Gauge-invariant Adiabatic Two-Qubit Gates for Exchange-Only Qubits

TL;DR

This paper develops a gauge-invariant, adiabatic two-qubit gate for exchange-only spin qubits that functions correctly without assuming polarized spins, addressing gauge-dependent issues in previous designs.

Contribution

It introduces a new gauge-invariant gate construction that maintains entangling operations across uninitialized gauge spins, improving robustness in exchange-only qubit systems.

Findings

The gate performs the same logical operation in different gauge subspaces.

Second-order errors decrease quadratically with gate duration.

An optimal gate duration exists considering charge noise effects.

Abstract

We extend recent work on a leakage-protected, adiabatic entangling gate for exchange-only spin qubits [Doherty and Wardrop, PRL 111, 050503 (2013)] by adapting to a setting where single spins are not assumed to be polarized on preparation. Previous gate constructions do not function correctly when "gauge spins" are uninitialized, because the entangling gate has different, non-trivial action in different gauge subspaces. Our construction inherits many of the desirable features of the previous work while addressing the gauge-dependent behavior. Using numerical simulation, we show that the resulting gate implements the same logical operation in both gauge subspaces to first order in perturbation theory, and second-order terms introduce an error that decreases quadratically in the duration of the gate. We add $1/f$ charge noise to voltages modulating exchange in this model, which introduces errors that increase with gate time, to show that there is an optimal gate duration for a given set of device parameters.