Natalie Chi

EECS Department, University of California, Berkeley

Technical Report No. UCB/

May 1, 2026

This report is delayed

Simulating quantum many-body systems, such as the Transverse-Field Ising Model (TFIM), is fundamentally hindered by the exponential growth of the Hilbert space and the non-commuting nature of quantum operators. Traditional numerical methods often struggle to scale efficiently without encountering severe memory or computational bottlenecks. This thesis presents a highly parallelizable methodology to overcome these limitations by mapping the one-dimensional quantum TFIM onto a two-dimensional classical Ising model, and subsequently solving it using a Convolutional Restricted Boltzmann Machine (CRBM). By leveraging the Suzuki-Trotter decomposition, the 1D quantum Hamiltonian is systematically approximated as a 2D classical network, where the additional dimension represents imaginary time (Trotter slices). To sample the ground-state energy of this mapped system, we utilize a CRBM, which inherently exploits the discrete translational symmetry of the physical lattice. This convolutional approach drastically reduces the parameter count compared to dense, fully connected RBMs, mitigating memory overhead and improving thermalization times. We de- rive the precise analytical weight filters required to encode the classical spatial and temporal interactions directly into the hidden and visible neurons of the neural network. Extensive numerical scaling analyses are performed to validate the architecture, benchmarking the CRBM’s sampled energy against exact Density Matrix Renormalization Group (DMRG) calculations. The results demonstrate that by scaling the Trotter slices appropriately, the Suzuki-Trotter commutator error is effectively suppressed. The CRBM achieves highly accu- rate ground-state energy estimations, maintaining a strict error margin of less than 6 percent for continuous spin chains scaling up to 25 spins across various transverse field strengths. Ulti- mately, this work proves the viability of using physics-informed, probabilistic machine learning models to accelerate the simulation of complex quantum lattice problems.

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BibTeX citation:

@mastersthesis{Chi:32166,
    Author= {Chi, Natalie},
    Title= {Accelerating Quantum Lattice Problem Calculations},
    School= {EECS Department, University of California, Berkeley},
    Year= {2026},
    Month= {May},
    Number= {UCB/},
    Abstract= {Simulating quantum many-body systems, such as the Transverse-Field Ising Model (TFIM), is
fundamentally hindered by the exponential growth of the Hilbert space and the non-commuting
nature of quantum operators. Traditional numerical methods often struggle to scale efficiently
without encountering severe memory or computational bottlenecks. This thesis presents a
highly parallelizable methodology to overcome these limitations by mapping the one-dimensional
quantum TFIM onto a two-dimensional classical Ising model, and subsequently solving it using
a Convolutional Restricted Boltzmann Machine (CRBM).
By leveraging the Suzuki-Trotter decomposition, the 1D quantum Hamiltonian is systematically
approximated as a 2D classical network, where the additional dimension represents imaginary
time (Trotter slices). To sample the ground-state energy of this mapped system, we utilize a
CRBM, which inherently exploits the discrete translational symmetry of the physical lattice.
This convolutional approach drastically reduces the parameter count compared to dense, fully
connected RBMs, mitigating memory overhead and improving thermalization times. We de-
rive the precise analytical weight filters required to encode the classical spatial and temporal
interactions directly into the hidden and visible neurons of the neural network.
Extensive numerical scaling analyses are performed to validate the architecture, benchmarking
the CRBM’s sampled energy against exact Density Matrix Renormalization Group (DMRG)
calculations. The results demonstrate that by scaling the Trotter slices appropriately, the
Suzuki-Trotter commutator error is effectively suppressed. The CRBM achieves highly accu-
rate ground-state energy estimations, maintaining a strict error margin of less than 6 percent
for continuous spin chains scaling up to 25 spins across various transverse field strengths. Ulti-
mately, this work proves the viability of using physics-informed, probabilistic machine learning
models to accelerate the simulation of complex quantum lattice problems.},
}

EndNote citation:

%0 Thesis
%A Chi, Natalie 
%T Accelerating Quantum Lattice Problem Calculations
%I EECS Department, University of California, Berkeley
%D 2026
%8 May 1
%@ UCB/
%F Chi:32166