Interpretable Machine Learning for Building Analytic Quantum Circuits: the Case of Diagonal Operators
Year: 2026
Type: preprint
Abstract: Machine Learning has become a useful instrument across many fields, but the opacity of typical ``black-box'' models limits their value for scientific discovery. In this paper we present a methodology that uses \emph{interpretable} Machine Learning to generate analytic mathematical hypotheses about a physical system, which can then be confirmed by a formal derivation. We demonstrate the methodology on the problem of decomposing unitary operators into elementary quantum gates. By training an interpretable model on circuits obtained numerically and analyzing its weights, we are led to a hypothesis for the analytic structure of the decomposition. Applied to the family of diagonal operators, this hypothesis yields a universal, analytic quantum circuit valid for an arbitrary number of qubits, whose $CNOT$ count scales as $\mathcal{O}(2^n)$, improving on the $\mathcal{O}(2.5^n)$ of standard numerical methods. The resulting decomposition is proved rigorously in a companion paper.
Source: arXiv (Cornell University)
Authors: Fedin, Matvei, Morozov, Andrey
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G7087920317
OpenAlex ID: W7160647161