Superadiabatic Controlled Evolutions and Universal Quantum Computation

TL;DR

This paper introduces a superadiabatic approach for universal quantum computation using piecewise controlled evolutions with simple counter-diabatic Hamiltonians, enabling faster quantum gates within energy limits set by the quantum speed limit.

Contribution

It presents a novel superadiabatic method for implementing universal quantum gates with simple Hamiltonians, improving speed and efficiency over traditional adiabatic techniques.

Findings

Fast rotation and controlled gates demonstrated

Energy cost bounded by quantum speed limit

Method applicable to arbitrary n-qubit gates

Abstract

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts.