arXiv subjects

Roger G. Melko

Publications and source records attributed to Roger G. Melko.

At least 37 records · Page 2Linked to original sources

arXiv2024

CaloQVAE : Simulating high-energy particle-calorimeter interactions using hybrid quantum-classical generative models

The Large Hadron Collider's high luminosity era presents major computational challenges in the analysis of collision events. Large amounts of Monte Carlo (MC) simulation will be required to constrain the statistical uncertainties of the simulated datasets below these of the experimental data. Modelling of high-energy particles propagating through the calorimeter section of the detector is the most computationally intensive MC simulation task. We introduce a technique combining recent advancements in generative models and quantum annealing for fast and efficient simulation of high-energy particle-calorimeter interactions.

hep-ex↗

arXiv2024

Autoregressive model path dependence near Ising criticality

Autoregressive models are a class of generative model that probabilistically predict the next output of a sequence based on previous inputs. The autoregressive sequence is by definition one-dimensional (1D), which is natural for language tasks and hence an important component of modern architectures like recurrent neural networks (RNNs) and transformers. However, when language models are used to predict outputs on physical systems that are not intrinsically 1D, the question arises of which choice of autoregressive sequence -- if any -- is optimal. In this paper, we study the reconstruction of critical correlations in the two-dimensional (2D) Ising model, using RNNs and transformers trained on binary spin data obtained near the thermal phase transition. We compare the training performance for a number of different 1D autoregressive sequences imposed on finite-size 2D lattices. We find that paths with long 1D segments are more efficient at training the autoregressive models compared to space-filling curves that better preserve the 2D locality. Our results illustrate the potential importance in choosing the optimal autoregressive sequence ordering when training modern language models for tasks in physics.

cs.LG↗

arXiv2024

GraphiQ: Quantum circuit design for photonic graph states

GraphiQ is a versatile open-source framework for designing photonic graph state generation schemes, with a particular emphasis on photon-emitter hybrid circuits. Built in Python, GraphiQ consists of a suite of design tools, including multiple simulation backends and optimization methods. The library supports scheme optimization in the presence of circuit imperfections, as well as user-defined optimization goals. Our framework thus represents a valuable tool for the development of practical schemes adhering to experimentally-relevant constraints. As graph states are a key resource for measurement-based quantum computing, all-photonic quantum repeaters, and robust quantum metrology, among others, we envision GraphiQ's broad impact for advancing quantum technologies.

quant-ph↗

arXiv2024

RydbergGPT

We introduce a generative pretained transformer (GPT) designed to learn the measurement outcomes of a neutral atom array quantum computer. Based on a vanilla transformer, our encoder-decoder architecture takes as input the interacting Hamiltonian, and outputs an autoregressive sequence of qubit measurement probabilities. Its performance is studied in the vicinity of a quantum phase transition in Rydberg atoms in a square lattice array. We explore the ability of the architecture to generalize, by producing groundstate measurements for Hamiltonian parameters not seen in the training set. We focus on examples of physical observables obtained from inference on three different models, trained in fixed compute time on a single NVIDIA A100 GPU. These can act as benchmarks for the scaling of larger RydbergGPT models in the future. Finally, we provide RydbergGPT open source, to aid in the development of foundation models based off of a wide variety of quantum computer interactions and data sets in the future.

quant-ph↗

arXiv2024

Operator Learning Renormalization Group

In this paper, we present a general framework for quantum many-body simulations called the operator learning renormalization group (OLRG). Inspired by machine learning perspectives, OLRG is a generalization of Wilson's numerical renormalization group and White's density matrix renormalization group, which recursively builds a simulatable system to approximate a target system of the same number of sites via operator maps. OLRG uses a loss function to minimize the error of a target property directly by learning the operator map in lieu of a state ansatz. This loss function is designed by a scaling consistency condition that also provides a provable bound for real-time evolution. We implement two versions of the operator maps for classical and quantum simulations. The former, which we call the Operator Matrix Map, can be implemented via neural networks on classical computers. The latter, which we call the Hamiltonian Expression Map, generates device pulse sequences to leverage the capabilities of quantum computing hardware. We illustrate the performance of both maps for calculating time-dependent quantities in the quantum Ising model Hamiltonian.

