Direct dialling of Haar random unitary matrices

TL;DR

This paper presents a straightforward optical method to directly implement Haar random unitary matrices, crucial for quantum information applications like boson sampling, without complex matrix calculations.

Contribution

It introduces a simple, physically-motivated approach to generate Haar random unitaries in optical circuits, extending to qubit systems.

Findings

Provides a direct optical implementation method for Haar random unitaries.

Extends the approach to qubit-based unitaries.

Eliminates the need for explicit matrix calculations.

Abstract

Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically-motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits.