Decision and function problems based on boson sampling

TL;DR

This paper explores whether boson sampling can be used to create computationally hard decision and function problems with potential cryptographic applications, beyond its role in demonstrating quantum supremacy.

Contribution

It introduces a general theoretical framework for designing such problems and analyzes their solution complexity using numerical methods and non-boson samplers.

Findings

Sample sizes for solving these problems are independent of Hilbert space size.

Numerical approaches and non-boson samplers can solve the problems.

Potential cryptographic applications are identified.

Abstract

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of non-boson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space.