Transferable Equivariant Quantum Circuits for TSP: Generalization Bounds and Empirical Validation

• URL: http://arxiv.org/abs/2510.14533v1
• Date: Thu, 16 Oct 2025 10:25:14 GMT
• Title: Transferable Equivariant Quantum Circuits for TSP: Generalization Bounds and Empirical Validation
• Authors: Monit Sharma, Hoong Chuin Lau,
• Abstract summary: We address the challenge of generalization in quantum reinforcement learning (QRL) for optimization, focusing on the Traveling Salesman Problem (TSP)<n>To mitigate this, we employed Equivariant Quantum Circuits (EQCs) that respect the permutation symmetry of the TSP graph.<n>This symmetry-aware ansatz enabled zero-shot transfer of trained parameters from $n-$city training instances to larger m-city problems.
• Score: 3.652509571098291
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we address the challenge of generalization in quantum reinforcement learning (QRL) for combinatorial optimization, focusing on the Traveling Salesman Problem (TSP). Training quantum policies on large TSP instances is often infeasible, so existing QRL approaches are limited to small-scale problems. To mitigate this, we employed Equivariant Quantum Circuits (EQCs) that respect the permutation symmetry of the TSP graph. This symmetry-aware ansatz enabled zero-shot transfer of trained parameters from $n-$city training instances to larger m-city problems. Building on recent theory showing that equivariant architectures avoid barren plateaus and generalize well, we derived novel generalization bounds for the transfer setting. Our analysis introduces a term quantifying the structural dissimilarity between $n-$ and $m-$node TSPs, yielding an upper bound on performance loss under transfer. Empirically, we trained EQC-based policies on small $n-$city TSPs and evaluated them on larger instances, finding that they retained strong performance zero-shot and further improved with fine-tuning, consistent with classical observations of positive transfer between scales. These results demonstrate that embedding permutation symmetry into quantum models yields scalable QRL solutions for combinatorial tasks, highlighting the crucial role of equivariance in transferable quantum learning.

Related papers

• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• TensoMeta-VQC: A Tensor-Train-Guided Meta-Learning Framework for Robust and Scalable Variational Quantum Computing [60.996803677584424]
  TensoMeta-VQC is a novel tensor-train (TT)-guided meta-learning framework designed to improve the robustness and scalability of VQC significantly.<n>Our framework fully delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware.
  arXiv  Detail & Related papers  (2025-08-01T23:37:55Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning [5.673361333697935]
  Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning (Dist-QTRL)<n>We introduce Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning (Dist-QTRL)
  arXiv  Detail & Related papers  (2024-12-12T00:51:41Z)
• Projective Quantum Eigensolver with Generalized Operators [0.0]
  We develop a methodology for determining the generalized operators in terms of a closed form residual equations in the PQE framework. With the application on several molecular systems, we have demonstrated our ansatz achieves similar accuracy to the (disentangled) UCC with singles, doubles and triples.
  arXiv  Detail & Related papers  (2024-10-21T15:40:22Z)
• Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits [70.97518416003358]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning on noisy intermediate-scale quantum (NISQ) devices. While tensor-train networks (TTNs) can enhance VQC representation and generalization, the resulting hybrid model, TTN-VQC, faces optimization challenges due to the Polyak-Lojasiewicz (PL) condition. To mitigate this challenge, we introduce Pre+TTN-VQC, a pre-trained TTN model combined with a VQC.
  arXiv  Detail & Related papers  (2023-05-18T03:08:18Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems [0.0]
  Current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as variational quantum eigensolver (VQE) In this study, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively. We demonstrate that symmetry-projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations.
  arXiv  Detail & Related papers  (2022-05-14T17:08:18Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Non-trivial symmetries in quantum landscapes and their resilience to quantum noise [0.0]
  Parametrized Quantum Circuits (PQCs) are employed in Quantum Neural Networks and Variational Quantum Algorithms. We find an exponentially large symmetry in PQCs, yielding an exponentially large degeneracy of the minima in the cost landscape. We introduce an optimization method called Symmetry-based Minima Hopping (SYMH), which exploits the underlying symmetries in PQCs.
  arXiv  Detail & Related papers  (2020-11-17T16:43:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.