Equivariant quantum circuits for learning on weighted graphs

• URL: http://arxiv.org/abs/2205.06109v2
• Date: Mon, 24 Apr 2023 07:15:48 GMT
• Title: Equivariant quantum circuits for learning on weighted graphs
• Authors: Andrea Skolik, Michele Cattelan, Sheir Yarkoni, Thomas B\"ack, Vedran Dunjko
• Abstract summary: We introduce an ansatz for learning tasks on weighted graphs. We evaluate the performance of this ansatz on a complex learning task, namely neural optimization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.

Related papers

• Reinforcement Learning for Variational Quantum Circuits Design [10.136215038345012]
  Variational Quantum Algorithms have emerged as promising tools for solving optimization problems on quantum computers. In this study, we leverage the powerful and flexible Reinforcement Learning paradigm to train an agent capable of autonomously generating quantum circuits. Our results indicate that the $R_yz$-connected circuit achieves high approximation ratios for Maximum Cut problems.
  arXiv  Detail & Related papers  (2024-09-09T10:07:12Z)
• On the relation between trainability and dequantization of variational quantum learning models [1.7999333451993955]
  We study the relation between trainability and dequantization of variational quantum machine learning (QML) We introduce recipes for building PQC-based QML models which are both trainable and nondequantizable. Our work however does point toward a way forward for finding more general constructions, for which finding applications may become feasible.
  arXiv  Detail & Related papers  (2024-06-11T08:59:20Z)
• Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimization [2.536162003546062]
  We introduce Hamiltonian-based Quantum Reinforcement Learning (QRL) an approach at the intersection of Quantum Computing (QC) and Neuralial Optimization (NCO) Our ansatzes show favourable trainability properties when compared to the hardware efficient ansatzes, while also not being limited to graph-based problems, unlike previous works. In this work, we evaluate the performance of Hamiltonian-based QRL on a diverse set of optimization problems to demonstrate the broad applicability of our approach and compare it to QAOA.
  arXiv  Detail & Related papers  (2024-05-13T14:36:22Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms [65.268245109828]
  We take inspiration from Kearns' SQ oracle and Valiant's weak evaluation oracle. We introduce an extensive yet intuitive framework that yields unconditional lower bounds for learning from evaluation queries.
  arXiv  Detail & Related papers  (2023-10-26T18:23:21Z)
• QNEAT: Natural Evolution of Variational Quantum Circuit Architecture [95.29334926638462]
  We focus on variational quantum circuits (VQC), which emerged as the most promising candidates for the quantum counterpart of neural networks. Although showing promising results, VQCs can be hard to train because of different issues, e.g., barren plateau, periodicity of the weights, or choice of architecture. We propose a gradient-free algorithm inspired by natural evolution to optimize both the weights and the architecture of the VQC.
  arXiv  Detail & Related papers  (2023-04-14T08:03:20Z)
• A didactic approach to quantum machine learning with a single qubit [68.8204255655161]
  We focus on the case of learning with a single qubit, using data re-uploading techniques. We implement the different proposed formulations in toy and real-world datasets using the qiskit quantum computing SDK.
  arXiv  Detail & Related papers  (2022-11-23T18:25:32Z)
• Diagrammatic Analysis for Parameterized Quantum Circuits [0.0]
  We describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits. We provide several new ZX-diagram rewrite rules and generalizations for this setting. We demonstrate that the diagrammatic approach offers useful insights into algorithm structure and performance.
  arXiv  Detail & Related papers  (2022-04-04T08:26:20Z)
• Quantum circuit architecture search on a superconducting processor [56.04169357427682]
  Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability. We demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique to enhance VQAs on an 8-qubit superconducting quantum processor.
  arXiv  Detail & Related papers  (2022-01-04T01:53:42Z)
• Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits [15.279642278652654]
  We present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
  arXiv  Detail & Related papers  (2021-12-21T12:41:31Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)

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.