Filter design for hybrid spin gates

TL;DR

This paper develops a filter-based framework for designing and tuning control sequences in hybrid spin systems, enhancing gate fidelity and noise decoupling capabilities in quantum information processing.

Contribution

It extends the filter description to long-time evolution, enabling the construction of tunable, noise-resistant quantum gates with improved fidelity.

Findings

Filter resonance dependence allows coupling tuning.

Time-sliced sequences extend filter validity.

Alternating pulse sequences improve spin sensing.

Abstract

The impact of control sequences on the environmental coupling of a quantum system can be described in terms of a filter. Here we analyze how the coherent evolution of two interacting spins subject to periodic control pulses, at the example of a nitrogen vacancy center coupled to a nuclear spin, can be described in the filter framework in both the weak and the strong coupling limit. A universal functional dependence around the filter resonances then allows for tuning the coupling type and strength. Originally limited to small rotation angles, we show how the validity range of the filter description can be extended to the long time limit by time-sliced evolution sequences. Based on that insight, the construction of tunable, noise decoupled, conditional gates composed of alternating pulse sequences is proposed. In particular such an approach can lead to a significant improvement in fidelity as compared to a strictly periodic control sequence. Moreover we analyze the decoherence impact, the relation to the filter for classical noise known from dynamical decoupling sequences, and we outline how an alternating sequence can improve spin sensing protocols.