Transversal gates for probabilistic implementation of multi-qubit Pauli rotations

• URL: http://arxiv.org/abs/2510.08290v1
• Date: Thu, 09 Oct 2025 14:42:35 GMT
• Title: Transversal gates for probabilistic implementation of multi-qubit Pauli rotations
• Authors: Nobuyuki Yoshioka, Alireza Seif, Andrew Cross, Ali Javadi-Abhari,
• Abstract summary: We introduce a general framework for weak gates -- probabilistic implementation of logical unitaries realized by local physical unitaries.<n>We propose a novel partially fault-tolerant quantum computing architecture that surpasses the standard Clifford+T architecture on workloads with millions of million-scale Clifford+T gate counts.
• Score: 1.3136863945420865
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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+$\phi$ 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+$\phi$ 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.

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