Differentiation of Linear Optical Circuits

Linear optical circuits with single-photon sources offer a promising platform for quantum chemistry and machine learning. However, current applications are all based on support vector machines or gradient-free optimization methods. This paper develops classical and quantum algorithms for evaluating...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: de Felice, Giovanni, Corlett, Christopher
Format: Article
Language:English
Subjects:
Algorithms
Circuits
Extraction procedures
Machine learning
Optimization
Parameters
Photons
Quantum chemistry
Qubits (quantum computing)
Sampling
Support vector machines
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Linear optical circuits with single-photon sources offer a promising platform for quantum chemistry and machine learning. However, current applications are all based on support vector machines or gradient-free optimization methods. This paper develops classical and quantum algorithms for evaluating the analytic gradients of linear optical circuits with respect to their phase parameters. First, we set up a general framework by characterising the class of observables whose expectation values can be estimated efficiently by sampling from a passive linear optical circuit with finitely many photons. We then show how to compute the gradients of the expectation values of a special class of ``non-interacting'' observables arising in full-counting-statistics. Our differentiation algorithm uses the Halmos dilation and requires evaluating two circuits of twice the size, using one additional photon. Building on the methods of full-counting-statistics, we show how to recover the gradients of arbitrary observables from the gradient of a non-interacting characteristic function. Throughout the paper, we compare the performance of classical and quantum algorithms on the same estimation problems, analysing the sampling complexity of the algorithms and suggesting different cases for which quantum speed-ups could be obtained.
ISSN:2331-8422