Energetic cost of superadiabatic quantum computation

TL;DR

This paper analyzes the energetic costs associated with superadiabatic quantum computation, focusing on energy-time trade-offs and the implications for quantum search efficiency.

Contribution

It demonstrates how probabilistic dynamics can minimize energy costs in superadiabatic models and compares energy-time complexity with adiabatic methods.

Findings

Probabilistic dynamics reduce energy costs in superadiabatic evolutions.

Superadiabatic quantum search has the same energy-time complexity as adiabatic search.

Counter-diabatic Hamiltonians in superadiabatic search are non-oracular.

Abstract

We discuss the energetic cost of superadiabatic models of quantum computation. Specifically, we investigate the energy-time complementarity in general transitionless controlled evolutions and in shortcuts to the adiabatic quantum search over an unstructured list. We show that the additional energy resources required by superadiabaticity for arbitrary controlled evolutions can be minimized by using probabilistic dynamics, so that the optimal success probability is fixed by the choice of the evolution time. In the case of analog quantum search, we show that the superadiabatic approach induces a non-oracular counter-diabatic Hamiltonian, with the same energy-time complexity as equivalent adiabatic implementations.