Superrobust Geometric Control of a Superconducting Circuit

TL;DR

This paper demonstrates a superconducting circuit method for constructing nonadiabatic holonomic quantum gates with significantly improved robustness against errors, surpassing conventional schemes by suppressing cross coupling effects.

Contribution

It introduces a new set of constraints for NHQC to reduce cross coupling, achieving higher fidelity and robustness in quantum gates compared to traditional methods.

Findings

High-fidelity holonomic gates with up to fourth-order error suppression.

Reduced dynamical phase accumulation due to cross coupling.

Enhanced robustness of two-qubit NHQC gates.

Abstract

Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a different set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.