Fault-tolerant hyperbolic Floquet quantum error correcting codes
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912577137672192 |
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| author | Fahimniya, Ali Dehghani, Hossein Bharti, Kishor Mathew, Sheryl Kollár, Alicia J. Gorshkov, Alexey V. Gullans, Michael J. |
| author_facet | Fahimniya, Ali Dehghani, Hossein Bharti, Kishor Mathew, Sheryl Kollár, Alicia J. Gorshkov, Alexey V. Gullans, Michael J. |
| contents | A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes.'' These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for $n$ qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate $(1/8+2/n)$ while still requiring only two-body measurements. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in $n$. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model and 0.25% in an entangling measurements noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10033 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fault-tolerant hyperbolic Floquet quantum error correcting codes Fahimniya, Ali Dehghani, Hossein Bharti, Kishor Mathew, Sheryl Kollár, Alicia J. Gorshkov, Alexey V. Gullans, Michael J. Quantum Physics A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes.'' These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for $n$ qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate $(1/8+2/n)$ while still requiring only two-body measurements. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in $n$. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model and 0.25% in an entangling measurements noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder. |
| title | Fault-tolerant hyperbolic Floquet quantum error correcting codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.10033 |