Conference

QuEra is a quantum computing start up located in Boston, spinning off from the groups in the physics and engineering departments of Harvard and MIT. I have spent this fall working at QuEra and will introduce you to the company and its neutral-atom quantum computing technology.

"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."

"Strong local passivity is a property of multipartite systems from which it is impossible to locally extract energy. Surprisingly, if the system in a strong local passive state displays entanglement, it could be possible to locally activate energy by adding classical communication between different partitions of the system, through so-called ‘quantum energy teleportation’ protocols. In this talk, first, I will present how to fully characterize this distinct notion of local passivity by giving necessary and sufficient conditions using optimization techniques from semidefinite programming [1]. Then, I will introduce the minimal theoretical model of energy activation with a fully unitary quantum energy teleportation protocol [2]. Finally, I will present the first experimental observation of the local activation of a strong local passive state on a bipartite quantum system using nuclear magnetic resonance [2]. Refs. [1] Fundamental limitations to local energy extraction in quantum systems. ÁM Alhambra, G Styliaris, NA Rodriguez-Briones, J Sikora, E Martin-Martinez. Physical review letters 123 19, 190601 [2] Experimental activation of strong local passive states with quantum information. NA Rodríguez-Briones, H Katiyar, R Laflamme, E Martín-Martínez. ArXiv preprint arXiv:2203.16269"

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"