Measure of decoherence in quantum error correction for solid-state quantum computing

TL;DR

This paper evaluates the effectiveness of quantum error correction codes in semiconductor quantum dots under realistic noisy conditions, demonstrating quadratic error rate improvements at low phonon noise levels.

Contribution

It introduces modified 5- and 9-qubit quantum error correction algorithms tailored for semiconductor qubits and assesses their performance in phonon environments.

Findings

Quantum error correction improves error rates quadratically at low noise levels.

Modified 5-qubit codes are effective for silicon charge double dot qubits.

Decoherence measures confirm the fault-tolerance of the implemented codes.

Abstract

We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5- and 9-qubit quantum error correction (QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were applied to quantum register. 5-qubit error correction procedures were implemented for Si charge double dot qubits in the presence of acoustic phonon environment. Chi-matrix, Choi-Jamiolkowski state and measure of decoherence techniques were used to quantify qubit fault-tolerance. Our results showed that the introduction of above quantum error correction techniques at small phonon noise levels provided quadratic improvement of output error rates. The efficiency of 5-qubits quantum error correction algorithm in semiconductor quantum information processors was demonstrated.