Density-Matrix Simulation of Logical Qubit using 3-qubit Quantum Error Correction Code

TL;DR

This paper uses density-matrix simulations to evaluate how quantum error correction codes and qubit layouts impact the fidelity of logical qubits, considering current technology constraints.

Contribution

It provides a detailed simulation-based analysis of logical qubit performance with small quantum error correction codes under realistic error rates.

Findings

Logical qubits with 5-qubit code have 0.25 higher fidelity than physical qubits at 0.1% gate error.

Performance depends on qubit layout and error correction code choice.

Simulations inform optimal design for fault-tolerant quantum computing.

Abstract

Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such limits, but imperfect gate operations introduce errors to the correction procedure as well. The additional gate operations required due to the physical layout of qubits exacerbate the situation. Here, we use density-matrix simulations to investigate the performance change of logical qubits according to quantum error correction codes and qubit layouts and the expected performance of logical qubits with gate operation time and gate error rates. Considering current qubit technology, the small quantum error correction codes are chosen. Assuming 0.1% gate error probability, a logical qubit encoded by a 5-qubit quantum error correction code is expected to have a fidelity 0.25 higher than its physical counterpart.