Subsystem spacetime circuit code[1,2] 

Description

Subsystem stabilizer code obtained from a spacetime circuit code by gauging logical operators that correspond to circuit faults with trivial effect [3; Sec. 5.4].

An \([[n,k,d]]\) stabilizer code can be mapped into a sparse subsystem code with the same \(k\) and \(d\) as follows. One can take the fault-tolerant syndrome extraction circuit associated with the stabilizer code, construct its spacetime circuit code, and then gauge qubits corresponding to trivial faults. The subsystem code can be made geometrically local at the cost of more ancilla qubits [1].

Rate

The spacetime circuit code construction is used to show the existance of spatially local subsystem codes that nearly saturate the subsystem BT bound [1].

Fault Tolerance

Fault-tolerant measurement gadget that is a modification based on the DiVincenzo-Shor cat-state method [4,5].

Parents

Cousin

  • Spacetime circuit code — Spacetime circuit codes can yield subsystem spacetime circuit codes by gauging a subgroup of the logical Pauli group which causes trivial faults in the corresponding Clifford circuit. This construction is used to show the existance of geometrically local subsystem codes that nearly saturate the subsystem BT bound [1].

References

[1]
D. Bacon et al., “Sparse Quantum Codes From Quantum Circuits”, IEEE Transactions on Information Theory 63, 2464 (2017) arXiv:1411.3334 DOI
[2]
D. Gottesman, “Opportunities and Challenges in Fault-Tolerant Quantum Computation”, (2022) arXiv:2210.15844
[3]
N. Delfosse and A. Paetznick, “Spacetime codes of Clifford circuits”, (2023) arXiv:2304.05943
[4]
P. W. Shor, “Fault-tolerant quantum computation”, (1997) arXiv:quant-ph/9605011
[5]
D. P. DiVincenzo and P. W. Shor, “Fault-Tolerant Error Correction with Efficient Quantum Codes”, Physical Review Letters 77, 3260 (1996) arXiv:quant-ph/9605031 DOI
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Zoo Code ID: subsystem_spacetime_circuit

Cite as:
“Subsystem spacetime circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/subsystem_spacetime_circuit
BibTeX:
@incollection{eczoo_subsystem_spacetime_circuit, title={Subsystem spacetime circuit code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/subsystem_spacetime_circuit} }
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Cite as:

“Subsystem spacetime circuit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/subsystem_spacetime_circuit

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/subsystem_spacetime_circuit.yml.