An Optimized Nearest Neighbor Compliant Quantum Circuit for 5-qubit Code

TL;DR

This paper introduces an optimized, nearest neighbor compliant quantum encoder circuit for the five-qubit code, reducing gate count and improving implementation efficiency for quantum error correction.

Contribution

It presents a systematic optimization method for stabilizer code encoders and proposes a nearest neighbor compliant design using fewer swap gates.

Findings

Reduced number of quantum gates in the encoder

Proposed NNC circuit uses only one swap gate

Applicable to larger stabilizer codes

Abstract

The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been proposed for it. In this paper, we propose a systematic procedure for optimization of encoder circuits for stabilizer codes. We start with the systematic construction of an encoder for a five-qubit code, and optimize the circuit in terms of the number of quantum gates. Our method is also applicable to larger stabilizer codes. We further propose nearest neighbor compliant (NNC) circuits for the proposed encoder using a single swap gate, as compared to three swap gates in a prior design.