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arXiv:2509.11861

Optimizing Quantum Photonic Integrated Circuits using Differentiable Tensor Networks

Mathias Van Regemortel, Thomas Van Vaerenbergh

Published Sep 15, 2025• 0 citations
arXivHTMLPDF

Abstract

Recent reports of large photonic nonlinearities in integrated photonic devices, using the strong excitonic light-matter coupling in semiconductors, necessitate a tailored design framework for quantum processing in the limit of low photon occupation. We present a gradient-based optimization method for quantum photonic integrated circuits, which are composed of nonlinear unitary coupling gates and stochastic, nonunitary components for sampling the photonic losses. As core of our method, differentiable tensor-networks are leveraged, which are accurate in the regime of low photonic occupation and modest intermode entanglement. After characterizing the circuit gate architecture with field simulations of GaAs-based samples, we demonstrate the applicability of our method by optimizing quantum photonic circuits for two key use cases: integrated designs for quantum optical state preparation and tailored optimal readout for quantum phase sensing.

DOI
10.48550/arxiv.2509.11861

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Quantum photonic devices are typically based on either discrete variable (DV) or continuous variable (CV) principles. In either case, their performance must meet strict “fidelity” requirements, especially when scaled using integrated photonic circuitry. DV devices must be robust to imperfections such as timing delays between photons, unwanted spectral correlations present in photons from nonideal single photon sources and variations in circuit components. Furthermore, it becomes increasingly important to have a methodology for characterizing the performance of devices in the presence of such errors. Here, we present a method for simulating quantum photonic integrated circuits (PICs) and use it to model the behavior of a circuit constructed to model the evolution of a quantum state subject to a Bose-Hubbard Hamiltonian, introducing variations to the coupling gaps in the directional couplers inside the circuit. Input states consisting of both indistinguishable and distinguishable photons are modelled. Compact models for the directional couplers and other photonic circuit elements that are parameterized for a specific fabrication process can be incorporated into the circuit using a foundry-associated compact model library, ensuring consistency between circuit design and manufactured component. In CV applications, the degree of squeezing provided by some nonlinear element is often a key metric. Here we describe how the degree of squeezing produced by spontaneous four-wave mixing (SFWM) in a microring resonator can be modelled in the low-power limit, accounting for the effects of self-phase modulation (SPM), cross-phase modulation (XPM), and component losses.
Semiconductor quantum dots (QDs) are a type of solid-state quantum emitter that can act as a near-ideal quantum light-matter interface when integrated with high-quality nanophotonic systems. Though QDs have typically been used to create state-of-the-art, on-demand single photon sources, here we widen the perspective on QDs, showing how to design quantum photonic integrated circuits based on both linear and nonlinear QD phase shifters. Specifically, we find that linear QD phase shifters can be used to realize cryogenically-compatible, fast, low-loss, and high-fidelity reconfigurable linear circuits. When paired with QDs that mediate interactions between photonic qubits, generating nonlinear phase shifts, deterministic quantum photonic logic gates can be achieved. Thus, our work paves the way for the realization of on-chip, cryogenically-compatible linear and nonlinear quantum photonic circuits, including quantum photonic neural networks, which can form the foundation for scalable and efficient quantum photonic technologies.