The complexity of NISQ - INSPIRE

DataBETA

The complexity of NISQ

Sitan Chen
(
- UC, Berkeley (main)
)
,
Jordan Cotler
(
- Harvard U. (main)
)
,
Hsin-Yuan Huang
(
- Caltech, Pasadena (main)
)
,
Jerry Li
(
- Microsoft, Redmond
)

Oct 13, 2022

52 pages

Published in:

Nature Commun. 14 (2023) 1, 6001,
Nature Commun. 15 (2024) 1, 1308 (erratum)

Published: Sep 26, 2023
and
Published: Feb 12, 2024

e-Print:

2210.07234 [quant-ph]

DOI:

10.1038/s41467-023-41217-6,
10.1038/s41467-024-45799-7 (erratum)

View in:

ADS Abstract Service

reference search77 citations

Citations per year

Abstract: (Springer)

The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class NISQ, which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, NISQ, and fault-tolerant quantum computation to solve some problems based on modifications of Simon’s problems. We then consider the power of NISQ for three well-studied problems. For unstructured search, we prove that NISQ cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that NISQ only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that NISQ is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.

Note:

52 pages, 3 figures

References(80)

Figures(3)

[1]

Universal Quantum Simulators

Seth Lloyd
(
- MIT
)

- Science 273 (1996) 5278, 1073
•
DOI:
- 10.1126/science.273.5278.1073

[2]

Quantum Simulation

I.M. Georgescu
(
- Wako, RIKEN
)
,
S. Ashhab
(
- Wako, RIKEN
)
,
Franco Nori
(
- Wako, RIKEN and
- Michigan U. and
- Korea U.
)

- Rev.Mod.Phys. 86 (2014) 153
•
e-Print:
- 1308.6253
•
DOI:
- 10.1103/RevModPhys.86.153

[3]

Scalable Quantum Simulation of Molecular Energies

P.J.J. O'Malley
(
- UC, Santa Barbara
)
,
R. Babbush
(
- Google Inc.
)
,
I.D. Kivlichan
(
- Harvard U., Phys. Dept.
)
,
J. Romero
(
- Harvard U., Phys. Dept.
)
,
J.R. McClean
(
- LBNL, Berkeley
)

et al.

- Phys.Rev.X 6 (2016) 3, 031007
•
DOI:
- 10.1103/PhysRevX.6.031007

[4]

Low-Depth Quantum Simulation of Materials

et al.

- Phys.Rev.X 8 (2018) 1, 011044
•
DOI:
- 10.1103/PhysRevX.8.011044

[5]

Hamiltonian Simulation by Qubitization

Guang Hao Low
(
- MIT, LNS
)
,
Isaac L. Chuang
(
- MIT
)

- Quantum 3 (2019) 163
•
e-Print:
- 1610.06546
•
DOI:
- 10.22331/q-2019-07-12-163

[6]

Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th Annual Symposium on Foundations of

P.W. Shor

- Comput.Sci. 124 (1994) 134

[7]

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

Peter W. Shor
(
- Unlisted
)

- SIAM Rev. 41 (2006) 2, 303-332
•
DOI:
- 10.1137/s0036144598347011

[8]

Simulated quantum annealing can be exponentially faster than classical simulated annealing. In

E. Crosson
,
A.W. Harrow

[8]

57th Annual Symposium on Foundations of Computer Science (FOCS), 714-723

E. Crosson
,
A.W. Harrow

[9]

Quantum Supremacy through the Quantum Approximate Optimization Algorithm

Edward Farhi
(
- Unlisted and
- MIT, Cambridge, CTP
)
,
Aram W. Harrow
(
- MIT, Cambridge, CTP
)

e-Print:
- 1602.07674

[10]

Quantum speed-ups for solving semidefinite programs. In

F.G. Brandao
,
K.M. Svore

[10]

58th Annual Symposium on Foundations of Computer Science (FOCS), 415-426

F.G. Brandao
,
K.M. Svore

[11]

Quantum SDP Solvers: Large Speed-ups, Optimality, and Applications to Quantum Learning

et al.

e-Print:
- 1710.02581

[12]

Quantum Algorithm for Linear Systems of Equations

Aram W. Harrow
(
- U. Bristol (main)
)
,
Avinatan Hassidim
(
- MIT
)
,
Seth Lloyd
(
- MIT
)

- Phys.Rev.Lett. 103 (2009) 15, 150502
•
e-Print:
- 0811.3171
•
DOI:
- 10.1103/physrevlett.103.150502

[13]

Quantum supremacy using a programmable superconducting processor

Frank Arute
(
- Google Inc.
)
,
Kunal Arya
(
- Google Inc.
)
,
Ryan Babbush
(
- Google Inc.
)
,
Dave Bacon
(
- Google Inc.
)
,
Joseph C. Bardin
(
- Google Inc. and
- Massachusetts U., Amherst
)

et al.

