Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session M62: Machine Learning for Quantum Matter IIIFocus
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Sponsoring Units: DCOMP Chair: George Booth, King's College London Room: Room 417 |
Wednesday, March 8, 2023 8:00AM - 8:36AM |
M62.00001: Simulating non-equilibrium quantum matter with neural quantum states Invited Speaker: Markus Schmitt The numerical simulation of many-body quantum dynamics constitutes a pivotal challenge of computational physics due to the typical growth of entanglement in the course of the evolution. I will discuss how combining the time-dependent variational principle with artificial neural networks as ansatz for the variational wave function allows us to overcome some of the current limitations. As an application I will address quantum phase transition dynamics in two spatial dimensions of a model that is experimentally realized in Rydberg quantum simulators. |
Wednesday, March 8, 2023 8:36AM - 8:48AM |
M62.00002: Recurrent Neural Network approximations of thermal states through Rényi ensembles Andrew Jreissaty, Juan Carrasquilla Recurrent neural networks have been shown to be effective variational ansatze for the representation of ground state wavefunctions of strongly correlated Hamiltonians. Their autoregressive nature allows for the efficient generation of samples and their expressivity allows for excellent variational exploration of the optimization landscape. In this work, we use recurrent neural networks (RNNs) to approximate density matrices at thermal equilibrium, focusing our initial efforts on various strongly correlated spin Hamiltonians. Instead of the Gibbs ensemble, we use the thermodynamic ensembles that minimize the Rényi free energy introduced in Phys. Rev. B 103, 205128 (2021). We find that our optimized density matrices perform very well compared to the analytically derived density matrices that minimize the Renyi free energy for several quantum spin systems. |
Wednesday, March 8, 2023 8:48AM - 9:00AM |
M62.00003: Quantum-Inspired Tempering for Ground State Approximation using Artificial Neural Networks Conor Smith, Tameem Albash, Quinn Campbell, Andrew D Baczewski Parameterized artificial neural networks (ANNs) have been shown to efficiently approximate to high accuracy ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update the ANN parameters can get trapped in local minima even if the ANN is sufficiently expressive. To escape these local minima, we propose a method inspired by quantum parallel tempering, where we train multiple ANNs governed by Hamiltonians with different "driver" strengths and allow for the exchange of neighboring ANN parameterizations after a fixed number of training steps. We study instances from two classes of Hamiltonians. The first is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it to a false minimum. The second is the second quantized electronic structure Hamiltonian of four Hydrogen atoms arranged in a rectangle, which is then discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem's small size. We show that our quantum parallel tempering inspired method is useful for finding good approximations to the ground states of these problems. |
Wednesday, March 8, 2023 9:00AM - 9:12AM |
M62.00004: Bounding errors in Neural Quantum Dynamics Filippo Vicentini, Giuseppe Carleo Integrating the Schroedinger's equation for a Many-Body Quantum System is a challenging task whose complexity grows exponentially with the number of degrees of freedom. Variational ansatzes for the Wave-Function such as Neural Quantum States (NQS) have been shown to avoid such exponential growth in the complexity by foregoing an exact description. While NQS have produced state-of-the-art results in computations involving the physical properties of the ground- and excited-states of hamiltonians, their results when integrating the variational dynamics induced by the same hamiltonians are limited. A major issue plaguing the variational dynamics is the emergence of two different, competing timescales relating to the Many-Body Hamiltonian and to the nonlinear parametrisation of the Hilbert Space. In this contribution I will show how to quantify such time-scales and use such knowledge to better solve the problem of the variational dynamics with Neural Quantum States. |
Wednesday, March 8, 2023 9:12AM - 9:24AM |
M62.00005: Efficient Study of Finite Temperature Dynamics using Isometrically Compressed Purification MPS Sajant Anand, Michael P Zaletel, Johannes Hauschild A standard approach for studying quantum systems at finite temperature is to represent the thermal density matrix as a purification matrix product state (MPS), a pure state with additional ancilla degrees of freedom. The increased bond dimension due to the ancilla degrees of freedom makes the study of low temperature physics computationally expensive. Here, inspired by the unitary gauge freedom on the ancilla legs and algorithms introduced in the context of two-dimensional isometric tensor networks, we demonstrate that the ancillas can be dynamically discarded as the purification MPS is cooled from infinite temperature towards the ground state. This approach produces a lower bond dimension purification MPS than achievable with existing methods. Coupled with a novel sampling scheme to extract independently distributed computational-basis "snapshots" from a purification MPS, this method can be used to simulate and benchmark cold atom and quantum computing experiments in which individual atoms/qubits are projectively measured. |
Wednesday, March 8, 2023 9:24AM - 9:36AM |
M62.00006: Gradient-Based Algorithms for Infinite Strip Tensor Network States Sajant Anand, Sheng-Hsuan Lin, Yantao Wu, Michael P Zaletel, Frank Pollmann, Laurens Vanderstraeten Matrix-product state (MPS) methods have proven to be successful numerical and analytical tools for studying one-dimensional (1D) quantum many-body systems. MPS methods are also used extensively for systems on quasi-two-dimensional (2D) geometries, e.g., infinite cylinder, despite the exponential scaling in the computational complexity in system width. In this work, we consider the setup of 2D tensor network states (TNS) on finite by infinite lattices, which differs from the typical setup of finite by finite or infinite by infinite geometries. We develop gradient-based algorithms with both 2D TNS and 2D isometric TNS (isoTNS) for finding the ground states of the given Hamiltonian and finding the state with the maximum overlap with the given state. The latter algorithm leads to the applications including (i) quantum state compression, (ii) transforming TNS into isoTNS, and (iii) time evolution algorithm. We benchmark the aforementioned algorithms on the transverse field Ising model and compare the result with the MPS-based algorithm and the isoTNS-based algorithm. |
