# 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:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). 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.
```

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

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

```
@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 = {2019},

month = {5}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

Works referenced in this record:

##
Compiling quantum circuits to realistic hardware architectures using temporal planners

journal, February 2018

- Venturelli, Davide; Do, Minh; Rieffel, Eleanor
- Quantum Science and Technology, Vol. 3, Issue 2

##
Max 2-SAT with up to 108 qubits

journal, April 2014

- Santra, Siddhartha; Quiroz, Gregory; Ver Steeg, Greg
- New Journal of Physics, Vol. 16, Issue 4

##
Characterizing quantum supremacy in near-term devices

journal, April 2018

- Boixo, Sergio; Isakov, Sergei V.; Smelyanskiy, Vadim N.
- Nature Physics, Vol. 14, Issue 6

##
Restless Tuneup of High-Fidelity Qubit Gates

journal, April 2017

- Rol, M. A.; Bultink, C. C.; O’Brien, T. E.
- Physical Review Applied, Vol. 7, Issue 4

##
0-1 Quadratic programming approach for optimum solutions of two scheduling problems

journal, February 1994

- Alidaee, Bahram; Kochenberger, Gary A.; Ahmadian, Ahmad
- International Journal of Systems Science, Vol. 25, Issue 2

##
Evidence for quantum annealing with more than one hundred qubits

journal, February 2014

- Boixo, Sergio; Rønnow, Troels F.; Isakov, Sergei V.
- Nature Physics, Vol. 10, Issue 3

##
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

journal, February 2019

- Hadfield, Stuart; Wang, Zhihui; O'Gorman, Bryan
- Algorithms, Vol. 12, Issue 2

##
Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation

journal, June 2016

- Sawaya, Nicolas P. D.; Smelyanskiy, Mikhail; McClean, Jarrod R.
- Journal of Chemical Theory and Computation, Vol. 12, Issue 7

##
Superconducting quantum circuits at the surface code threshold for fault tolerance

journal, April 2014

- Barends, R.; Kelly, J.; Megrant, A.
- Nature, Vol. 508, Issue 7497

##
Two-step approach to scheduling quantum circuits

journal, July 2018

- Guerreschi, Gian Giacomo; Park, Jongsoo
- Quantum Science and Technology, Vol. 3, Issue 4

##
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

journal, November 1995

- Goemans, Michel X.; Williamson, David P.
- Journal of the ACM, Vol. 42, Issue 6

##
Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3

journal, September 2008

- Bazgan, Cristina; Tuza, Zsolt
- Journal of Discrete Algorithms, Vol. 6, Issue 3

##
MAX CUT in cubic graphs

journal, November 2004

- Halperin, Eran; Livnat, Dror; Zwick, Uri
- Journal of Algorithms, Vol. 53, Issue 2

##
Applications of cut polyhedra — I

journal, November 1994

- Deza, Michel; Laurent, Monique
- Journal of Computational and Applied Mathematics, Vol. 55, Issue 2

##
Quantum Mechanics Helps in Searching for a Needle in a Haystack

journal, July 1997

- Grover, Lov K.
- Physical Review Letters, Vol. 79, Issue 2

##
Noise gates for decoherent quantum circuits

journal, March 2008

- Bassi, Angelo; Deckert, Dirk-André
- Physical Review A, Vol. 77, Issue 3

##
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

journal, October 2018

- Romero, Jonathan; Babbush, Ryan; McClean, Jarrod R.
- Quantum Science and Technology, Vol. 4, Issue 1

##
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

journal, September 2017

- Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan
- Nature, Vol. 549, Issue 7671

##
Superconducting Circuits for Quantum Information: An Outlook

journal, March 2013

- Devoret, M. H.; Schoelkopf, R. J.
- Science, Vol. 339, Issue 6124

##
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

journal, January 1999

- Shor, Peter W.
- SIAM Review, Vol. 41, Issue 2

##
Quantum approximate optimization algorithm for MaxCut: A fermionic view

journal, February 2018

- Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang
- Physical Review A, Vol. 97, Issue 2

##
A blueprint for demonstrating quantum supremacy with superconducting qubits

journal, April 2018

- Neill, C.; Roushan, P.; Kechedzhi, K.
- Science, Vol. 360, Issue 6385

##
Scalable Quantum Simulation of Molecular Energies

journal, July 2016

- O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.
- Physical Review X, Vol. 6, Issue 3

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*