Universal Weakly Fault-Tolerant Quantum Computation via Code Switching in the [[8,3,2]] Code

TL;DR

This paper introduces a fault-tolerant quantum computation scheme using code switching between two [[8,3,2]] codes, enabling universal operations through error detection and postselection.

Contribution

It presents a novel fault-tolerant code-switching protocol between two [[8,3,2]] codes supporting different sets of logical gates for universal quantum computation.

Findings

Protocol achieves quadratic suppression of logical error rates.

Numerical simulations validate state preparation, code switching, and Grover's search implementation.

Enables universal fault-tolerant quantum computation via postselection.

Abstract

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the $[[8, 3, 2]]$ code. One version supports weakly fault-tolerant single-qubit Clifford gates, while the other supports a logical $\overline{\mathrm{CCZ}}$ gate via transversal $T/T^\dagger$ together with logical $\overline{\mathrm{CZ}}$, $\overline{\mathrm{CNOT}}$, and $\overline{\mathrm{SWAP}}$ gates. Because both codes have distance 2, the protocol operates in a postselected, error-detecting regime: single faults lead to detectable outcomes, and accepted runs exhibit quadratic suppression of logical error rates. This yields a universal scheme for postselected fault-tolerant computation. We validate the protocol numerically through simulations of state preparation, code switching, and a three-logical-qubit implementation of Grover's search.