Built on

S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph]
1998
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
D. Poulin, Stabilizer formalism for operator quantum error correction, Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
A. Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321
2006
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Physical review letters 97
2006
Earlier work this paper cites.
D. Bacon, Operator quantum error-correcting subsystems for self-correcting quantum memories, Phys. Rev. A 73
2006
Earlier work this paper cites.
N. P. Breuckmann, Quantum subsystem codes: Their theory and use (bachelor thesis) (2010)
2010
Earlier work this paper cites.
S. Bravyi, Subsystem codes with spatially local generators, Phys. Rev. A 83
2011
Earlier work this paper cites.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86
2012
Earlier work this paper cites.
M. Li, D. Miller, M. Newman, Y. Wu, and K. R. Brown, 2d compass codes, Phys. Rev. X 9
2019
Earlier work this paper cites.
M. B. Hastings and J. Haah, Dynamically Generated Logical Qubits, Quantum 5
2021
Earlier work this paper cites.
C. Vuillot, Planar floquet codes (2021), arXiv:2110.05348 [quant-ph]
Original
2021
Earlier work this paper cites.
C. Gidney, M. Newman, A. Fowler, and M. Broughton, A Fault-Tolerant Honeycomb Memory, Quantum 5
2021
Earlier work this paper cites.

Similar

C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5
2021
Cited alongside, same era.
O. Higgott and N. P. Breuckmann, Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead, Physical Review X 11
2021
Cited alongside, same era.
J. Haah and M. B. Hastings, Boundaries for the Honeycomb Code, Quantum 6
2022
Cited alongside, same era.
C. Gidney, M. Newman, and M. McEwen, Benchmarking the Planar Honeycomb Code, Quantum 6
2022
Cited alongside, same era.
J. R. Wootton, Measurements of floquet code plaquette stabilizers (2022), arXiv:2210.13154 [quant-ph]
Original
2022
Cited alongside, same era.
M. S. Kesselring, J. C. M. de la Fuente, F. Thomsen, J. Eisert, S. D. Bartlett, and B. J. Brown, Anyon condensation and the color code (2022), arXiv:2212.00042 [quant-ph]

Then

T. D. Ellison, J. Sullivan, and A. Dua, Floquet codes with a twist (2023), arXiv:2306.08027 [quant-ph]
Original
2023
Later among the works it cites.
H. Bombin, D. Litinski, N. Nickerson, F. Pastawski, and S. Roberts, Unifying flavors of fault tolerance with the zx calculus (2023), arXiv:2303.08829 [quant-ph]
Original
2023
Later among the works it cites.
M. Davydova, Logical operations in floquet codes (talk at simons institute, berkeley) (2023)
2023
Later among the works it cites.
C. Gidney and D. Bacon, Less bacon more threshold (2023), arXiv:2305.12046 [quant-ph]
Original
2023
Later among the works it cites.
P. Hilaire, T. Dessertaine, B. Bourdoncle, A. Denys, G. de Gliniasty, G. Valentí-Rojas, and S. Mansfield, Enhanced fault-tolerance in photonic quantum computing: Floquet code outperforms surface code in tailored architecture (2024), arXiv:2410.07065 [quant-ph]

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2024

Dynamical Logical Qubits in the Bacon-Shor Code

Alam, M. Sohaib, Rieffel, Eleanor

Understand

The Bacon-Shor code is a quantum error correcting subsystem code composed of weight 2 check operators that admits a single logical qubit, and has distance $d$ on a $d \times d$ square lattice.

We show that when viewed as a Floquet code, by choosing an appropriate measurement schedule of the check operators, it can additionally host several dynamical logical qubits.
Specifically, we identify a period 4 measurement schedule of the check operators that preserves logical information between the instantaneous stabilizer groups.
Such a schedule measures not only the usual stabilizers of the Bacon-Shor code, but also additional stabilizers that protect the dynamical logical qubits against errors.

