Classical Simulation of Limited-Width Cluster-State Quantum Computation

Abstract

We present a classical protocol, using the matrix product-state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d---the width of the cluster. We use this result to show that any log-depth quantum computation in the gate array model, with gates linking only nearby qubits, can be simulated efficiently on a classical computer.