quant-ph↗

arXiv2024

Corner entanglement of a resonating valence bond wavefunction

We perform a quantum Monte Carlo simulation of the resonating valence bond wavefunction on a two-dimensional square lattice with periodic boundary conditions. Using two replicas of the system, we calculate the second Renyi entropy on a spatial bipartition with a square geometry. Through a finite-size scaling analysis, we extract the logarithmic correction to the area law due to the presence of the sharp corners in the entangling surface. We find that the coefficient of this logarithm is positive with a value of 0.073 for a single $90^{\circ}$ corner.

cond-mat.str-el↗

arXiv2024

Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy

Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these architectures were shown to be powerful ansatze to approximate the ground state of quantum systems. Here, we build over the results of [Phys. Rev. Research 2, 023358 (2020)] and construct a more powerful RNN wave function ansatz in two dimensions. We use symmetry and annealing to obtain accurate estimates of ground state energies of the two-dimensional (2D) Heisenberg model, on the square lattice and on the triangular lattice. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to $14 \times 14$ on the triangular lattice.

cond-mat.dis-nn↗

arXiv2023

Investigating Topological Order using Recurrent Neural Networks

Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. Here, we employ 2D RNNs to investigate two prototypical quantum many-body Hamiltonians exhibiting topological order. Specifically, we demonstrate that RNN wave functions can effectively capture the topological order of the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating their topological entanglement entropies. We also find that RNNs favor coherent superpositions of minimally-entangled states over minimally-entangled states themselves. Overall, our findings demonstrate that RNN wave functions constitute a powerful tool to study phases of matter beyond Landau's symmetry-breaking paradigm.

cond-mat.str-el↗

arXiv2023

Enhancing variational Monte Carlo using a programmable quantum simulator

Programmable quantum simulators based on Rydberg atom arrays are a fast-emerging quantum platform, bringing together long coherence times, high-fidelity operations, and large numbers of interacting qubits deterministically arranged in flexible geometries. Today's Rydberg array devices are demonstrating their utility as quantum simulators for studying phases and phase transitions in quantum matter. In this paper, we show that unprocessed and imperfect experimental projective measurement data can be used to enhance in silico simulations of quantum matter, by improving the performance of variational Monte Carlo simulations. As an example, we focus on data spanning the disordered-to-checkerboard transition in a $16 \times 16$ square lattice array [S. Ebadi et al. Nature 595, 227 (2021)] and employ data-enhanced variational Monte Carlo to train powerful autoregressive wavefunction ansätze based on recurrent neural networks (RNNs). We observe universal improvements in the convergence times of our simulations with this hybrid training scheme. Notably, we also find that pre-training with experimental data enables relatively simple RNN ansätze to accurately capture phases of matter that are not learned with a purely variational training approach. Our work highlights the promise of hybrid quantum--classical approaches for large-scale simulation of quantum many-body systems, combining autoregressive language models with experimental data from existing quantum devices.

cond-mat.quant-gas↗

arXiv2023

Stochastic Series Expansion Quantum Monte Carlo for Rydberg Arrays

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on arbitrary lattices. We describe a cluster update that allows for the efficient sampling and calculation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results on large Rydberg arrays in one and two dimensions.

cond-mat.str-el↗

arXiv2022

A quantum phase transition in the one-dimensional water chain

The concept of quantum phase transitions (QPT) plays a central role in the description of condensed matter systems. In this contribution, we perform high-quality wavefunction-based simulations to demonstrate the existence of a quantum phase transition in a crucially relevant molecular system, namely water, forming linear chains of rotating molecules. We determine various critical exponents and reveal the water chain QPT to belong to the (1+1) dimensional Ising universality class. Furthermore, the effect of breaking symmetries is examined and it is shown that by breaking the inversion symmetry, the ground state degeneracy of the ordered quantum phase is lifted to yield two many-body states with opposite polarization. The possibility of forming ferroelectric phases together with a thermal stability of the quantum critical regime up to ~10 K makes the linear water chain a promising candidate as a platform for quantum devices.

