Low-weight high-distance error-correcting fermionic encodings - INSPIRE

DataBETA

Low-weight high-distance error-correcting fermionic encodings

Fedor Šimkovic IV
(
- Unlisted, DE
)
,
Martin Leib
(
- Unlisted, DE
)
,
Francisco Revson F. Pereira
(
- Unlisted, DE
)

Feb 23, 2024

18 pages

Published in:

Phys.Rev.Res. 6 (2024) 4, 043123

Published: Nov 12, 2024

e-Print:

2402.15386 [quant-ph]

DOI:

10.1103/PhysRevResearch.6.043123 (publication)

View in:

ADS Abstract Service

reference search1 citation

Citations per year

Abstract: (APS)

We perform an extended numerical search for practical fermion-to-qubit encodings with error-correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: First generate encodings with code distances up to

d \leq 4

by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with

d \leq 7

; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.

qubit
stability
connectivity
hardware
deformation
Clifford

References(39)

Figures(8)

[1]

Quantum algorithms: A survey of applications and end-to-end complexities

Alexander M. Dalzell
(
- Unlisted, US, CA
)
,
Sam McArdle
(
- Unlisted, US, CA
)
,
Mario Berta
(
- Unlisted, US, CA and
- RWTH Aachen U. and
- Imperial Coll., London
)
,
Przemyslaw Bienias
(
- Unlisted, US, CA
)
,
Chi-Fang Chen
(
- Unlisted, US, CA and
- Caltech, IQI
)

et al.

e-Print:
- 2310.03011

[2]

Quantum error mitigation

Zhenyu Cai
(
- U. Oxford (main) and
- Unlisted, UK
)
,
Ryan Babbush
(
- Unlisted, US, CA
)
,
Simon C. Benjamin
(
- U. Oxford (main) and
- Unlisted, UK
)
,
Suguru Endo
(
- NTT, Musashino
)
,
William J. Huggins
(
- Unlisted, US, CA
)

et al.

- Rev.Mod.Phys. 95 (2023) 4, 045005
•
e-Print:
- 2210.00921
•
DOI:
- 10.1103/RevModPhys.95.045005

[3]

Algebraic methods for quantum codes on lattices

Jeongwan Haah
(
- Unlisted
)

- Rev.Col.Mat. 50 (2016) 2, 299-349
•
DOI:
- 10.15446/recolma.v50n2.62214

[4]

Superfast encodings for fermionic quantum simulation

Kanav Setia
(
- Dartmouth Coll. and
- IBM Watson Res. Ctr.
)
,
Sergey Bravyi
(
- IBM Watson Res. Ctr.
)
,
Antonio Mezzacapo
(
- IBM Watson Res. Ctr.
)
,
James D. Whitfield
(
- Dartmouth Coll.
)

- Phys.Rev.Res. 1 (2019) 3, 033033
•
DOI:
- 10.1103/PhysRevResearch.1.033033

[5]

Mitigating errors in localfermionic encodings

J. Bausch
,
T. Cubitt
,
C. Derby
,
J. Klassen

•
e-Print:
- 2003.07125

[6]

Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order

Nathanan Tantivasadakarn
(
- Harvard U.
)

- Phys.Rev.Res. 2 (2020) 2, 023353
•
e-Print:
- 2002.11345
•
DOI:
- 10.1103/PhysRevResearch.2.023353

[7]

Error-correcting codes for fermionic quantum simulation

Yu-An Chen
(
- Joint Quantum Inst., College Park and
- Maryland U.
)
,
Alexey V. Gorshkov
(
- Joint Quantum Inst., College Park
)
,
Yijia Xu
(
- Joint Quantum Inst., College Park and
- Maryland U.
)

- SciPost Phys. 16 (2024) 1, 033,
- SciPost Phys. 16 (2024) 033
•
e-Print:
- 2210.08411
•
DOI:
- 10.21468/SciPostPhys.16.1.033

[8]

The hubbard model

D.P. Arovas
,
E. Berg
,
S.A. Kivelson
,
S. Raghu

- Ann.Rev.Condensed Matter Phys. 13 (2022) 239
•
DOI:
- 10.1146/annurev-conmatphys-031620-102024

[9]

The Hubbard model: A computational perspective

Mingpu Qin
(
- Shanghai SSRF and
- Shanghai Jiaotong U.
)
,
Thomas Schäfer
(
- Stuttgart, MPI Solid State Res.
)
,
Sabine Andergassen
(
- Tubingen U.
)
,
Philippe Corboz
(
- Amsterdam U. and
- Hamburg U., Inst. Theor. Phys. II
)
,
Emanuel Gull
(
- Michigan U.
)

- Ann.Rev.Condensed Matter Phys. 13 (2022) 275-302
•
e-Print:
- 2104.00064
•
DOI:
- 10.1146/annurev-conmatphys-090921-033948

[10]

About the Pauli exclusion principle

Pascual Jordan
(
- Gottingen U.
)
,
Eugene P. Wigner
(
- Gottingen U.
)

- Z.Phys. 47 (1928) 631-651
•
DOI:
- 10.1007/BF01331938

[11]

Tapering off qubits to simulate fermionic Hamiltonians

Sergey Bravyi
(
- IBM Watson Res. Ctr.
)
,
Jay M. Gambetta
(
- IBM Watson Res. Ctr.
)
,
Antonio Mezzacapo
(
- IBM Watson Res. Ctr.
)
,
Kristan Temme
(
- IBM Watson Res. Ctr.
)

e-Print:
- 1701.08213

[12]

