2020

Benchmarking the quantum approximate optimization algorithm journal, June 2020

Methods for Classically Simulating Noisy Networked Quantum Architectures text, January 2018

Parameterized quantum circuits as machine learning models text, January 2019

Classical symmetries and the Quantum Approximate Optimization Algorithm journal, October 2021

Compiling quantum circuits to realistic hardware architectures using temporal planners
journal, February 2018

Max 2-SAT with up to 108 qubits
journal, April 2014

Characterizing quantum supremacy in near-term devices
journal, April 2018

Numerical Optimization
book, January 1999

Restless Tuneup of High-Fidelity Qubit Gates
journal, April 2017

0-1 Quadratic programming approach for optimum solutions of two scheduling problems
journal, February 1994

Evidence for quantum annealing with more than one hundred qubits
journal, February 2014

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
journal, February 2019

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation
journal, June 2016

Superconducting quantum circuits at the surface code threshold for fault tolerance
journal, April 2014

Two-step approach to scheduling quantum circuits
journal, July 2018

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
journal, November 1995

Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3
journal, September 2008

MAX CUT in cubic graphs
journal, November 2004

Applications of cut polyhedra — I
journal, November 1994

Quantum Computing in the NISQ era and beyond
journal, August 2018

Quantum Mechanics Helps in Searching for a Needle in a Haystack
journal, July 1997

Noise gates for decoherent quantum circuits
journal, March 2008

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
journal, October 2018

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017

Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
journal, January 1999

Quantum approximate optimization algorithm for MaxCut: A fermionic view
journal, February 2018

A blueprint for demonstrating quantum supremacy with superconducting qubits
journal, April 2018

Scalable Quantum Simulation of Molecular Energies
journal, July 2016

Numerical Optimization
book, January 2006

Scalable Quantum Simulation of Molecular Energies
text, January 2015

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation
preprint, January 2016

Characterizing Quantum Supremacy in Near-Term Devices
text, January 2016

Restless Tuneup of High-Fidelity Qubit Gates
text, January 2016

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
preprint, January 2017

Compiling quantum circuits to realistic hardware architectures using temporal planners
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Two-step approach to scheduling quantum circuits
text, January 2017

A blueprint for demonstrating quantum supremacy with superconducting qubits
text, January 2017

Quantum Computing in the NISQ era and beyond
text, January 2018

MAX CUT in cubic graphs
journal, November 2004

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journal, September 2008

Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
journal, August 2003

Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation
journal, June 2016

Superconducting quantum circuits at the surface code threshold for fault tolerance
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journal, February 2014

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journal, February 1994

Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013

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journal, November 1995

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journal, January 2022

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preprint, January 2012

Characterizing Quantum Supremacy in Near-Term Devices
text, January 2016

Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
text, January 2017

Compiling quantum circuits to realistic hardware architectures using temporal planners
text, January 2017

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
text, January 2017

A blueprint for demonstrating quantum supremacy with superconducting qubits
text, January 2017

Quantum Computing in the NISQ era and beyond
text, January 2018

Parameterized quantum circuits as machine learning models
journal, October 2019

Methods for classically simulating noisy networked quantum architectures
journal, November 2019

Benchmarking the quantum approximate optimization algorithm
text, January 2020

Benchmarking the quantum approximate optimization algorithm
journal, June 2020

Methods for Classically Simulating Noisy Networked Quantum Architectures
text, January 2018

Parameterized quantum circuits as machine learning models
text, January 2019

Classical symmetries and the Quantum Approximate Optimization Algorithm
journal, October 2021