Dynamical simulation via quantum machine learning with provable generalization

• URL: http://arxiv.org/abs/2204.10269v1
• Date: Thu, 21 Apr 2022 17:15:24 GMT
• Title: Dynamical simulation via quantum machine learning with provable generalization
• Authors: Joe Gibbs, Zo\"e Holmes, Matthias C. Caro, Nicholas Ezzell, Hsin-Yuan Huang, Lukasz Cincio, Andrew T. Sornborger, and Patrick J. Coles
• Abstract summary: We develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We rigorously analyze the training data requirements of an algorithm within this framework. Our numerics exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota.
• Score: 2.061594137938085
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. This provides a guarantee that our algorithm is resource-efficient, both in terms of qubit and data requirements. Our numerics exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Higher order quantum reservoir computing for non-intrusive reduced-order models [0.0]
  Quantum reservoir computing technique (QRC) is a hybrid quantum-classical framework employing an ensemble of interconnected small quantum systems. We show that QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner.
  arXiv  Detail & Related papers  (2024-07-31T13:37:04Z)
• Compact quantum algorithms for time-dependent differential equations [0.0]
  We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems. We generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations.
  arXiv  Detail & Related papers  (2024-05-16T02:14:58Z)
• Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation [49.1574468325115]
  This study presents the theoretical background and the hardware aware circuit implementation of a quantum tunneling simulation. We use error mitigation techniques (ZNE and REM) and multiprogramming of the quantum chip for solving the hardware under-utilization problem.
  arXiv  Detail & Related papers  (2024-04-10T14:27:07Z)
• Benchmarking Quantum Generative Learning: A Study on Scalability and Noise Resilience using QUARK [0.3624329910445628]
  This paper investigates the scalability and noise resilience of quantum generative learning applications. We employ rigorous benchmarking techniques to track progress and identify challenges in scaling QML algorithms. We show that QGANs are not as affected by the curse of dimensionality as QCBMs and to which extent QCBMs are resilient to noise.
  arXiv  Detail & Related papers  (2024-03-27T15:05:55Z)
• Quantum-Assisted Simulation: A Framework for Developing Machine Learning Models in Quantum Computing [0.0]
  We investigate the history of quantum computing, examine existing QML algorithms, and present a simplified procedure for setting up simulations of QML algorithms. We conduct simulations on a dataset using both traditional machine learning and quantum machine learning approaches.
  arXiv  Detail & Related papers  (2023-11-17T07:33:42Z)
• Classical-to-Quantum Transfer Learning Facilitates Machine Learning with Variational Quantum Circuit [62.55763504085508]
  We prove that a classical-to-quantum transfer learning architecture using a Variational Quantum Circuit (VQC) improves the representation and generalization (estimation error) capabilities of the VQC model. We show that the architecture of classical-to-quantum transfer learning leverages pre-trained classical generative AI models, making it easier to find the optimal parameters for the VQC in the training stage.
  arXiv  Detail & Related papers  (2023-05-18T03:08:18Z)
• Scalable Quantum Computation of Highly Excited Eigenstates with Spectral Transforms [0.76146285961466]
  We use the HHL algorithm to prepare excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is enabled by the efficient computation of the expectation values of inverse Hamiltonians on quantum computers. We detail implementations of this scheme for both fault-tolerant and near-term quantum computers.
  arXiv  Detail & Related papers  (2023-02-13T19:01:02Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)

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.