Transversal gates for probabilistic implementation of multi-qubit Pauli rotations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915542239019008 |
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| author | Yoshioka, Nobuyuki Seif, Alireza Cross, Andrew Javadi-Abhari, Ali |
| author_facet | Yoshioka, Nobuyuki Seif, Alireza Cross, Andrew Javadi-Abhari, Ali |
| contents | We introduce a general framework for weak transversal gates -- probabilistic implementation of logical unitaries realized by local physical unitaries -- and propose a novel partially fault-tolerant quantum computing architecture that surpasses the standard Clifford+T architecture on workloads with million-scale Clifford+T gate counts. First, we prove the existence of weak transversal gates on the class of Calderbank-Shor-Steane codes, covering high-rate qLDPC and topological codes such as surface code or color codes, and present an efficient algorithm to determine the physical multi-qubit Pauli rotations required for the desired logical rotation. Second, we propose a partially fault-tolerant Clifford+$ϕ$ architecture that performs in-place Pauli rotations via a repeat-until-success strategy; phenomenological simulations indicate that a rotation of 0.003 attains logical error of $9.5\times10^{-5}$ on a surface code with $d=7$ at physical error rate of $10^{-4}$, while avoiding the spacetime overheads of magic state factories, small angle synthesis, and routing. Finally, we perform resource estimation on surface and gross codes for a Trotter-like circuit with $N=108$ logical qubits to show that the Clifford+$ϕ$ architecture outperforms the conventional Clifford+T approach by a factor of tens to a hundred in runtime due to natural rotation-gate parallelism. This work open a novel paradigm for realizing logical operations beyond the constraints of conventional design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transversal gates for probabilistic implementation of multi-qubit Pauli rotations Yoshioka, Nobuyuki Seif, Alireza Cross, Andrew Javadi-Abhari, Ali Quantum Physics We introduce a general framework for weak transversal gates -- probabilistic implementation of logical unitaries realized by local physical unitaries -- and propose a novel partially fault-tolerant quantum computing architecture that surpasses the standard Clifford+T architecture on workloads with million-scale Clifford+T gate counts. First, we prove the existence of weak transversal gates on the class of Calderbank-Shor-Steane codes, covering high-rate qLDPC and topological codes such as surface code or color codes, and present an efficient algorithm to determine the physical multi-qubit Pauli rotations required for the desired logical rotation. Second, we propose a partially fault-tolerant Clifford+$ϕ$ architecture that performs in-place Pauli rotations via a repeat-until-success strategy; phenomenological simulations indicate that a rotation of 0.003 attains logical error of $9.5\times10^{-5}$ on a surface code with $d=7$ at physical error rate of $10^{-4}$, while avoiding the spacetime overheads of magic state factories, small angle synthesis, and routing. Finally, we perform resource estimation on surface and gross codes for a Trotter-like circuit with $N=108$ logical qubits to show that the Clifford+$ϕ$ architecture outperforms the conventional Clifford+T approach by a factor of tens to a hundred in runtime due to natural rotation-gate parallelism. This work open a novel paradigm for realizing logical operations beyond the constraints of conventional design. |
| title | Transversal gates for probabilistic implementation of multi-qubit Pauli rotations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.08290 |