Code switching revisited: low-overhead magic state preparation using color codes - INSPIRE

DataBETA

Code switching revisited: low-overhead magic state preparation using color codes

Lucas Daguerre
(
- UC, Davis
)
,
Isaac H. Kim
(
- UC, Davis
)

Oct 9, 2024

11 pages

e-Print:

2410.07327 [quant-ph]

View in:

ADS Abstract Service

reference search2 citations

Citations per year

Abstract: (arXiv)

We propose a protocol to prepare a high-fidelity magic state on a 2D color code using a 3D color code. Our method modifies the known code switching protocol with (i) a transversal gate between the 2D and the 3D code and (ii) a judicious use of flag-based post-selection. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state. For instance, subjected to a uniform circuit-level noise of

10^{-3}

, our code switching protocol yields a magic state encoded in the distance-

3

2D color code with a logical infidelity of

4.6\times 10^{-5}\pm 1.6 \times 10^{-5}

(quantified by an error-corrected logical state tomography) with a

84\%

of acceptance rate. Used in conjunction with a more recently proposed post-selection approach, extrapolation from a polynomial fit suggests a fidelity improvement to

5.1 \times 10^{-7}

for the same code. Finally, we also present a novel simulation technique akin to an extended stabilizer simulator which effectively incorporates the non-Clifford

T

-gate.

Note:

11 pages, 9 figures. v2: minor changes

References(57)

Figures(4)

[1]

Scheme for reducing decoherence in quantum computer memory

Peter W. Shor
(
- Bell Labs
)

- Phys.Rev.A 52 (1995) 4, R2493-R2496
•
DOI:
- 10.1103/physreva.52.r2493

[2]

Fault-tolerant quantum computation with constant error, in Proceedings of the twenty-ninth annual ACM symposium on Theory of computing pp. 176-188

D. Aharonov
,
M. Ben-Or

[3]

Fault-Tolerant Quantum Computation with Constant Overhead

Daniel Gottesman
(
- Perimeter Inst. Theor. Phys. and
- Canadian Inst. Advanced Res.
)

e-Print:
- 1310.2984

[4]

Universal quantum computation with ideal clifford gates and noisy ancillas, Physical Review A--Atomic

S. Bravyi
,
A. Kitaev

- Physics 71 (2005) 022316

[5]

Magic-state distillation with the four-qubit code, arXiv preprint

A.M. Meier
,
B. Eastin
,
E. Knill

•
e-Print:
- 1204.4221

[6]

Magic-state distillation with low overhead, Physical Review A--Atomic

S. Bravyi
,
J. Haah

- Physics 86 (2012) 052329

[7]

Low-overhead constructions for the fault-tolerant Toffoli gate

Cody Jones
(
- Stanford U., Ginzton Lab.
)

- Phys.Rev.A 87 (2013) 2, 022328
•
DOI:
- 10.1103/PhysRevA.87.022328

[8]

Surface code implementation of block code state distillation

A.G. Fowler
,
S.J. Devitt
,
C. Jones

- Sci.Rep. 3 (2013) 1939

[9]

Multilevel distillation of magic states for quantum computing, Physical Review A--Atomic

C. Jones

- Physics 87 (2013) 042305

[10]

Distillation of nonstabilizer states for universal quantum computation, Physical Review A--Atomic

G. Duclos-Cianci
,
K.M. Svore

- Physics 88 (2013) 042325

[11]

Reducing the quantum-computing overhead with complex gate distillation

G. Duclos-Cianci
,
D. Poulin

- Phys.Rev.A 91 (2015) 042315

[12]

A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost

Earl T. Campbell
(
- Sheffield U.
)
,
Mark Howard
(
- Sheffield U.
)

- Phys.Rev.A 95 (2017) 022316
•
e-Print:
- 1606.01904
•
DOI:
- 10.1103/PhysRevA.95.022316

[13]

Quantum computation with realistic magic-state factories

Joe O'Gorman
(
- U. Oxford (main)
)
,
Earl T. Campbell
(
- Sheffield U.
)

- Phys.Rev.A 95 (2017) 3, 032338
•
DOI:
- 10.1103/PhysRevA.95.032338

[14]

Codes and protocols for distilling t, controlled-s, and toffoli gates

J. Haah
,
M.B. Hastings

- Quantum 2 (2018) 71

[15]

Efficient magic state factories with a catalyzed |CCZ⟩ to 2|T⟩ transformation

C. Gidney
,
A.G. Fowler

- Quantum 3 (2019) 135

[16]

A bridge to lower overhead quantum computation

Austin G. Fowler
(
- Melbourne U.
)
,
Simon J. Devitt
(
- NII, Tokyo
)

e-Print:
- 1209.0510

[17]

Magic State Distillation: Not as Costly as You Think

D. Litinski

- Quantum 3 (2019) 205

[18]

A magic state’s fidelity can be superior to the operations that created it

Ying Li
(
- U. Oxford (main)
)

- New J.Phys. 17 (2015) 2, 023037
•
DOI:
- 10.1088/1367-2630/17/2/023037

[19]

The surface code with a twist

T.J. Yoder
,
I.H. Kim

- Quantum 1 (2017) 2

[20]

Quantum Error Correction with Only Two Extra Qubits

- Phys.Rev.Lett. 121 (2018) 5, 050502
•
DOI:
- 10.1103/PhysRevLett.121.050502

[21]

Fault-tolerant quantum computation with few qubits

- npj Quantum Inf. 4 (2018) 42
•
DOI:
- 10.1038/s41534-018-0085-z

[22]

Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits

Christopher Chamberland
(
- Unlisted, US, CA and
- Caltech, IQI
)
,
Kyungjoo Noh
(
- Unlisted, US, CA
)

- npj Quantum Inf. 6 (2020) 91
•
DOI:
- 10.1038/s41534-020-00319-5

[23]

Fault-Tolerant Code-Switching Protocols for Near-Term Quantum Processors

Friederike Butt
(
- Aachen, Tech. Hochsch. and
- Julich, NIC
)
,
Sascha Heußen
(
- Aachen, Tech. Hochsch. and
- Julich, NIC
)
,
Manuel Rispler
(
- Aachen, Tech. Hochsch. and
- Julich, NIC
)
,
Markus Müller
(
- Aachen, Tech. Hochsch. and
- Julich, NIC
)

- PRX Quantum 5 (2024) 2, 020345
•
e-Print:
- 2306.17686
•
DOI:
- 10.1103/PRXQuantum.5.020345

[24]

Even more efficient magic state distillation by zero-level distillation

e-Print:
- 2403.03991

[25]

Magic state cultivation: growing T states as cheap as CNOT gates

e-Print:
- 2409.17595

1-25 of 57
1
2
3
25 / page