Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation

TL;DR

This paper proves that adiabatic quantum computation is polynomially equivalent to standard quantum computation, establishing a foundational equivalence that broadens understanding and approaches in quantum algorithm design and fault tolerance.

Contribution

It demonstrates an efficient simulation of any quantum algorithm via adiabatic processes, establishing their polynomial equivalence and extending this to realistic physical systems.

Findings

Adiabatic quantum computation can simulate any quantum algorithm efficiently.

The equivalence holds even for particles on a 2D grid with nearest neighbor interactions.

The result links quantum computational questions to spectral gap analysis of sparse matrices.

Abstract

Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models provides a new vantage point from which to tackle the central issues in quantum computation, namely designing new quantum algorithms and constructing fault tolerant quantum computers. In particular, by translating the main open questions in the area of quantum algorithms to the language of spectral gaps of sparse matrices, the result makes these questions accessible to a wider scientific audience, acquainted with mathematical physics, expander theory and rapidly mixing Markov chains.