Hardware-efficient error-correcting codes for large nuclear spins

TL;DR

This paper proposes a hardware-efficient quantum error correction protocol for large nuclear spins in silicon, utilizing the nuclear and electron spins of donors to improve logical qubit fidelity.

Contribution

It introduces the MAUS encoding scheme that leverages large nuclear spin Hilbert space and feasible operations for error correction in silicon-based quantum systems.

Findings

Simulations predict significant fidelity improvements with current experimental fidelities.

The protocol corrects phase flips using explicit, experimentally feasible operations.

Provides a blueprint for implementing corrected spin-based qubits in silicon.

Abstract

Universal quantum computers require a large network of qubits robust against errors. Recent theoretical and experimental studies on donor nuclear spins in silicon, engineered on semiconductor platforms compatible with industrial fabrication, show their coherent behavior and potential for scalability. Here we present a hardware-efficient quantum protocol that corrects phase flips of a nuclear spin using explicit experimentally feasible operations. We introduce the MAUS encoding (Moment AngUlar System encoding) which uses the large Hilbert space provided by the nuclear spin of the donor to encode the information and employ the electron spin of the donor as an ancilla for error correction. Simulations using present-day experimental manipulation fidelities predict significant improvement in logical qubit fidelity over existing spin quantum-error-correction protocols. These results provides a realizable blueprint for a corrected spin-based qubit.