Universal fault-tolerant quantum computation with Bacon-Shor codes

TL;DR

This paper introduces a fault-tolerant universal gate set for Bacon-Shor codes, enabling efficient implementation of complex quantum gates with reduced overhead, advancing practical quantum computing.

Contribution

It presents a novel fault-tolerant universal gate set on Bacon-Shor codes, including transversal non-Clifford gates and techniques to lower overhead for fault-tolerance.

Findings

Calculated pseudothresholds for the 3x3 Bacon-Shor code

Compared gate performance with magic-states in ion trap architecture

Demonstrated reduction in overhead for fault-tolerant CCZ

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 $m\times m^k$ 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 $3\times3$ Bacon-Shor code and also compare our gates with magic-states within the framework of a proposed ion trap architecture.