Universal computation by multi-particle quantum walk

TL;DR

This paper demonstrates that multi-particle quantum walks, involving interactions among particles, can perform universal quantum computation, potentially enabling scalable quantum computers without time-dependent control.

Contribution

It introduces a model of multi-particle quantum walk that is capable of universal quantum computation, linking it to known many-body systems.

Findings

Multi-particle quantum walk can perform universal quantum computation.

The model includes systems like the Bose-Hubbard model and fermionic systems.

It suggests a scalable quantum computer architecture without time-dependent control.

Abstract

A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we consider a generalization of quantum walk to systems with more than one walker. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. Multi-particle quantum walk includes a broad class of interacting many-body systems such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions. We show that multi-particle quantum walk is capable of universal quantum computation. Since it is also possible to efficiently simulate a multi-particle quantum walk of the type we consider using a universal quantum computer, this model exactly captures the power of quantum computation. In principle our construction could be used as an architecture for building a scalable quantum computer with no need for time-dependent control.