Low-overhead pieceable fault-tolerant construction of logical controlled-phase circuit for degenerate quantum code

TL;DR

This paper presents a novel search algorithm to construct fault-tolerant logical controlled-phase gates for degenerate quantum codes, reducing resource overhead and enabling scalable quantum computation.

Contribution

The authors introduce a new search method for fault-tolerant logical gates on degenerate codes and demonstrate its effectiveness with a simplified, resource-efficient circuit example.

Findings

Successfully designed a fault-tolerant logical CZ circuit with fewer ancillary qubits.

The circuit exhibits lower logical error rates in simulations.

The approach simplifies syndrome measurement circuits for large-scale quantum computing.

Abstract

We designed an search algorithm in order to find a non-transversal but fault-tolerant construction of a logical controlled-phase gate for general [[n,1,d]] degenerate quantum code. Then we give an example to illustrate our algorithm for a quantum code called bare [[7, 1, 3]] code. This code is obtained under certain search criteria, and it possesses a simpler flag-assisted fault-tolerant syndrome measurement circuit under a standard depolarizing error model. Since a syndrome extraction circuit requiring fewer ancillary qubit resources would facilitate the realization of large-scale quantum computations, such as concatenated high level elementary logical gate circuits when aim to achieve lower logical error rates, we follow our search scheme and find a 3-pieceable fault-tolerant logical CZ circuit on this code. Numerical simulations are also performed to further analyze the logical error rate of our circuit.