Fault-Tolerant Quantum Computation for Singlet-Triplet Qubits with Leakage Errors

TL;DR

This paper addresses leakage errors in singlet-triplet spin qubits, proposing correction protocols compatible with surface code error correction, which can be implemented efficiently with minimal additional resources.

Contribution

It introduces explicit leakage reduction units that operate without measurements, requiring only a few extra steps and qubits, enhancing fault-tolerance in quantum dot spin qubits.

Findings

Leakage errors can be corrected without measurements.

Leakage correction requires minimal additional gates and ancilla qubits.

Protocols are compatible with surface code quantum error correction.

Abstract

We describe and analyze leakage errors of singlet-triplet qubits. Even though leakage errors are a natural problem for spin qubits encoded using quantum dot arrays, they have obtained little attention in previous studies. We describe the realization of leakage correction protocols that can be implemented together with the quantum error correction protocol of the surface code. Furthermore we construct explicit leakage reduction units that need, in the ideal setup, as few as three manipulation steps. Our study shows that leakage errors can be corrected without the need of measurements and at the cost of only a few additional ancilla qubits and gate operations compared to standard quantum error correction codes.