Universal fault-tolerant quantum computation with Bacon-Shor codes

2017/05/04 by Theodore J. Yoder, Yoder, Theodore J. · 3 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1705.01686

openalex publication_date 2017/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford hierarchy become accessible as the code becomes more asymmetric. For instance, in an appropriate gauge, Bacon-Shor codes on an m× m^k lattice have transversal k-qubit-controlled Z. Through a variety of tricks, including intermediate error-correction and non-Pauli recovery, we reduce the overhead required for fault-tolerant CCZ. We calculate pseudothresholds for our universal gate set on the smallest 3×3 Bacon-Shor code and also compare our gates with magic-states within the framework of a proposed ion trap architecture.

Citations

• Universal quantum computation with ideal Clifford gates and noisy ancillas
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Cited by

• Transversal Toffoli-gate in Hybrid-code System
• Low Overhead Universal Quantum Computation with Triorthogonal Codes
• Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning

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