Derandomizing quantum circuits with measurement based unitary designs

TL;DR

This paper demonstrates how entangled multipartite states and graph state techniques can derandomize quantum circuits by creating ensembles of unitaries that mimic random distributions, enabling efficient pseudorandomness without adaptive feed-forward.

Contribution

It introduces methods to derandomize quantum circuits using graph states, producing t-design ensembles that replicate properties of truly random unitaries without adaptive measurements.

Findings

Ensembles can match moments of Haar-random unitaries up to order t

Graph state techniques enable derandomization of quantum circuits

New t-design ensembles can be generated without adaptive feed-forward

Abstract

Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state techniques, we show that these resources can `derandomize' circuit results by sampling the same kinds of ensembles quantum mechanically, (analogously to a quantum random number generator). Furthermore, we find simple examples that give rise to new ensembles whose statistical moments exactly match those of the uniformly random distribution over all unitaries up to order $t$, while foregoing adaptive feed-forward entirely. Such ensembles -- known as $t$-designs -- often cannot be distinguished from the `truly' random ensemble, and so they find use in many applications that require this implied notion of pseudorandomness.