Universal quantum computation by discontinuous quantum walk

TL;DR

This paper introduces a hybrid quantum walk scheme that enables universal quantum computation through discrete steps of continuous evolution, utilizing perfect state transfer to implement gates efficiently without extra coin spaces.

Contribution

It presents a novel hybrid 'discontinuous' quantum walk method for universal quantum computation using perfect state transfer, avoiding ancillary coin spaces.

Findings

Run time scales linearly with number of qubits and gates

Multiple algorithm runs can be executed simultaneously

Universal gate set implemented via specific subgraph design

Abstract

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.