Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

TL;DR

This paper introduces a new subclass of IQP circuits called ancilla-driven IQP (ADIQP), which are easier to implement experimentally yet still hard to simulate classically, advancing the pursuit of quantum supremacy.

Contribution

It proposes ADIQP as a practically feasible subclass of IQP, demonstrating its classical hardness and potential for experimental realization.

Findings

ADIQP circuits are classically hard to simulate.

ADIQP is easier to implement than general IQP.

Properties of ADIQP facilitate verifiability and experimental realization.

Abstract

Instantaneous quantum polynomial time (IQP) is a model of (probably) non-universal quantum computation. Since it has been proven that IQP circuits are unlikely to be simulated classically up to a multiplicative error and an error in the $l_1$ norm, IQP is considered as one of the promising classes that demonstrates quantum supremacy. Although IQP circuits can be realized more easily than a universal quantum computer, demonstrating quantum supremacy is still difficult. It is therefore desired to find subclasses of IQP that are easy to implement. In this paper, by imposing some restrictions on IQP, we propose ancilla-driven IQP (ADIQP) as the subclass of commuting quantum computation suitable for many experimental settings. We show that even though ADIQP circuits are strictly weaker than IQP circuits in a sense, they are also hard to simulate classically up to a multiplicative error and an error in the $l_1$ norm. Moreover, the properties of ADIQP make it easy to investigate the verifiability of ADIQP circuits and the difficulties in realizing ADIQP circuits.