Operator locality in the quantum simulation of fermionic models

Vojtěch Havlíček
(
- Oxford U. and
- Zurich, ETH
)
,
Matthias Troyer
(
- Microsoft, Redmond
)
,
James D. Whitfield
(
- Dartmouth Coll.
)

- Phys.Rev.A 95 (2017) 3, 032332
•
DOI:
- 10.1103/PhysRevA.95.032332

[13]

Fermion-to-qubit mappings with varying resource requirements for quantum simulation

Mark Steudtner
(
- Leiden U. and
- KIN, Delft
)
,
Stephanie Wehner
(
- KIN, Delft
)

- New J.Phys. 20 (2018) 6, 063010
•
DOI:
- 10.1088/1367-2630/aac54f

[14]

Majorana Loop Stabilizer Codes for Error Mitigation in Fermionic Quantum Simulations

- Phys.Rev.Applied 12 (2019) 6, 064041,
- Phys.Rev.Applied. 12 (2019) 064041
•
e-Print:
- 1812.08190
•
DOI:
- 10.1103/PhysRevApplied.12.064041

[15]

Reducing the qubit requirement of Jordan-Wigner encodings of $N$ -mode, $K$ -fermion systems from $N$ to $\lceil \log_2 {N \choose K} \rceil$

Brent Harrison
(
- Dartmouth Coll. (main)
)
,
Dylan Nelson
,
Daniel Adamiak
(
- Ohio State U.
)
,
James Whitfield
(
- Dartmouth Coll. (main) and
- Unlisted, UK
)

e-Print:
- 2211.04501

[16]

Second-Quantized Fermionic Operators with Polylogarithmic Qubit and Gate Complexity

William Kirby
(
- Tufts U. and
- IBM Watson Res. Ctr.
)
,
Bryce Fuller
(
- IBM Watson Res. Ctr.
)
,
Charles Hadfield
(
- IBM Watson Res. Ctr.
)
,
Antonio Mezzacapo
(
- IBM Watson Res. Ctr.
)

- PRX Quantum 3 (2022) 2, 020351
•
e-Print:
- 2109.14465
•
DOI:
- 10.1103/PRXQuantum.3.020351

[17]

Optimizing fermionic encodings for both Hamiltonian and hardware

Riley W. Chien
(
- Unlisted and
- Dartmouth Coll.
)
,
Joel Klassen
(
- Unlisted
)

e-Print:
- 2210.05652

[18]

Discovering optimal fermion-qubit mappings through algorithmic enumeration

- Quantum 7 (2023) 1145,
- Quantum 7 (2023) 1145
•
e-Print:
- 2110.12792
•
DOI:
- 10.22331/q-2023-10-18-1145

[19]

Low-depth simulations of fermionic systems on square-grid quantum hardware

- Quantum 8 (2024) 1327,
- Quantum 8 (2024) 1327
•
e-Print:
- 2302.01862
•
DOI:
- 10.22331/q-2024-04-30-1327

[20]

Bonsai Algorithm: Grow Your Own Fermion-to-Qubit Mappings

Aaron Miller
(
- Unlisted, FI
)
,
Zoltán Zimborás
(
- Unlisted, FI
)
,
Stefan Knecht
(
- Unlisted, FI
)
,
Sabrina Maniscalco
(
- Unlisted, FI
)
,
Guillermo García-Pérez
(
- Unlisted, FI
)

- PRX Quantum 4 (2023) 3, 030314
•
e-Print:
- 2212.09731
•
DOI:
- 10.1103/PRXQuantum.4.030314

[21]

Treespilation: Architecture- and State-Optimised Fermion-to-Qubit Mappings

Aaron Miller
(
- Unlisted, FI and
- Hamilton Math. Inst., Dublin
)
,
Adam Glos
(
- Unlisted, FI
)
,
Zoltán Zimborás
(
- Unlisted, FI and
- Wigner RCP, Budapest
)

e-Print:
- 2403.03992

[22]

Mapping local Hamiltonians of fermions to local Hamiltonians of spins

- J.Stat.Mech. 0509 (2005) P09012
•
e-Print:
- cond-mat/0508353
•
DOI:
- 10.1088/1742-5468/2005/09/P09012

[23]

Compact fermion to qubit mappings

Charles Derby
(
- Unlisted, UK and
- University Coll. London
)
,
Joel Klassen
(
- Unlisted, UK
)
,
Johannes Bausch
(
- Unlisted, UK and
- Cambridge U., DAMTP
)
,
Toby Cubitt
(
- Unlisted, UK
)

- Phys.Rev.B 104 (2021) 3, 035118
•
DOI:
- 10.1103/PhysRevB.104.035118

[24]

Fermions without Fermi fields

R.C. Ball
(
- Warwick U.
)

- Phys.Rev.Lett. 95 (2005) 176407
•
e-Print:
- cond-mat/0409485
•
DOI:
- 10.1103/PhysRevLett.95.176407

[25]

Lowering qubit requirements for quantum simulations of fermionic systems

M. Steudtner
,
S. Wehner

e-Print:
- 1712.07067

1-25 of 39
1
2
25 / page