Wednesday, March 8, 2023 9:36AM - 9:48AM |
M62.00007: Transformer Quantum State: A Multi-Purpose Model for Quantum Many-Body Problems Yuan-Hang Zhang, Massimiliano Di Ventra Recent advancements in machine learning have led to the introduction of the transformer, a versatile, task-agnostic architecture with minimal requirements for hand-crafting features across different tasks. Here, we show that with appropriate modifications, such an architecture is well suited as a multi-purpose model for the solution of quantum many-body problems. We call the resulting model the transformer quantum state (TQS). In sharp contrast to previous Hamiltonian/task-specific models, TQS is capable of generating the entire phase diagram, predicting field strengths with as few as one experimental measurement, and transferring such knowledge to new systems it has never seen before, all within a single model. When focusing on a specific task, fine-tuning on a pre-trained TQS produces high-accuracy results with small computational cost. Versatile by design, the TQS architecture can be easily adapted to new tasks, thereby pointing towards a general-purpose model for various challenging quantum problems. |
Wednesday, March 8, 2023 9:48AM - 10:00AM |
M62.00008: Applying the Variational Principle to Quantum Field Theory with Neural-Networks John M Martyn, Di Luo, Khadijeh Najafi Physicists dating back to Feynman have lamented the challenges of applying the variational principle to quantum field theories, most notably evaluating and optimizing expectation values of a quantum field state. In the context of non-relativistic quantum field theories, this approach requires one to parameterize and optimize over the infinitely many n-particle wave functions comprising the state's Fock space representation, a seemingly daunting task. In this Letter, we introduce a variational ansatz to enable the application of the variational principle to 1D bosonic quantum field theories directly in the continuum. Our ansatz is a neural-network quantum state, and uses the Fock space representation to model a quantum field state as a superposition of n-particle wave functions, each of which is parameterized by a common neural-network architecture that is both permutation-invariant and able to accept an arbitrary number of arguments. We develop a novel algorithm for variational Monte Carlo in Fock space and employ it on our ansatz to approximate ground states of the Lieb-Liniger model, the Calogero-Sutherland model, and a regularized Klein-Gordon model. Our ansatz can be seen as the neural-network-based analog of continuous matrix product states, which have traditionally been deployed on 1D field theories but struggle on inhomogenous systems and long-range interactions. The utility of our ansatz lies in its flexibility and broad applicability to such systems, providing a powerful new tool for probing quantum field theories. |
Wednesday, March 8, 2023 10:00AM - 10:12AM |
M62.00009: Simulating 2+1D Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions Zhuo Chen, Di Luo, Kaiwen Hu, Bryan K Clark We variationally simulate the 2+1D quantum electrodynamics with finite density dynamical fermions using a newly developed neural flow wavefunction, Gauge-Fermion FlowNet. The Gauge-Fermion FlowNet allows us to study the U(1) gauge theory with no truncation. It obeys Gauss's law by construction, performs autoregressive sampling without equilibration time, and simulates gauge-fermion systems with sign problems. Using our approach, we first study the string breaking phenomena in the U(1) gauge theory. Then we investigate the phase transition from the vacuum phase to the charge crystal phase due to the effect the electric field energy and the fermion mass at both the zero and finite density regime. In addition, we find a phase transition in the magnetic field driven by the competition between the kinetic energy of fermions and the magnetic energy of the gauge field. Our neural network methods provide state-of-the-art tools for studying various lattice gauge theories coupled to matter. |
Wednesday, March 8, 2023 10:12AM - 10:24AM |
M62.00010: Neutron matter Variational Monte Carlo calculations with artificial neural network wave functions Bryce Fore We utilize the hidden-fermion family of neural network quantum states as the wave function ansatz for Variational Monte Carlo (VMC) calculations of periodic neutron matter. This same method has been used to accurately approximate wave functions for nuclei as large as 16O. The trained neural network wave functions have approximately the same energies predicted by previous Diffusion Monte Carlo (DMC) calculations. Using the same wave functions we compute singlet and triplet channel pair distribution functions and find evidence of pairing in the singlet channel at low densities, signaling the expected neutron superfluid. We will soon be able to apply these techniques to more realistic nuclear potentials to obtain even more accurate neutron matter wave functions. |
Wednesday, March 8, 2023 10:24AM - 10:36AM |
M62.00011: Efficient and scalable modeling of strongly correlated electronic systems with NQS in continuous space Gabriel M Pescia In recent years, neural network quantum states (NQS) have become a viable tool to tackle the simulation of the ground-state of strongly interacting many-body quantum systems defined in continuous space. While the first applications of these methods have been focused on the simulation of molecules, we broadened their scope to the simulation of extended systems by encorporating periodic boundary conditions to the NQS.1 Most accurate NQS architectures are still restricted to rather small system sizes due to their need for a very high number of parameters to reach the accuracy of more traditional state-of-the-art methods. |
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