Condensed Matter

"Motivated by applications in machine learning, we present a quantum algorithm for Gibbs sampling from continuous real-valued functions defined on high dimensional tori. We show that these families of functions satisfy a Poincare inequality. We then use the techniques for solving linear systems and partial differential equations to design an algorithm that performs zeroeth order queries to a quantum oracle computing the energy function to return samples from its Gibbs distribution. We further analyze the query and gate complexity of our algorithm and prove that the algorithm has a polylogarithmic dependence on approximation error (in total variation distance) and a polynomial dependence on the number of variables, although it suffers from an exponentially poor dependence on temperature."

The backbones of modern-day Deep Learning, Neural Networks (NN), define field theories on Euclidean background through their architectures, where field interaction strengths depend on the choice of NN architecture width and stochastic parameters. Infinite width limit of NN architectures, combined with independently distributed stochastic parameters, lead to generalized free field theories by the Central Limit Theorem (CLT). Small and large deviations from the CLT, due to finite architecture width and/or correlated stochastic parameters, respectively give rise to weakly coupled field theories and non-perturbative non-Lagrangian field theories in Neural Networks. I will present a systematic exploration of Neural Network field theories via a dual framework of NN parameters: non-Gaussianity, locality by cluster decomposition, and symmetries are studied without necessitating the knowledge of an action. Such a dual description to statistical or quantum field theories in Neural Networks can have potential implications for physics.

In this talk, I'll describe new tomographic protocols for efficiently estimating various fermionic quantities, including both local observables (i.e., expectation values of local fermionic operators) and certain global properties (e.g., inner products between an unknown quantum state and arbitrary fermionic Gaussian states). Our protocols are based on classical shadows arising from random matchgate circuits. As a concrete application, they enable us to implement the recently introduced quantum-classical hybrid quantum Monte Carlo algorithm, without the exponential post-processing cost incurred by the original approach.

"One of the central challenges in quantum information science is to design quantum algorithms that outperform their classical counterparts in combinatorial optimization. In this talk, I will describe a modification of the quantum adiabatic algorithm (QAA) [1] that achieves a Grover-type speedup in solving a wide class of combinatorial optimization problem instances. The speedup is obtained over classical Markov chain algorithms including simulated annealing, parallel tempering, and quantum Monte Carlo. I will then introduce a framework to predict the relative performance of the standard QAA and classical Markov chain algorithms, and show problem instances with quantum speedup and slowdown. Finally, I will apply this framework to interpret results from a recent Rydberg atom array experiment [2], which suggest a superlinear speedup in solving the Maximum Independent Set problem on unit-disk graphs. [1] Farhi et al. (2001) Science 292, 5516 [2] Ebadi et al. (2022) Science 376, 6598"

Just seven years after their first detection, gravitational waves (GWs) have revealed the first glimpses of a previously hidden dark Universe. Using the GW signature of distant compact-object collisions, we have discovered a new population of stellar remnants and unlocked new tests of general relativity, cosmology, and ultra-dense matter. Materials with low mechanical loss (and strong constraints on other properties, e.g. reflectivity) are integral to the design and success of the GW detectors making these groundbreaking measurements. I'll summarize recent results from LIGO-Virgo and their wide-reaching implications, and discuss quantum materials advances required to enable future ground-based gravitational wave detectors, including Cosmic Explorer, to sense black hole collisions all the way back to the dawn of cosmic time.

I will discuss our recent work on the use of autoregressive neural networks for many-body physics. In particular, I will discuss two approaches to represent quantum states using these models and their applications to the reconstruction of quantum states, the simulation of real-time dynamics of open quantum systems, and the approximation of ground states of many-body systems displaying long-range order, frustration, and topological order. Finally, I will discuss how annealing in these systems can be used for combinatorial optimization where we observe solutions to problems that are orders of magnitude more accurate than simulated and simulated quantum annealing.

While sharply-quantized topological features are conventionally associated with gapped phases of matter, there are a growing number of examples of gapless systems with topologically protected edge states. A particularly striking set of examples are "intrinsically gapless" symmetry-protected topological states (igSPTs), which host topological surface states that could not arise in a gapped system with the same symmetries. Examples include familiar non-interacting Weyl semimetals with Fermi arc surface states, as well as more exotic examples like deconfined quantum critical points with topological edge states. In this talk, I will discuss recent progress in formally understanding the bulk-boundary correspondence of strongly-interacting igSPTs using tools from group cohomology. In these examples, the gapless-ness of the bulk and presence of topological surface states can be understood in a unified way due to the presence of an emergent anomaly. Our formalism allows construction of lattice-models with such emergent anomalies whose topological properties can be deduced exactly.