Magic State Injection on IBM Quantum Processors Above the Distillation Threshold

TL;DR

This paper demonstrates high-fidelity logical magic state injection on IBM quantum processors using a rotated surface code, surpassing previous error thresholds and enabling non-Clifford gates for fault-tolerant quantum computing.

Contribution

It introduces a qubit-efficient surface code implementation and reports improved error thresholds and magic state fidelities on IBM quantum hardware.

Findings

Error thresholds of ~0.37% for bit-flip and ~0.31% for phase-flip logical errors.

Fidelities of 0.8806 for |H_L⟩ and 0.8665 for |T_L⟩ magic states.

Minimum fidelity of 0.8356 for arbitrary logical states.

Abstract

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (\texttt{ibm\_fez}) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of $\approx0.37\%$ and $\approx0.31\%$, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states $|H_L\rangle$ and $|T_L\rangle$ achieve fidelities of $0.8806\pm0.0002$ and $0.8665\pm0.0003$, respectively, which are both above the magic state distillation threshold. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as $0.8356\pm0.0003$. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.