Universal quantum computation via scalable measurement-free error correction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909906797330432 |
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| author | Veroni, Stefano Paler, Alexandru Giudice, Giacomo |
| author_facet | Veroni, Stefano Paler, Alexandru Giudice, Giacomo |
| contents | We show that universal quantum computation can be concretely made fault-tolerant without mid-circuit measurements. To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $\mathit{CCZ}$ gate. Combined with a fold-transversal logical Hadamard gate, this enables a universal set of fault-tolerant operations using only transversal gates and qubit permutations. For the purpose of benchmarking under circuit-level noise, we develop an efficient method to simulate non-Clifford circuits with a small number of Hadamard gates. Separately, we demonstrate that certain CSS codes can be concatenated without measurements or having to rely on a universal logical gate set. This is made possible by means of a resource-efficient gadget -- termed the ``disposable Toffoli gadget'' -- that realizes the error-correcting feedback. Then, under concatenation of the Bacon-Shor code, we observe a fault-tolerance threshold at a circuit-level depolarizing noise rate of approximately $0.12\,\%$. Together, the deformation and concatenation protocols outline a blueprint for a fully fault-tolerant architecture without any feed-forward operation, particularly suited to state-of-the-art neutral-atom platforms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_15187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal quantum computation via scalable measurement-free error correction Veroni, Stefano Paler, Alexandru Giudice, Giacomo Quantum Physics We show that universal quantum computation can be concretely made fault-tolerant without mid-circuit measurements. To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $\mathit{CCZ}$ gate. Combined with a fold-transversal logical Hadamard gate, this enables a universal set of fault-tolerant operations using only transversal gates and qubit permutations. For the purpose of benchmarking under circuit-level noise, we develop an efficient method to simulate non-Clifford circuits with a small number of Hadamard gates. Separately, we demonstrate that certain CSS codes can be concatenated without measurements or having to rely on a universal logical gate set. This is made possible by means of a resource-efficient gadget -- termed the ``disposable Toffoli gadget'' -- that realizes the error-correcting feedback. Then, under concatenation of the Bacon-Shor code, we observe a fault-tolerance threshold at a circuit-level depolarizing noise rate of approximately $0.12\,\%$. Together, the deformation and concatenation protocols outline a blueprint for a fully fault-tolerant architecture without any feed-forward operation, particularly suited to state-of-the-art neutral-atom platforms. |
| title | Universal quantum computation via scalable measurement-free error correction |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.15187 |