Hybrid quantum-classical reservoir computing of thermal convection flow

• URL: http://arxiv.org/abs/2204.13951v2
• Date: Mon, 8 Aug 2022 16:41:06 GMT
• Title: Hybrid quantum-classical reservoir computing of thermal convection flow
• Authors: Philipp Pfeffer, Florian Heyder, J\"org Schumacher
• Abstract summary: We simulate the chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with 3 and 8 degrees of freedom. The high-dimensional quantum reservoir dynamics are established by universal quantum gates that rotate and entangle the individual qubits of the tensor product quantum state. Our work thus opens the door to model the dynamics of classical complex systems in a high-dimensional phase space effectively with an algorithm that requires a small number of qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We simulate the nonlinear chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with 3 and 8 degrees of freedom by a hybrid quantum--classical reservoir computing model. The high-dimensional quantum reservoir dynamics are established by universal quantum gates that rotate and entangle the individual qubits of the tensor product quantum state. A comparison of the quantum reservoir computing model with its classical counterpart shows that the same prediction and reconstruction capabilities of classical reservoirs with thousands of perceptrons can be obtained by a few strongly entangled qubits. We demonstrate that the mean squared error between model output and ground truth in the test phase of the quantum reservoir computing algorithm increases when the reservoir is decomposed into separable subsets of qubits. Furthermore, the quantum reservoir computing model is implemented on a real noisy IBM quantum computer for up to 7 qubits. Our work thus opens the door to model the dynamics of classical complex systems in a high-dimensional phase space effectively with an algorithm that requires a small number of qubits.

Related papers

• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• 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)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• Reduced-order modeling of two-dimensional turbulent Rayleigh-B\'enard flow by hybrid quantum-classical reservoir computing [0.0]
  Two hybrid quantum-classical reservoir computing models are presented to reproduce low-order statistical properties of a turbulent Rayleigh-B'enard convection flow. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared to the classical reservoir network.
  arXiv  Detail & Related papers  (2023-07-06T15:17:54Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Entanglement Forging with generative neural network models [0.0]
  We show that a hybrid quantum-classical variational ans"atze can forge entanglement to lower quantum resource overhead. The method is efficient in terms of the number of measurements required to achieve fixed precision on expected values of observables.
  arXiv  Detail & Related papers  (2022-05-02T14:29:17Z)
• Expanding variational quantum eigensolvers to larger systems by dividing the calculations between classical and quantum hardware [0.0]
  We present a hybrid classical/quantum algorithm for efficiently solving the eigenvalue problem of many-particle Hamiltonians on quantum computers with limited resources. This algorithm reduces the needed number of qubits at the expense of an increased number of quantum evaluations.
  arXiv  Detail & Related papers  (2021-12-09T17:37:41Z)
• Phase diagram of quantum generalized Potts-Hopfield neural networks [0.0]
  We introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network. The dynamics of this many-body system is formulated in terms of a Markovian master equation of Lindblad type.
  arXiv  Detail & Related papers  (2021-09-21T12:48:49Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• 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)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)

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.