468 citations · 1k across the 30 of their papers we have counts for
30 papers
Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations
Chuhao Sun, Asaf Cohen, James Stokes +1
Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, in…
Digital quantum simulation of Schrödinger dynamics using adaptive approximations of potential functions
Tenzan Araki, James Stokes, Shravan Veerapaneni
Digital quantum simulation (DQS) of continuous-variable quantum systems in the position basis requires efficient implementation of diagonal unitaries approximating the time evoluti…
Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation
Di Luo, Shunyue Yuan, James Stokes +1
Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of latti…
Toward Neural Network Simulation of Variational Quantum Algorithms
Oliver Knitter, James Stokes, Shravan Veerapaneni
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Desp…
Scalable neural quantum states architecture for quantum chemistry
Tianchen Zhao, James Stokes, Shravan Veerapaneni
Variational optimization of neural-network representations of quantum states has been successfully applied to solve interacting fermionic problems. Despite rapid developments, sign…
Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing
Tianchen Zhao, Chuhao Sun, Asaf Cohen +2
Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of…
Numerical and geometrical aspects of flow-based variational quantum Monte Carlo
James Stokes, Brian Chen, Shravan Veerapaneni
This article aims to summarize recent and ongoing efforts to simulate continuous-variable quantum systems using flow-based variational quantum Monte Carlo techniques, focusing for…
Fermionic Wave Functions from Neural-Network Constrained Hidden States
Javier Robledo Moreno, Giuseppe Carleo, Antoine Georges +1
We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinan…
Continuous-variable neural-network quantum states and the quantum rotor model
James Stokes, Saibal De, Shravan Veerapaneni +1
We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-vari…
Overcoming barriers to scalability in variational quantum Monte Carlo
Tianchen Zhao, Saibal De, Brian Chen +2
The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-…
Gauge equivariant neural networks for quantum lattice gauge theories
Di Luo, Giuseppe Carleo, Bryan K. Clark +1
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Mot…
Meta Variational Monte Carlo
Tianchen Zhao, James Stokes, Oliver Knitter +2
An identification is found between meta-learning and the problem of determining the ground state of a randomly generated Hamiltonian drawn from a known ensemble. A model-agnostic m…
Holographic 2-Point Functions in the Pseudo-Conformal Universe
Mariana Carrillo-Gonzalez, Kurt Hinterbichler, James Stokes +1
We holographically calculate two-point functions in the pseudo-conformal universe, an early universe alternative to inflation. The pseudo-conformal universe can be modeled as a def…
Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states
James Stokes, Javier Robledo Moreno, Eftychios A. Pnevmatikakis +1
First-quantized deep neural network techniques are developed for analyzing strongly coupled fermionic systems on the lattice. Using a Slater-Jastrow inspired ansatz which exploits…
Natural evolution strategies and variational Monte Carlo
Tianchen Zhao, Giuseppe Carleo, James Stokes +1
A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical blac…
Quantum Natural Gradient
James Stokes, Josh Izaac, Nathan Killoran +1
A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is…
Mean-field Analysis of Batch Normalization
Mingwei Wei, James Stokes, David J Schwab
Batch Normalization (BatchNorm) is an extremely useful component of modern neural network architectures, enabling optimization using higher learning rates and achieving faster conv…
Probabilistic Modeling with Matrix Product States
James Stokes, John Terilla
Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algor…
Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networks
Tengyuan Liang, James Stokes
Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local…
Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
Tengyuan Liang, Tomaso Poggio, Alexander Rakhlin +1
We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao nor…
Nonlinear Sigma Models with Compact Hyperbolic Target Spaces
Steven Gubser, Zain H. Saleem, Samuel S. Schoenholz +2
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Rie…
Holographic CFTs on maximally symmetric spaces: correlators, integral transforms and applications
Kurt Hinterbichler, James Stokes, Mark Trodden
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral…
The curious case of large-N expansions on a (pseudo)sphere
Alexander M. Polyakov, Zain H. Saleem, James Stokes
We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular mom…
Holography for a Non-Inflationary Early Universe
Kurt Hinterbichler, James Stokes, Mark Trodden
We construct a gravitational dual of the pseudo-conformal universe, a proposed alternative to inflation in which a conformal field theory in nearly flat space develops a time depen…