Quantum pseudo-randomness from cluster-state quantum computation

TL;DR

This paper presents a method to efficiently generate pseudo-random quantum states using cluster-state quantum computation, optimizing circuit design and analyzing convergence to approximate Haar measure.

Contribution

It introduces a new approach to pseudo-random state generation via cluster states and provides an analysis for optimizing convergence rates.

Findings

Optimized pseudo-random circuits with single-qubit rotations

Markov chain analysis of convergence rates

Alternative construction of approximate unitary 2-designs

Abstract

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for optimizing pseudo-random circuits by properly choosing single-qubit rotations. A Markov chain analysis provides the tool for analyzing convergence rates to the Haar measure and finding the optimal single-qubit gate distribution. Our results may be viewed as an alternative construction of approximate unitary 2-designs.