Dynamical Logical Qubits in the Bacon-Shor Code
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915433607593984 |
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| author | Alam, M. Sohaib Rieffel, Eleanor |
| author_facet | Alam, M. Sohaib Rieffel, Eleanor |
| contents | 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. We show that the code distance of these Floquet-Bacon-Shor codes scales as $Θ(d/\sqrt{k})$ on an $n = d \times d$ lattice with $k$ dynamical logical qubits, along with the logical qubit of the parent subsystem code. Unlike the usual Bacon-Shor code, the Floquet-Bacon-Shor code family introduced here can therefore saturate the subsystem bound $kd = O(n)$. Moreover, several errors are shown to be self-corrected purely by the measurement schedule itself. This work provides insights into the design space for dynamical codes and expands the known approaches for constructing Floquet codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Logical Qubits in the Bacon-Shor Code Alam, M. Sohaib Rieffel, Eleanor Quantum Physics 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. We show that the code distance of these Floquet-Bacon-Shor codes scales as $Θ(d/\sqrt{k})$ on an $n = d \times d$ lattice with $k$ dynamical logical qubits, along with the logical qubit of the parent subsystem code. Unlike the usual Bacon-Shor code, the Floquet-Bacon-Shor code family introduced here can therefore saturate the subsystem bound $kd = O(n)$. Moreover, several errors are shown to be self-corrected purely by the measurement schedule itself. This work provides insights into the design space for dynamical codes and expands the known approaches for constructing Floquet codes. |
| title | Dynamical Logical Qubits in the Bacon-Shor Code |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.03291 |