quant-ph↗

arXiv2022

Persistent Homology of $\mathbb{Z}_2$ Gauge Theories

Topologically ordered phases of matter display a number of unique characteristics, including ground states that can be interpreted as patterns of closed strings. In this paper, we consider the problem of detecting and distinguishing closed strings in Ising spin configurations sampled from the classical $\mathbb{Z}_2$ gauge theory. We address this using the framework of persistent homology, which computes the size and frequency of general loop structures in spin configurations via the formation of geometric complexes. Implemented numerically on finite-size lattices, we show that the first Betti number of the Vietoris-Rips complexes achieves a high density at low temperatures in the $\mathbb{Z}_2$ gauge theory. In addition, it displays a clear signal at the finite-temperature deconfinement transition of the three-dimensional theory. We argue that persistent homology should be capable of interpreting prominent loop structures that occur in a variety of systems, making it an useful tool in theoretical and experimental searches for topological order.

cond-mat.stat-mech↗

arXiv2022

Neural network enhanced measurement efficiency for molecular groundstates

It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of such states, which are typically estimated using projective measurements on the qubits. At present, measurement data is costly and time-consuming to obtain on any quantum computing architecture, which has significant consequences for the statistical errors of estimators. In this paper, we adapt common neural network models (restricted Boltzmann machines and recurrent neural networks) to learn complex groundstate wavefunctions for several prototypical molecular qubit Hamiltonians from typical measurement data. By relating the accuracy $\varepsilon$ of the reconstructed groundstate energy to the number of measurements, we find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables. This enhancement yields an asymptotic scaling near $\varepsilon^{-1}$ for the model-based approaches, as opposed to $\varepsilon^{-2}$ in the case of classical shadow tomography.

quant-ph↗

arXiv2022

Data-Enhanced Variational Monte Carlo Simulations for Rydberg Atom Arrays

Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. Due to long experimental preparation times, obtaining projective measurement data can be relatively slow for large arrays, which poses a challenge for state reconstruction methods such as tomography. Today, novel groundstate wavefunction ansätze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational Monte Carlo (VMC). In this paper, we demonstrate how pretraining modern RNNs on even small amounts of data significantly reduces the convergence time for a subsequent variational optimization of the wavefunction. This suggests that essentially any amount of measurements obtained from a state prepared in an experimental quantum simulator could provide significant value for neural-network-based VMC strategies.

quant-ph↗

arXiv2022

Neural annealing and visualization of autoregressive neural networks in the Newman-Moore model

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results despite their representational power and entanglement content, thus, suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman-Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman-Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

cond-mat.dis-nn↗

arXiv2022

Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning

We use voxel deep neural networks to predict energy densities and functional derivatives of electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. We show that the ground-state electron density can be found via direct minimization for a graphene lattice without any projection scheme using a voxel deep neural network trained with the Thomas-Fermi model. Additionally, we predict the kinetic energy of a graphene lattice within chemical accuracy after training from only 2 Kohn-Sham density functional theory (DFT) calculations. We identify an important sampling issue inherent in Kohn-Sham DFT calculations and propose future work to rectify this problem. Furthermore, we demonstrate an alternative, functional derivative-free, Monte Carlo based orbital free density functional theory algorithm to calculate an accurate 2-electron density in a double inverted Gaussian potential with a machine-learned kinetic energy functional.

cond-mat.mes-hall↗

arXiv2021

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important new insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

quant-ph↗

arXiv2021

Simulating a measurement-induced phase transition for trapped ion circuits

The rise of programmable quantum devices has motivated the exploration of circuit models which could realize novel physics. A promising candidate is a class of hybrid circuits, where entangling unitary dynamics compete with disentangling measurements. Novel phase transitions between different entanglement regimes have been identified in their dynamical states, with universal properties hinting at unexplored critical phenomena. Trapped ion hardware is a leading contender for the experimental realization of such physics, which requires not only traditional two-qubit entangling gates, but a constant rate of local measurements accurately addressed throughout the circuit. Recent progress in engineering high-precision optical addressing of individual ions makes preparing a constant rate of measurements throughout a unitary circuit feasible. Using tensor network simulations, we show that the resulting class of hybrid circuits, prepared with native gates, exhibits a volume-law to area-law transition in the entanglement entropy. This displays universal hallmarks of a measurement-induced phase transition. Our simulations are able to characterize the critical exponents using circuit sizes with tens of qubits and thousands of gates. We argue that this transition should be robust against additional sources of experimental noise expected in modern trapped ion hardware, and will rather be limited by statistical requirements on post selection. Our work highlights the powerful role that tensor network simulations can play in advancing the theoretical and experimental frontiers of critical phenomena.

quant-ph↗