Superadiabatic Holonomic Quantum Computation in Cavity QED

TL;DR

This paper introduces a superadiabatic holonomic quantum computation scheme in cavity QED that combines speed and robustness by speeding up adiabatic processes using non-Abelian geometric phases, suitable for fast, error-resilient quantum gates.

Contribution

It presents a feasible method for universal holonomic quantum computation that is both fast and robust, overcoming the slow speed of traditional adiabatic methods.

Findings

The scheme is implementable in a cavity QED system with a tripod configuration.

It retains robustness against timing errors while significantly increasing speed.

Comparison shows improved performance over conventional adiabatic strategies.

Abstract

Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition requires that the process should be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited coherent times of the quantum systems. Here, we propose a feasible scheme to implement universal holonomic quantum computation based on non-Abelian geometric phases with superadiabatic quantum control, where the adiabatic manipulation is sped up while retaining its robustness against errors in the timing control. Consolidating the advantages of both strategies, our proposal is thus both robust and fast. The quantum cavity QED system is adopted as a typical example to illustrate the merits, where the proposed scheme can be realized in a tripod configuration by appropriately controlling the pulse shapes and their relative strength. To demonstrate the distinct performance of our proposal, we also compare our scheme with the conventional adiabatic strategy.