Doubly geometric quantum control

TL;DR

This paper introduces a novel doubly geometric control method for holonomic quantum gates that effectively suppresses both pulse errors and transverse noise, enhancing robustness in quantum computation.

Contribution

It presents a general procedure combining holonomy loops and geometric space curves to design gates with simultaneous error suppression, a novel approach in quantum control.

Findings

Design of explicit doubly geometric holonomic gates

Demonstration of error suppression against pulse and transverse noise

Enhanced robustness in quantum gate implementation

Abstract

In holonomic quantum computation, single-qubit gates are performed using driving protocols that trace out closed loops on the Bloch sphere, making them robust to certain pulse errors. However, dephasing noise that is transverse to the drive, which is significant in many qubit platforms, lies outside the family of correctable errors. Here, we present a general procedure that combines two types of geometry -- holonomy loops on the Bloch sphere and geometric space curves in three dimensions -- to design gates that simultaneously suppress pulse errors and transverse noise errors. We demonstrate this doubly geometric control technique by designing explicit examples of such dynamically corrected holonomic gates.