Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates

TL;DR

This paper demonstrates an experimental implementation of nonadiabatic holonomic quantum computation using shortcut to adiabaticity with only three energy levels in a superconducting qubit, enhancing speed and stability of quantum gates.

Contribution

It introduces a simplified three-level scheme for nonadiabatic holonomic quantum gates using shortcut to adiabaticity, with experimental validation on a superconducting qubit platform.

Findings

Successfully implemented nonadiabatic holonomic gates with shortcut to adiabaticity.

Benchmarked stability of STA+HQC against NHQC in the same platform.

Scheme is adaptable to other quantum systems like NV centers and quantum dots.

Abstract

When a quantum system is driven adiabatically through a parametric cycle in a degenerate Hilbert space, the state would acquire a non-Abelian geometric phase, which is stable and forms the foundation for holonomic quantum computation (HQC). However, in the adiabatic limit, the environmental decoherence becomes a significant source of errors. Recently, various non-adiabatic HQC schemes have been proposed, but all at the price of increased sensitivity to control errors. Alternatively, there exist theoretical proposals for speeding up HQC by the technique of "shortcut to adiabaticity" (STA), but no experimental demonstration has been reported so far, as these proprosals involve a complicated control of four energy levels simultaneously. Here we propose and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture. With this scheme, all holonomic single-qubit operations can be realized non-adiabatically through a single cycle of state evolution. As a result, we are able to experimentally benchmark the stability of STA+HQC against NHQC in the same platform. The flexibility and simplicity of our scheme makes it also implementable on other systems, such as nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance.