arXiv subjects

Scott Lawrence

Publications and source records attributed to Scott Lawrence.

At least 19 recordsLinked to original sources

arXiv2026

Light nuclear scattering from neural quantum states

We present a method of studying few-body nuclear scattering by means of neural quantum states, without requiring time-evolution. A recently developed family of stable minimum principles for Schrodinger's equation provides conservative uncertainties on cross sections and partial wave amplitudes computed in this way. We use this method to study both elastic and inelastic neutron-deuteron scattering with realistic nuclear two-body forces.

nucl-th↗

arXiv2026

Stable minimum principles for scattering states

Quantum-mechanical scattering states are energy eigenstates obeying particular boundary conditions, whose behavior at infinity encodes the S-matrix which defines the outcoming of scattering experiments. With an eye toward numerical algorithms for computing nonrelativistic S-matrices, we present a family of stable minimum principles for scattering states. States that approximately satisfy these minimum principles are shown to have a bounded difference with the true scattering states. These minimum principles and stability estimates can be used to obtain rigorous bounds on scattering amplitudes. We show that these minimum principles are applicable to momentum-dependent potentials, long-range (Coulomb) interactions, and elastic or inelastic scattering of bound states.

quant-ph↗

arXiv2025

Efficient Learning of Lattice Gauge Theories with Fermions

We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.

hep-lat↗

arXiv2025

Quantum bootstrap for central potentials

We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such as the Yukawa potential (which asymptotically decays as an exponential) and a Gaussian potential. We additionally review the bootstrap of the Coulomb potential, demonstrate a high-precision bootstrap of the Cornell potential, and study conformal quantum mechanics. These results further recommend the bootstrap as a numerical method for high-precision calculations of ground-state physics, where applicable: for example, we are able to determine the critical coupling in the Cornell potential to better than one part in $10^7$, the most precise determination to date. Lower bounds on energies are also of high precision, occasionally one part in greater than $10^8$. Finally, we discuss the circumstances under which we are able to obtain meaningful upper bounds on ground-state energies.

quant-ph↗

arXiv2025

Machine-learning approaches to accelerating lattice simulations

The last decade has seen an explosive growth of interest in exploiting developments in machine learning to accelerate lattice QCD calculations. On the sampling side, generative models are a promising approach to mitigating critical slowing down and topological freezing. Meanwhile, signal-to-noise problems have been shown to be improvable by the use of optimized improved observables. Both techniques can be made free of bias, resulting in trustworthy but reduced statistical errors. This talk reviews recent developments in this field.

hep-lat↗

arXiv2025

Real-time dynamics from convex geometry

A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of exponential (e.g.~in volume) dimension, but low-dimensional projections can be efficiently explored by standard algorithms. Such approaches have been used to precisely constrain critical exponents of conformal field theories ("conformal bootstrap") and, more recently, to constrain the ground state physics of various quantum-mechanical systems, including lattice field theories. In this talk we discuss related approaches to systematically constraining the real-time dynamics of quantum systems, which are otherwise obstructed from study by sign problems and the ill-posed nature of analytic continuation.

hep-lat↗

arXiv2024

Bootstrapping time-evolution in quantum mechanics

We present a method for obtaining a hierarchy of rigorous bounds on the time-evolution of a quantum mechanical system from an arbitrary initial state, systematically generalizing Mandelstam-Tamm-like relations. For any fixed level in the hierarchy, the bounds are tightest after short time-evolution and gradually loosen over time; we present evidence that for any fixed amount of time-evolution, the bounds can be made arbitrarily tight by moving up in the hierarchy. The computational effort to obtain the bounds scales polynomially with the number of degrees of freedom in the system being simulated. We demonstrate the method on both a single anharmonic oscillator and a system of two coupled anharmonic oscillators.

hep-th↗

arXiv2024

Model-free spectral reconstruction via Lagrange duality

Various physical quantities -- including real-time response, inclusive cross-sections, and decay rates -- may not be directly determined from Euclidean correlators. They are, however, easily determined from the spectral density, motivating the task of estimating a spectral density from a Euclidean correlator. This spectral reconstruction problem can be written as an ill-posed inverse Laplace transform; incorporating positivity constraints allows one to obtain finite-sized bounds on the region of spectral density functions consistent with the Euclidean data. Expressing the reconstruction problem as a convex optimization problem and exploiting Lagrange duality, bounds on arbitrary integrals of the spectral density can be efficiently obtained from Euclidean data. This paper applies this approach to reconstructing a smeared spectral density and determining smeared real-time evolution. Bounds of this form are information-theoretically complete, in the sense that for any point within the bounds one may find an associated spectral density consistent with both the available Euclidean data and positivity.

hep-lat↗

arXiv2024

Potential Applications of Quantum Computing at Los Alamos National Laboratory

The emergence of quantum computing technology over the last decade indicates the potential for a transformational impact in the study of quantum mechanical systems. It is natural to presume that such computing technologies would be valuable to large scientific institutions, such as United States national laboratories. However, detailed descriptions of what these institutions would like to use these computers for are limited. To help provide some initial insights into this topic, this report develops detailed use cases of how quantum computing technology could be utilized to enhance a variety of quantum physics research activities at Los Alamos National Laboratory, including quantum magnetic materials, high-temperature superconductivity and nuclear astrophysics simulations. The report discusses how current high-performance computers are used for scientific discovery today and develops detailed descriptions of the types of quantum physics simulations that Los Alamos National Laboratory scientists would like to conduct, if a sufficient computing technology became available. While the report strives to highlight the breadth of potential application areas for quantum computation, this investigation has also indicated that many more use cases exist at Los Alamos National Laboratory, which could be documented in similar detail with sufficient time and effort.

