Shortcuts to adiabaticity and applications to Quantum Computation

TL;DR

This paper introduces two models for universal superadiabatic quantum computing using shortcuts to adiabaticity, enabling faster quantum gate implementation with potential applications in quantum information processing.

Contribution

It presents novel models for superadiabatic quantum computing based on counter-diabatic Hamiltonians, including quantum teleportation and controlled evolutions, advancing the speed and efficiency of quantum gates.

Findings

Superadiabatic quantum teleportation for arbitrary n-qubit gates.

Implementation of n-controlled quantum gates with time-independent counter-diabatic Hamiltonians.

Superadiabatic evolution can be performed in arbitrarily small times constrained by energetic costs.

Abstract

Adiabatic evolution is a powerful technique in quantum information and computation. 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. In this dissertation we introduce two different models to perform universal superadiabatic quantum computing, which are based on the use of shortcuts to adiabaticity by counter-diabatic Hamiltonians. The first model is based on the use of superadiabatic quantum teleportation, introduced in this dissertation, as a primitive to quantum computing. Thus, we provide the counter-diabatic driving for arbitrary $n$-qubit gates. In addition, our approach maps the counter-diabatic Hamiltonian for an arbitrary $n$-qubit {\it gate} teleportation into the implementation of a rotated counter-diabatic Hamiltonian for an $n$-qubit {\it state} teleportation. In the second model we use the concept of controlled superadiabatic evolutions to show how we can implement arbitrary $n$-controlled quantum gates. Remarkably, this task can be performed by simple time-independent counter-diabatic Hamiltonians. These two models can be used to design different sets of universal quantum gates. We show that the use of the quantum speed limit suggests that the superadiabatic time evolution is compatible with arbitrarily small time intervals, where this arbitrariness is constrained to the energetic cost necessary to perform the superadiabatic evolution.