Quantum advantage in temporally flat measurement-based quantum computation

TL;DR

This paper demonstrates that measurement-based quantum computation with a flat temporal structure can efficiently compute Boolean functions, showing quantum advantage with fewer qubits and gates than classical circuits.

Contribution

It introduces new constructions for deterministic Boolean function computation in flat MBQC, reducing qubit requirements and identifying functions with quantum advantage.

Findings

Deterministic Boolean function computation in flat MBQC is possible.

Quantum advantage achieved in width and gate count over classical circuits.

Reduced qubit requirements compared to previous methods.

Abstract

Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible simplifications in experimental demonstrations. In this paper we study the efficiency of measurement-based quantum computation with a completely flat temporal ordering of measurements. We propose new constructions for the deterministic computation of arbitrary Boolean functions, drawing on correlations present in multi-qubit Greenberger, Horne, and Zeilinger (GHZ) states. We characterize the necessary measurement complexity using the Clifford hierarchy, and also generally decrease the number of qubits needed with respect to previous constructions. In particular, we identify a family of Boolean functions for which deterministic evaluation using non-adaptive MBQC is possible, featuring quantum advantage in width and number of gates with respect to classical circuits.