quant-ph↗

arXiv2024

Quantum states from normalizing flows

We introduce an architecture for neural quantum states for many-body quantum-mechanical systems, based on normalizing flows. The use of normalizing flows enables efficient uncorrelated sampling of configurations from the probability distribution defined by the wavefunction, mitigating a major cost of using neural states in simulation. We demonstrate the use of this architecture for both ground-state preparation (for self-interacting particles in a harmonic trap) and real-time evolution (for one-dimensional tunneling). Finally, we detail a procedure for obtaining rigorous estimates of the systematic error when using neural states to approximate quantum evolution.

quant-ph↗

arXiv2024

Schwinger-Dyson control variates for lattice fermions

Previous work has shown that high-quality control variates for lattice Monte Carlo methods may be constructed from lattice Schwinger-Dyson relations. This paper extends that method to theories with lattice fermions, using the Thirring model in $1+1$ spacetime dimensions as a testbed. Past construction of these control variates involved a number of fitting parameters that scaled with lattice volume. By computing the control variate in perturbation theory, the number of fitting parameters required for an order-of-magnitude improvement in the signal-to-noise ratio at weak coupling is reduced to be of order one.

hep-lat↗

arXiv2024

Contour deformations for non-holomorphic actions

We show how contour deformations may be used to control the sign problem of lattice Monte Carlo calculations with non-holomorphic actions. Such actions arise naturally in quantum mechanical scattering problems. The approach is demonstrated in conjunction with the holomorphic gradient flow. As our central example we compute the real-time evolution of a particle in a one-dimensional analog of the Yukawa potential.

hep-lat↗

arXiv2023

Mitigating a discrete sign problem with extreme learning machines

An extreme learning machine is a neural network in which only the weights in the last layer are changed during training; for such networks training can be performed efficiently and deterministically. We use an extreme learning machine to construct a control variate that tames the sign problem in the classical Ising model at imaginary external magnetic field. Using this control variate, we directly compute the partition function at imaginary magnetic field in two and three dimensions, yielding information on the positions of Lee-Yang zeros.

hep-lat↗

arXiv2023

Convex optimization and contour deformations

We discuss various formal aspects of contour deformations used to alleviate sign problems; most importantly, relating these contour deformations to a certain convex optimization problem. As a consequence of this connection we describe a general method for proving upper bounds on the average phase achievable by the contour deformation method. Using this method we show that Abelian lattice Yang-Mills in two spacetime dimensions possesses, for many values of the complex coupling, an exponential sign problem that cannot be removed via any contour deformation.

hep-lat↗

arXiv2023

Control variates for lattice field theory

In most lattice field theories, correlators are plagued by a signal-to-noise problem of exponential difficulty in the time separation. We propose a method for improving the signal-to-noise ratio, in which control variates are systematically constructed from lattice Schwinger-Dyson relations. The method is demonstrated on various two-dimensional lattices in scalar field theory, and a strategy for scaling to larger systems is explored.

hep-lat↗

arXiv2023

Instantons, analytic continuation, and $\mathcal{PT}$-symmetric field theory

Ordinary Hermitian $\lambda \phi^4$ theory is known to exist in $d<4$ dimensions when $\lambda>0$. For negative values of the coupling, it has been suggested that a physical meaningful definition of the interacting theory can be given in terms of ${\cal PT}$-symmetric field theory. In this work, we critically re-examine the relation between analytically continued Hermitian field theory with quartic interaction, and ${\cal PT}$-symmetric field theory, including $O(N)$ models. We find that in general ${\cal PT}$-symmetric field theory does not correspond to the analytic continuation of the Hermitian theory, except at high temperature where the instanton contribution present in the analytically continued theory can be neglected.

hep-th↗

arXiv2022

Deep Learning of Fermion Sign Fluctuations

We describe a procedure for alleviating the fermion sign problem in which phase fluctuations are explicitly subtracted from the Boltzmann factor. Several ans\"atze for fluctuations are designed and compared. In the absence of a sufficiently high-quality ansatz, a neural network can be trained to parameterize the fluctuations. Demonstrating on the staggered Thirring model in $1+1$ dimensions, we examine the performance of this method as deeper neural networks are used, and in conjunction with the well-studied contour deformation methods.

hep-lat↗

arXiv2022

Semidefinite Programs at Finite Fermion Density

Semidefinite programs can be constructed to provide a non-perturbative view of the zero-temperature behavior of quantum systems. This paper examines the properties of these semidefinite programs when applied to lattice-regulated field theories exhibiting fermion sign problems. Specifically on the finite-density Thirring model, there is no indication that the accuracy of semidefinite programs suffers from any difficulty analogous to the sign problem.

hep-lat↗