Hamiltonian Transformability, Fast Adiabatic Dynamics and Hidden Adiabaticity

TL;DR

This paper proves a unitary transformation exists that can convert any two Hamiltonians into each other, enabling rapid adiabatic quantum computation by transforming slow, adiabatic Hamiltonians into fast-evolving ones.

Contribution

It establishes a foundational theorem for Hamiltonian transformability, facilitating the implementation of fast adiabatic dynamics in quantum computing.

Findings

Existence of a unitary transformation between arbitrary Hamiltonians

Enabling rapid adiabatic quantum computation through Hamiltonian transformation

Illustrative examples demonstrating the theorem's application

Abstract

We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to implementing or mimicking dynamics with the most controllable Hamiltonian. As a promising application, this existence theorem allows for a rapidly evolving realization of adiabatic quantum computation by transforming a Hamiltonian where dynamics is in the adiabatic regime into a rapidly evolving one. We illustrate the theorem with examples.