Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session B21: Machine Learning for Quantum Matter IIFocus Live
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Sponsoring Units: DCOMP GDS DMP Chair: Mohamed Hibat-Allah, University of Waterloo |
Monday, March 15, 2021 11:30AM - 11:42AM Live |
B21.00001: Neural network wave functions and the sign problem Attila Szabo, Claudio Castelnovo Neural quantum states are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Neural networks struggle to converge to ground states with a nontrivial sign structure. In this talk, I present a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent such states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets. In the first case, the neural network correctly recovers the Marshall sign rule without any prior knowledge. For frustrated magnets, our approach uncovers low-energy states that exhibit the Marshall sign rule but does not reach the true ground state, which is expected to have a different sign structure. I discuss strategies for overcoming this "residual sign problem" that may allow using neural quantum states for challenging spin liquid problems. |
Monday, March 15, 2021 11:42AM - 11:54AM Live |
B21.00002: Neural Networks for Analytic Continuation of Response Functions Simon Verret, Reza Nourafkan, Quinton Weyrich, Samuel Desrosiers, A.-M. S. Tremblay In the last few years, it was shown that deep neural networks can outperform Maximum Entropy methods for the analytical continuation of noisy Matsubara Green’s function [1,2,3,4]. Extending these tools to correlation function for transport quantities would be beneficial because, in some cases, such as Hall conductivity and Seebeck effect [5,6], the spectral weight is not strictly positive, restricting the use of the maximum entropy method. In this work, we extend the use of deep neural networks to the case of the longitudinal conductivity, in particular the DC conductivity. We also introduce a rescaling procedure that allows trained networks to generalize to all temperatures. |
Monday, March 15, 2021 11:54AM - 12:06PM Live |
B21.00003: Spiking Neuromorphic Chip Encodes Quantum Entanglement Correlations Stefanie Czischek, Andreas Baumbach, Sebastian Billaudelle, Benjamin Cramer, Lukas Kades, Jan M. Pawlowski, Johannes Schemmel, Markus Oberthaler, Mihai Petrovici, Thomas Gasenzer, Martin Gaerttner Analog neuromorphic chips, inspired by structural and dynamical properties of the biological brain, show a high energy efficiency in running artificial neural-network architectures for the profit of generative applications. Together with recent proposals for artificial neural networks to encode quantum states, this encourages employing such hardware systems as platforms for simulations of quantum system or quantum state tomography. |
Monday, March 15, 2021 12:06PM - 12:42PM Live |
B21.00004: Reinforcement Learning for Many-Body Ground State Preparation based on Counter-Diabatic Driving Invited Speaker: Marin Bukov The Quantum Approximate Optimization Ansatz (QAOA) is a prominent example of variational quantum algorithms. We propose a generalized QAOA ansatz called CD-QAOA, which is inspired by the counter-diabatic (CD) driving procedure, designed for quantum many-body systems, and optimized using a reinforcement learning (RL) approach. The resulting hybrid control algorithm proves versatile in preparing the ground state of quantum-chaotic many-body spin chains, by minimizing the energy. We show that using terms occurring in the adiabatic gauge potential as additional control unitaries, it is possible to achieve fast high-fidelity many-body control away from the adiabatic regime. While each unitary retains the conventional QAOA-intrinsic continuous control degree of freedom such as the time duration, we take into account the order of the multiple available unitaries appearing in the control sequence as an additional discrete optimization problem. Endowing the policy gradient algorithm with an autoregressive deep learning architecture to capture causality, we train the RL agent to construct optimal sequences of unitaries. The algorithm has no access to the quantum state, and we find that the protocol learned on small systems may generalize to larger systems. By scanning a range of protocol durations, we present numerical evidence for a finite quantum speed limit in the nonintegrable mixed-field spin-1/2 Ising model, and for the suitability of the ansatz to prepare ground states of the spin-1 Heisenberg chain in the long-range and topologically ordered parameter regimes. This work paves the way to incorporate recent success from deep learning for the purpose of quantum many-body control. |
Monday, March 15, 2021 12:42PM - 12:54PM Live |
