Robust quantum control using smooth pulses and topological winding

TL;DR

This paper introduces an analytical method for designing smooth quantum control pulses that cancel leading-order noise errors by leveraging topological winding numbers, enhancing robustness of quantum gates in solid-state qubits.

Contribution

It provides explicit constraints on control fields to eliminate dominant noise effects, using topological concepts to achieve noise-resilient quantum operations.

Findings

Successfully constructed robust quantum gates for silicon and diamond qubits.

Derived explicit noise-cancellation conditions for slow energy fluctuations.

Demonstrated topological winding as a tool for quantum control robustness.

Abstract

The greatest challenge in achieving the high level of control needed for future technologies based on coherent quantum systems is the decoherence induced by the environment. Here, we present an analytical approach that yields explicit constraints on the driving field which are necessary and sufficient to ensure that the leading-order noise-induced errors in a qubit's evolution cancel exactly. We derive constraints for two of the most common types of noise that arise in qubits: slow fluctuations of the qubit energy splitting and fluctuations in the driving field itself. By theoretically recasting a phase in the qubit's wavefunction as a topological winding number, we can satisfy the noise-cancelation conditions by adjusting driving field parameters without altering the target state or quantum evolution. We demonstrate our method by constructing robust quantum gates for two types of spin qubit: phosphorous donors in silicon and nitrogen-vacancy centers in diamond.