End-to-end variational quantum sensing.

Harnessing quantum correlations can enable sensing beyond classical precision limits, with the realization of such sensors poised for transformative impacts across science and engineering. Real devices, however, face the accumulated impacts of noise and architecture constraints, making the design and success of practical quantum sensors challenging. Numerical and theoretical frameworks to optimize and analyze sensing protocols in their entirety are thus crucial for translating quantum advantage into widespread practice.

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.

Language models for quantum simulation.

A key challenge in the effort to simulate today's quantum computing devices is the ability to learn and encode the complex correlations that occur between qubits. Emerging technologies based on language models adopted from machine learning have shown unique abilities to learn quantum states. We highlight the contributions that language models are making in the effort to build quantum computers and discuss their future role in the race to quantum advantage.

Quantum Phase Transition in the One-Dimensional Water Chain.

The concept of quantum phase transitions (QPTs) plays a central role in the description of condensed matter systems. In this Letter, we perform high-quality wave-function-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.

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 two Kohn-Sham density functional theory (DFT) calculations.

Commercial applications of quantum computing.

Despite the scientific and engineering challenges facing the development of quantum computers, considerable progress is being made toward applying the technology to commercial applications. In this article, we discuss the solutions that some companies are already building using quantum hardware. Framing these as examples of combinatorics problems, we illustrate their application in four industry verticals: cybersecurity, materials and pharmaceuticals, banking and finance, and advanced manufacturing.

Integrating Neural Networks with a Quantum Simulator for State Reconstruction.

We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator by means of a neural-network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine wave functions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Rényi mutual information.

Latent Space Purification via Neural Density Operators.

Machine learning is actively being explored for its potential to design, validate, and even hybridize with near-term quantum devices. A central question is whether neural networks can provide a tractable representation of a given quantum state of interest. When true, stochastic neural networks can be employed for many unsupervised tasks, including generative modeling and state tomography.

Machine learning quantum phases of matter beyond the fermion sign problem.

State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample the many-fermion system, we show that the Green's function holds sufficient information to allow for the distinction of different fermionic phases via a CNN.

Neural Decoder for Topological Codes.

We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization.

Identifying polymer states by machine learning.

The ability of a feed-forward neural network to learn and classify different states of polymer configurations is systematically explored. Performing numerical experiments, we find that a simple network model can, after adequate training, recognize multiple structures, including gaslike coil, liquidlike globular, and crystalline anti-Mackay and Mackay structures. The network can be trained to identify the transition points between various states, which compare well with those identified by independent specific-heat calculations.

Cornering Gapless Quantum States via Their Torus Entanglement.

The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by χ. Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface.

Spinon Walk in Quantum Spin Ice.

We study a minimal model for the dynamics of spinons in quantum spin ice. The model captures the essential strong coupling between the spinon and the disordered background spins. We demonstrate that the spinon motion can be mapped to a random walk with an entropy-induced memory in imaginary time.

A two-dimensional spin liquid in quantum kagome ice.

Actively sought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at zero temperature. Despite ongoing searches, QSLs remain elusive, due to a lack of concrete knowledge of the microscopic mechanisms that inhibit magnetic order in materials. Here we study a model for a broad class of frustrated magnetic rare-earth pyrochlore materials called quantum spin ices.

Destroying a topological quantum bit by condensing Ising vortices.

The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons.

Path-integral Monte Carlo method for Rényi entanglement entropies.

We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions.

Geometric mutual information at classical critical points.

A practical use of the entanglement entropy in a 1D quantum system is to identify the conformal field theory describing its critical behavior. It is exactly (c/3)lnℓ for an interval of length ℓ in an infinite system, where c is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points.

Angular fluctuations of a multicomponent order describe the pseudogap of YBa2Cu3O(6+x).

The hole-doped cuprate high-temperature superconductors enter the pseudogap regime as their superconducting critical temperature, Tc, falls with decreasing hole density. Recent x-ray scattering experiments in YBa2Cu3O(6+x) observe incommensurate charge-density wave fluctuations whose strength rises gradually over a wide temperature range above Tc, but then decreases as the temperature is lowered below Tc. We propose a theory in which the superconducting and charge-density wave orders exhibit angular fluctuations in a six-dimensional space.

Self-correcting quantum memories beyond the percolation threshold.

We analyze several high dimensional generalizations of the toric code at a nonzero temperature. We find that in a large enough dimension, there can be a distinct separation between the critical temperature Tc, given by thermodynamic singularities, and the percolation temperature Tp, given by the percolation of defects. We argue that the regime Tp View Article and Find Full Text PDF

Fate of CPN-1 fixed points with q monopoles.

We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point.

Entanglement at a two-dimensional quantum critical point: a numerical linked-cluster expansion study.

We develop a method to calculate the bipartite entanglement entropy of quantum models, in the thermodynamic limit, using a numerical linked-cluster expansion (NLCE) involving only rectangular clusters. It is based on exact diagonalization of all n×m rectangular clusters at the interface between entangled subsystems A and B. We use it to obtain the Renyi entanglement entropy of the two-dimensional transverse field Ising model, for arbitrary real Renyi index α.

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations.

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition.

Generalized Monte Carlo loop algorithm for two-dimensional frustrated Ising models.

We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures.

Universal signatures of fractionalized quantum critical points.

Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*.

Finite-temperature critical behavior of mutual information.

We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that, for n>1, the critical behavior is manifest at two temperatures T(c) and nT(c). For the XXZ model with Ising anisotropy, the coefficient of the area law has a t lnt singularity, whereas the subleading correction from corners has a logarithmic divergence, with a coefficient related to the exact results of Cardy and Peschel.