B21.00005: Entanglement and Tensor Networks for Supervised Image Classification John Martyn, Guifre Vidal, Chase Roberts, Stefan Leichenauer Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, while the success of tensor network approaches in quantum physics is well understood, very little is known about why these techniques work for machine learning. Here, we investigate entanglement properties of tensor network models in current machine learning applications in order to uncover general principles that may guide future developments. We revisit the use of tensor networks for supervised image classification, as pioneered by Stoudenmire and Schwab. Firstly, we hypothesize a plausible candidate state that the tensor network might learn during training and discover that this hypothesis state is too entangled to be approximated by the tensor networks used in previous works, indicating that tensor networks must learn a very different state. Secondly, we use tensor networks with a block product structure and find that these states are extremely expressive, suggesting that long-range entanglement may not be essential for image classification. However, in our current implementation, optimization leads to overfitting, resulting in test accuracies that are not competitive with other current approaches. |
Monday, March 15, 2021 12:54PM - 1:06PM Live |
B21.00006: Continuous monitoring and feedback control of qubit dynamics using differentiable programming Frank Schäfer, Pavel Sekatski, Martin Koppenhoefer, Niels Loerch, Christoph Bruder, Michal Kloc In quantum state control, protocols that allow one to prepare desired target states are developed. Starting from a distribution of initial states, we aim to find the optimal control scheme to fulfill the control task over a certain time interval. The dynamics of a (dissipative) quantum system can be described by a (stochastic) Schrödinger equation. Thus, given an initial state and a sequence of all measurement results, it is conceptually straightforward to determine the time evolution of the system. However, solving the control problem by deriving a performant control scheme is generally hard. |
Monday, March 15, 2021 1:06PM - 1:18PM Live |
B21.00007: Machine Learned Predictions of Complex Quantities from Differentiable Networks Olivier Malenfant-Thuot, Kevin Ryczko, Isaac Tamblyn, Michel Cote The use of machine learning methods in condensed matter simulation presents some advantages in comparison to ab initio methods. Notably, using a trained model to calculate properties of a system can often be orders of magnitude faster than doing a DFT calculation, with a similar level of accuracy. However, a significant amount of data must be generated beforehand, which can cancel this advantage, especially when studying more complex quantities, such as vibrational properties and Raman spectra. |
Monday, March 15, 2021 1:18PM - 1:30PM Live |
B21.00008: Mitigating sign problem by automatic differentiation Zhouquan Wan, Shixin Zhang, Hong Yao As an intrinsically-unbiased method, quantum Monte Carlo (QMC) is of unique importance in simulating interacting quantum systems. Unfortunately, QMC often suffers from the notorious sign problem. Although generically curing sign problem is shown to be hard (NP-hard), sign problem of a given quantum model may be mitigated (sometimes even cured) by finding better choices of simulation scheme. A universal framework in identifying optimal QMC schemes has been desired. Here, we propose a general framework using automatic differentiation (AD) to automatically search for the best continuously-parameterized QMC scheme, which we call “automatic differentiable sign mitigation” (ADSM). As a showcase, we apply the ADSM framework to the honeycomb lattice Hubbard model with Rashba spin-orbit coupling and demonstrate ADSM’s effectiveness in mitigating its sign problem. For the model under study, ADSM leads a significant power-law acceleration in computation time (the computation time is reduced from M to the order of Mν with ν ≈ 2/3). |
Monday, March 15, 2021 1:30PM - 2:06PM Live |
B21.00009: Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines Invited Speaker: Estelle Inack Projective quantum Monte Carlo (QMC) simulations have been successfully used to simulate various relevant quantum many-body systems. They are systematically implemented in a two-step approach, in which a variational ansatz inspired by theory is first optimized using traditional variational optimization techniques. Later, the optimized ansatz is used as a guiding wave function in projective QMC simulations. In this work, we present a novel method that uses unsupervised machine learning techniques to combine the two steps above. It adaptively trains the guiding wave function (represented by a restricted Boltzmann machine) within QMC simulations, thus avoiding the need for separate variational optimization. On the one hand, this approach greatly increases the efficiency and accuracy of projective QMC simulations. On the other hand, it provides a new way to develop ground-state ansatzes, complementary to the common variational optimization schemes. We present extensive benchmarks that demonstrate the efficiency of our self-learning method. |
Monday, March 15, 2021 2:06PM - 2:18PM Live |
B21.00010: Improving training schemes for encoding quantum states on neuromorphic hardware Robert Klassert, Stefanie Czischek, Andreas Baumbach, Martin Gärttner, Thomas Gasenzer In recent years neural network quantum states have been |
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