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IEEE International Conference on Quantum Computing and Engineering (QCE)

Towards Synalgebraic Photonic Quantum Computing

Anderson Beraldo de Araujo

Published Aug 30, 2025• 1 citation
Publisher

Abstract

This article introduces a novel algebraic-logical formalism, called synalgebra, for describing, simulating, and reasoning about photonic quantum circuits. Existing approaches are typically limited to either descriptive languages or circuit simulators. In contrast, synalgebra employs the new concept of intergraphs as a core data structure for equational reasoning about photonic circuit architectures. Specifically, the article presents preliminary simulations of the variational quantum eigensolver (VQE) algorithm for up to 100 qubits, demonstrating how synalgebra can support higher-level abstractions of VQE as well as hardware optimization of photonic waveguides.

DOI
10.1109/qce65121.2025.00166

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This article introduces a novel algebraic-logical formalism, called synalgebra, for describing, simulating, and reasoning about photonic quantum circuits. Existing approaches are typically limited to either descriptive languages or circuit simulators. In contrast, synalgebra employs the new concept of intergraphs as a core data structure for equational reasoning about photonic circuit architectures. Specifically, the article presents preliminary simulations of the variational quantum eigensolver (VQE) algorithm for up to 100 qubits, demonstrating how synalgebra can support higher-level abstractions of VQE as well as hardware optimization of photonic waveguides.
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Quantum computers have the potential to deliver speed-ups for solving certain important problems that are intractable for classical counterparts, making them a promising avenue for advancing modern computation. However, many quantum algorithms require deep quantum circuits, which are challenging to implement on current noisy devices. To address this limitation, variational quantum algorithms (VQAs) have been actively developed, enabling practical quantum computing in the noisy intermediate-scale quantum (NISQ) era. Among them, the variational quantum eigensolver (VQE) stands out as a leading approach for solving problems in quantum chemistry, many-body physics, and even integer factorization. The VQE algorithm can be implemented on various quantum hardware platforms, including photonic systems, quantum dots, trapped ions, neutral atoms, and superconducting circuits. In particular, photonic platforms offer several advantages: they operate at room temperature, exhibit low decoherence, and support multiple degrees of freedom, making them suitable for scalable, high-dimensional quantum computation. Here we present methodologies for realizing VQE on photonic systems, highlighting their potential for practical quantum computing. We first provide a theoretical overview of the VQE framework, focusing on the procedure for variationally estimating ground state energies. We then explore how photonic systems can implement these processes, showing that a wide variety of problems can be addressed using either multiple qubit states or a single qudit state.
This report introduces a novel class of reasoning architectures, termed Quantum Circuit Reasoning Models (QCRM), which extend the concept of Variational Quantum Circuits (VQC) from energy minimization and classification tasks to structured logical inference and reasoning. We posit that fundamental quantum mechanical operations, superposition, entanglement, interference, and measurement, naturally map to essential reasoning primitives such as hypothesis branching, constraint propagation, consistency enforcement, and decision making. The resulting framework combines quantum-inspired computation with differentiable optimization, enabling reasoning to emerge as a process of amplitude evolution and interference-driven selection of self-consistent states. We develop the mathematical foundation of QCRM, define its parameterized circuit architecture, and show how logical rules can be encoded as unitary transformations over proposition-qubit states. We further formalize a training objective grounded in classical gradient descent over circuit parameters and discuss simulation-based implementations on classical hardware. Finally, we propose the Quantum Reasoning Layer (QRL) as a differentiable hybrid component for composable reasoning models applicable to scientific, biomedical, and chemical inference domains.
Following the simple observation that the interconnection of a set of quantum optical input-output devices can be specified using structural mode VHSIC hardware description language, we demonstrate a computer-aided schematic capture workflow for modelling and simulating multi-component photonic circuits. We describe an algorithm for parsing circuit descriptions to derive quantum equations of motion, illustrate our approach using simple examples based on linear and cavity-nonlinear optical components, and demonstrate a computational approach to hierarchical model reduction.
The Variational Quantum Eigensolver (VQE) has become a central hybrid quantum-classical method for addressing electronic structure and materials science problems on near-term quantum hardware. As researchers across physics, chemistry, and quantum information engage with VQE, they encounter a wide range of algorithmic choices, including problem encoding, ansatz construction, classical optimization, and measurement strategies to choose from. This article provides a structured overview of these components and discusses practical factors that influence VQE performance in real settings, such as noise characteristics, available error-mitigation techniques, and hardware-dependent circuit considerations. Drawing partly on our early experiences, we highlight aspects that may be especially relevant for newcomers and outline common challenges observed in practical workflows. Our aim is to offer an accessible entry point for researchers approaching VQE-based quantum simulation and to support informed decision-making as the method and underlying hardware continue to evolve, which we support by discussion of examples from physics and quantum chemistry.