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A silicon photonics quantum solver for the travelling salesman problem

Alessio Baldazzi, Stefano Azzini, Lorenzo Pavesi

Published Jan 1, 2026• 0 citations
Publisher

Abstract

We present a new variational quantum algorithm to solve the travelling salesman problem and its experimental validation for four-cities problems using a silicon photonics circuit with integrated photon-pair sources.
DOI
10.1364/cleo_fs.2026.fm3a.7

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The travelling salesman problem is a well-known example of computationally-hard combinatorial problem for classical machines. Here, we propose a novel variational quantum algorithm to solve it. The method is based on the preparation of two maximally entangled quantum registers whose correlations are assigned to different paths between pairs of cities. For NNN cities, this encoding requires 2⌈log⁡2N⌉2 \lceil\log_2 N\rceil2⌈log2​N⌉ qubits and the solution to the problem is directly found in the correlation matrix of the two registers composing the overall trial state. As a proof-of-concept experiment, we implement this algorithm for generic problems with four cities on a reconfigurable room-temperature silicon photonic circuit with integrated photon-pair sources, used to initialize maximally entangled path-encoded single-photon states.
Variational quantum algorithms are hybrid quantum-classical approaches extensively studied for their potential to leverage near-term quantum hardware for computational advantages. In this work, we successfully execute two variational quantum algorithms on a silicon photonic integrated circuit at room temperature: a variational quantum eigensolver for the Hydrogen molecule and a variational quantum factorization for semiprime numbers. In our reconfigurable silicon photonic circuit, four identical spontaneous-four-wave-mixing-based integrated photon pair sources are used to prepare two path-entangled ququarts, whose correlation gives rise to the resource for generic trial states’ preparation. This marks a first demonstration of variational quantum algorithms on a photonic quantum simulator with integrated photon pair sources.
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