Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916326617907200 |
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| author | Darmawan, Andrew S. Nakata, Yoshifumi Tamiya, Shiro Yamasaki, Hayata |
| author_facet | Darmawan, Andrew S. Nakata, Yoshifumi Tamiya, Shiro Yamasaki, Hayata |
| contents | Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the random circuits on $n$ qubits, embedded in one spatial dimension (1D), have a logarithmic depth $d=\mathcal{O}(\log{n})$. However, this was demonstrated only for a simple erasure noise model. In this work, we discover that this desired property indeed holds for the conventional Pauli noise model. Specifically, we numerically demonstrate that the hashing bound, i.e., a rate known to be achieved with $d=\mathcal{O}(n)$-depth random encoding circuits, can be attained even when the circuit depth is restricted to $d=\mathcal{O}(\log n)$ in 1D for depolarizing noise of various strengths. This analysis is made possible with our development of a tensor-network maximum-likelihood decoding algorithm that works efficiently for $\log$-depth encoding circuits in 1D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05071 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder Darmawan, Andrew S. Nakata, Yoshifumi Tamiya, Shiro Yamasaki, Hayata Quantum Physics Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the random circuits on $n$ qubits, embedded in one spatial dimension (1D), have a logarithmic depth $d=\mathcal{O}(\log{n})$. However, this was demonstrated only for a simple erasure noise model. In this work, we discover that this desired property indeed holds for the conventional Pauli noise model. Specifically, we numerically demonstrate that the hashing bound, i.e., a rate known to be achieved with $d=\mathcal{O}(n)$-depth random encoding circuits, can be attained even when the circuit depth is restricted to $d=\mathcal{O}(\log n)$ in 1D for depolarizing noise of various strengths. This analysis is made possible with our development of a tensor-network maximum-likelihood decoding algorithm that works efficiently for $\log$-depth encoding circuits in 1D. |
| title | Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2212.05071 |