- Nature 574 (2019) 7779, 505-510
•
e-Print:
- 1910.11333
•
DOI:
- 10.1038/s41586-019-1666-5

[14]

Quantum Computing in the NISQ era and beyond

John Preskill
(
- Caltech, IQI
)

- Quantum 2 (2018) 79
•
e-Print:
- 1801.00862
•
DOI:
- 10.22331/q-2018-08-06-79

[15]

Superconducting quantum bits

John Clarke
(
- UC, Berkeley, Astron. Dept. and
- LBNL, Berkeley
)
,
Frank K. Wilhelm
(
- Waterloo U.
)

- Nature 453 (2008) 1031-1042
•
DOI:
- 10.1038/nature07128

[16]

Demonstration of universal parametric entangling gates on a multi-qubit lattice

Matthew Reagor
(
- Rigetti Computing
)
,
Christopher B. Osborn
(
- Rigetti Computing
)
,
Nikolas Tezak
(
- Rigetti Computing
)
,
Alexa Staley
(
- Rigetti Computing
)
,
Guenevere Prawiroatmodjo
(
- Rigetti Computing
)

et al.

- Sci.Adv. 4 (2018) 2, aao3603
•
DOI:
- 10.1126/sciadv.aao3603

[17]

Supervised learning with quantum-enhanced feature spaces

Vojtech Havlicek
(
- IBM Watson Res. Ctr. and
- Oxford U.
)
,
Antonio D. Córcoles
(
- IBM Watson Res. Ctr.
)
,
Kristan Temme
(
- IBM Watson Res. Ctr.
)
,
Aram W. Harrow
(
- MIT, Cambridge, CTP
)
,
Abhinav Kandala
(
- IBM Watson Res. Ctr.
)

et al.

- Nature 567 (2019) 209-212,
- Nature 567 (2019) 209-212
•
e-Print:
- 1804.11326
•
DOI:
- 10.1038/s41586-019-0980-2

[18]

Demonstration of a small programmable quantum computer with atomic qubits

et al.

- Nature 536 (2016) 63-66
•
DOI:
- 10.1038/nature18648

[19]

Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator

et al.

- Nature 551 (2017) 601-604
•
e-Print:
- 1708.01044
•
DOI:
- 10.1038/nature24654

[20]

Observation of Entangled States of a Fully Controlled 20-Qubit System

Nicolai Friis
(
- IQOQI, Vienna
)
,
Oliver Marty
(
- Ulm U.
)
,
Christine Maier
(
- Innsbruck U., Quant. Opt. and Info. and
- Innsbruck U.
)
,
Cornelius Hempel
(
- Innsbruck U., Quant. Opt. and Info. and
- Innsbruck U.
)
,
Milan Holzäpfel
(
- Ulm U.
)

et al.

- Phys.Rev.X 8 (2018) 2, 021012
•
DOI:
- 10.1103/PhysRevX.8.021012

[21]

Benchmarking an 11-qubit quantum computer

et al.

- Nature Commun. 10 (2019) 5464
•
DOI:
- 10.1038/s41467-019-13534-2

[22]

Fast universal quantum gate above the fault-tolerance threshold in silicon

et al.

- Nature 601 (2022) 7893, 338-342,
- Nature 601 (2022) 338-342
•
e-Print:
- 2108.02626
•
DOI:
- 10.1038/s41586-021-04182-y

[23]

Computing with spin qubits at the surface code error threshold

Xiao Xue
(
- Delft Tech. U.
)
,
Maximilian Russ
(
- Delft Tech. U.
)
,
Nodar Samkharadze
(
- Delft Tech. U.
)
,
Brennan Undseth
(
- Delft Tech. U.
)
,
Amir Sammak
(
- Delft Tech. U.
)

et al.

- Nature 601 (2022) 343-347
•
e-Print:
- 2107.00628
•
DOI:
- 10.1038/s41586-021-04273-w

1-25 of 80
1
2
3
4
25 / page