Universal computation by multiparticle quantum walk

Quantum Institute Seminar Series

We show that multi-particle quantum walk is capable of universal quantum computation. 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. As in a previous single-particle construction, we use a discrete version of scattering theory to establish universality. However, we use a different encoding of quantum data and exploit interactions between particles to implement two-qubit gates. In our scheme, an n-qubit circuit with g gates can be simulated by the dynamics of O(n) particles evolving for time poly(n,g) on a planar graph of maximum degree 4 with poly(n,g) vertices. Thus our graphs are exponentially smaller (as a function of n) than those used in the single-particle construction, offering the potential for efficient implementation by a system with a physical degree of freedom for each vertex of the graph. Our results apply to a broad class of multi-particle quantum walk Hamiltonians, including the Bose-Hubbard model and models with nearest-neighbor interactions for fermions and distinguishable particles.
 
Based on joint work with David Gosset and Zak Webb.

For more information contact Prof. Ken Brown (404-385-3124).

Website:  Andrew Childs