Seeding neural network quantum states with tensor network states

• URL: http://arxiv.org/abs/2506.23550v2
• Date: Tue, 15 Jul 2025 03:56:08 GMT
• Title: Seeding neural network quantum states with tensor network states
• Authors: Ryui Kaneko, Shimpei Goto,
• Abstract summary: We find an efficient approach to convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial unit.<n>This method allows us to generate hidden initial neural network quantum states for many-body ground-state calculations.<n>We discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This method allows us to generate well-behaved initial neural network quantum states for quantum many-body ground-state calculations in polynomial time of the number of variational parameters and systematically shorten the distance between the initial states and the ground states with increasing the rank of the CP decomposition. We demonstrate the efficiency of our method by taking the transverse-field Ising model as an example and discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.

Related papers

• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Variational Quantum Simulation of the Interacting Schwinger Model on a Trapped-Ion Quantum Processor [26.47874938214435]
  In this work, we explore the multi-flavor lattice Schwinger model - a toy model inspired by quantum chromodynamics.<n>We employ a parametric quantum circuit executed on our quantum processor to identify ground states in different parameter regimes of the model.<n>The resulting states are analyzed via quantum state tomography, to reveal how characteristic properties such as correlations in the output state change.
  arXiv  Detail & Related papers  (2025-04-29T14:43:57Z)
• Tensor Cross Interpolation of Purities in Quantum Many-Body Systems [0.0]
  In quantum many-body systems the exponential scaling of the Hilbert space with the number of degrees of freedom renders a complete state characterization.<n>Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed.<n>In this work, we demonstrate that the entanglement feature can be efficiently defining using only a amount of samples in the number of degrees of freedom.
  arXiv  Detail & Related papers  (2025-03-21T15:33:00Z)
• Exploring quantum localization with machine learning [39.58317527488534]
  We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the pattern recognition capabilities of a modified convolutional model.
  arXiv  Detail & Related papers  (2024-06-01T08:50:26Z)
• Quantum quench dynamics as a shortcut to adiabaticity [31.114245664719455]
  We develop and test a quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. Our experiments show that this approach significantly outperforms the adiabatic algorithm.
  arXiv  Detail & Related papers  (2024-05-31T17:07:43Z)
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers [0.0]
  We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems.<n>We demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example.
  arXiv  Detail & Related papers  (2023-09-26T18:01:42Z)
• Coherent-State Ladder Time-Dependent Variational Principle for Open Quantum Systems [0.0]
  We present a new paradigm for the dynamical simulation of interacting bosonic systems. The method relies on a variational ansatz for the $n$-boson density matrix, in terms of a superposition of photon-added coherent states. We test our method on several examples, demonstrating its potential application to the predictive simulation of interacting bosonic systems and cat qubits.
  arXiv  Detail & Related papers  (2023-06-23T18:00:00Z)
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas [41.94295877935867]
  We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions.
  arXiv  Detail & Related papers  (2023-05-12T04:12:04Z)
• Efficiency of neural-network state representations of one-dimensional quantum spin systems [0.0]
  We study the Boltzmann machine (RBM) state representation of one-dimensional (1D) quantum spin systems. We define a class of long-rangefastdecay (LRFD) RBM states with quantifiable upper bounds on truncation errors. We conjecture that the ground states of a wide range of quantum systems may be exactly represented by LRFD RBMs or a variant of them.
  arXiv  Detail & Related papers  (2023-02-01T01:44:03Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• 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)
• Fock-space Schrieffer--Wolff transformation: classically-assisted rank-reduced quantum phase estimation algorithm [0.0]
  In this paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic Hamiltonians for molecular systems. We demonstrate that by employing Fock-space variants of the SW transformation one can significantly increase the locality of the qubit-mapped similarity transformed Hamiltonians. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.
  arXiv  Detail & Related papers  (2022-11-18T23:06:57Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences [41.42601188771239]
  We create non-classical states of light in three-dimensional microwave cavities. These states are useful for quantum computation. We show that this way of creating non-classical states is robust to fluctuations of the system parameters.
  arXiv  Detail & Related papers  (2021-11-15T18:20:38Z)
• Learning quantum many-body systems from a few copies [1.5229257192293197]
  Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. We identify conditions on states under which it is possible to infer the expectation values of all quasi-local observables of a state. We show that this constitutes a provable exponential improvement in the number of copies over state-of-the-art tomography protocols.
  arXiv  Detail & Related papers  (2021-07-07T16:21:51Z)

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.