Built on

S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary (1998), arXiv:quant-ph/9811052 [quant-ph]
1998
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.
D. Poulin, Stabilizer formalism for operator quantum error correction, Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
A. Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321
2006
Earlier work this paper cites.
H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Physical review letters 97
2006
Earlier work this paper cites.
D. Bacon, Operator quantum error-correcting subsystems for self-correcting quantum memories, Phys. Rev. A 73
2006
Earlier work this paper cites.
N. P. Breuckmann, Quantum subsystem codes: Their theory and use (bachelor thesis) (2010)
2010
Earlier work this paper cites.
S. Bravyi, Subsystem codes with spatially local generators, Phys. Rev. A 83
2011
Earlier work this paper cites.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86
2012
Earlier work this paper cites.
M. Li, D. Miller, M. Newman, Y. Wu, and K. R. Brown, 2d compass codes, Phys. Rev. X 9
2019
Earlier work this paper cites.
M. B. Hastings and J. Haah, Dynamically Generated Logical Qubits, Quantum 5
2021
Earlier work this paper cites.
C. Vuillot, Planar floquet codes (2021), arXiv:2110.05348 [quant-ph]
Original
2021
Earlier work this paper cites.
C. Gidney, M. Newman, A. Fowler, and M. Broughton, A Fault-Tolerant Honeycomb Memory, Quantum 5
2021
Earlier work this paper cites.

Similar

C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5
2021
Cited alongside, same era.
O. Higgott and N. P. Breuckmann, Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead, Physical Review X 11
2021
Cited alongside, same era.
J. Haah and M. B. Hastings, Boundaries for the Honeycomb Code, Quantum 6
2022
Cited alongside, same era.
C. Gidney, M. Newman, and M. McEwen, Benchmarking the Planar Honeycomb Code, Quantum 6
2022
Cited alongside, same era.
J. R. Wootton, Measurements of floquet code plaquette stabilizers (2022), arXiv:2210.13154 [quant-ph]
Original
2022
Cited alongside, same era.
M. S. Kesselring, J. C. M. de la Fuente, F. Thomsen, J. Eisert, S. D. Bartlett, and B. J. Brown, Anyon condensation and the color code (2022), arXiv:2212.00042 [quant-ph]

Then

T. D. Ellison, J. Sullivan, and A. Dua, Floquet codes with a twist (2023), arXiv:2306.08027 [quant-ph]
Original
2023
Later among the works it cites.
H. Bombin, D. Litinski, N. Nickerson, F. Pastawski, and S. Roberts, Unifying flavors of fault tolerance with the zx calculus (2023), arXiv:2303.08829 [quant-ph]
Original
2023
Later among the works it cites.
M. Davydova, Logical operations in floquet codes (talk at simons institute, berkeley) (2023)
2023
Later among the works it cites.
C. Gidney and D. Bacon, Less bacon more threshold (2023), arXiv:2305.12046 [quant-ph]
Original
2023
Later among the works it cites.
P. Hilaire, T. Dessertaine, B. Bourdoncle, A. Denys, G. de Gliniasty, G. Valentí-Rojas, and S. Mansfield, Enhanced fault-tolerance in photonic quantum computing: Floquet code outperforms surface code in tailored architecture (2024), arXiv:2410.07065 [quant-ph]

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2022

Cited alongside, same era.

D. Aasen, Z. Wang, and M. B. Hastings, Adiabatic paths of hamiltonians, symmetries of topological order, and automorphism codes, Phys. Rev. B 106

2022

Cited alongside, same era.

A. Paetznick, C. Knapp, N. Delfosse, B. Bauer, J. Haah, M. B. Hastings, and M. P. da Silva, Performance of planar floquet codes with majorana-based qubits, PRX Quantum 4

2023

Cited alongside, same era.

A. Townsend-Teague, J. Magdalena de la Fuente, and M. Kesselring, Floquetifying the colour code, Electronic Proceedings in Theoretical Computer Science 384

2023

Cited alongside, same era.

O. Higgott and N. P. Breuckmann, Constructions and performance of hyperbolic and semi-hyperbolic floquet codes (2023), arXiv:2308.03750 [quant-ph]

Original

2023

Cited alongside, same era.

A. Fahimniya, H. Dehghani, K. Bharti, S. Mathew, A. J. Kollár, A. V. Gorshkov, and M. J. Gullans, Fault-tolerant hyperbolic floquet quantum error correcting codes (2023), arXiv:2309.10033 [quant-ph]

Original

2023

Cited alongside, same era.

Z. Zhang, D. Aasen, and S. Vijay, x x -cube floquet code: A dynamical quantum error correcting code with a subextensive number of logical qubits, Phys. Rev. B 108

2023

Cited alongside, same era.

Original

2024

Closest in time.

A. Tanggara, M. Gu, and K. Bharti, Simple construction of qudit floquet codes on a family of lattices (2024), arXiv:2410.02022 [quant-ph]

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2024

Closest in time.

F. Setiawan and C. McLauchlan, Tailoring dynamical codes for biased noise: The x 3 z 3 floquet code (2024), arXiv:2411.04974 [quant-ph]

Original

2024