Talks

We present a quantum algorithm for simulating the classical dynamics of 2^n coupled oscillators (e.g.,  masses coupled by springs). Our approach leverages a mapping between the Schrodinger equation and Newton's equations for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators. When individual masses and spring constants can be efficiently queried, and when the initial state can be efficiently prepared, the complexity of our quantum algorithm is polynomial in n, almost linear in the evolution time, and sublinear in the sparsity. As an example application, we apply our quantum algorithm to efficiently estimate the kinetic energy of an oscillator at any time, for a specification of the problem that we prove is BQP-complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers. Finally, we show that under similar conditions our approach can efficiently simulate more general classical harmonic systems with 2^n modes.

Zoom link:  https://pitp.zoom.us/j/91882209363?pwd=UndJRVdaZW04RGtpL0M2SE52RDJwZz09

"Many relationships in causality, statistics or probability theory can be expressed as conditional independence relations between the occurring random variables. Since the invention of the notion of conditional independence one aim was to be able to also express such relationship between random and non-random variables, like the parameters of a stochastic model, the input variables of a probabilistic program or intervention variables in a causal model. Over time several different versions of such extended conditional independence notion have been proposed, each coming with their own advantages and disadvantages, oftentimes limited to certain subclasses of random variables like discrete variables or ones with densities. In this talk we present another such notion of conditional independence, which can easily be expressed in measure-theoretic generality and even in categorical probability. We will study its expressivity, present its (convenient) properties, and relate it to other notions of conditional independence."

According to recent new definitions, a multi-party behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. Three experimental results published in 2022 provide initial evidence, subject to postselection-related assumptions, for the existence of behaviors meeting these definitions of GMNL. The new definitions of GMNL differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources when classifying behaviors as​only bipartite nonlocal. I will discuss the interrelationships of these choices in three-party quantum networks, and present a behavior in the simplest nontrivial multi-partite measurement scenario (3 parties, 2 measurement settings, and 2 outcomes) that (A) cannot be simulated in a bipartite network prohibiting both entangled measurements and superquantum resources, (B) can be simulated with bipartite-only quantum states allowing for an entangled quantum measurement (indicating an approach to device independent certification of entangled measurements with fewer settings than in previous protocols), and surprisingly (C) can be simulated with bipartite-only superquantum states (Popescu-Rohrlich boxes) while maintaining a prohibition on entangled measurements. It turns out that other behaviors previously studied as device-independent witnesses of entangled measurements can also be simulated in the manner of (C), posing a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.

Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the tradeoff between the entropy of hidden cause and the conditional mutual information of observed variables to develop a scalable algorithmic approach for inferring causality in the presence of latent confounders (common causes) in quantum systems. As an application, we consider a system of three entangled qubits and transmit the second and third qubits over separate noisy quantum channels. In this model, we validate that the first qubit is a latent confounder and the common cause of the second and third qubits. In contrast, when two entangled qubits are prepared and one of them is sent over a noisy channel, there is no common confounder. We also demonstrate that the proposed approach outperforms the results of classical causal inference for the Tubingen database when the variables are classical by exploiting quantum dependence between variables through density matrices rather than joint probability distributions.

In this talk, I examine the massless 't Hooft equation. This integral equation governs meson bound state wavefunctions in 2D SU(N) gauge theory in the large-N limit, and it can also be obtained by quantizing a folded string in flat space. The folded string is a limiting case of a more general setup: a four-segmented string moving in three-dimensional anti-de Sitter (AdS) space. I compute its classical spectral curve using celestial variables and planar bipartite graphs, also known as on-shell diagrams or brane tilings. In this more general setup, the 't Hooft equation acquires an extra term, which has previously been proposed as an effective confining potential in QCD. After an integral transform, the equation can be inverted in terms of a finite difference equation. I show that this difference equation has a natural interpretation as the quantized (non-analytic) spectral curve of the string. The spectrum interpolates between equally spaced energy levels in the tensionless limit and 't Hooft's nearly linear Regge trajectory at infinite AdS radius.

Zoom link:  https://pitp.zoom.us/j/97373882483?pwd=NmphN0N3ckdHbHdlcVpKcGkzMHY1Zz09

Distinguishing causation from correlation from observational data requires assumptions. We consider the setting where the unobserved confounder between two observed variables is simple in an information-theoretic sense, captured by its entropy. When the observed dependence is not due to causation, there exists a small-entropy variable that can make the observed variables conditionally independent. The smallest such entropy is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the latent variable. We establish identifiability results with Renyi-0 common entropy, and a special case of (binary) Renyi-1 common entropy. To efficiently compute common entropy, we propose an iterative algorithm that can be used to discover the trade-off between the entropy of the latent variable and the conditional mutual information of the observed variables. We show that our algorithm can be used to distinguish causation from correlation in such simple two-variable systems. Additionally, we show that common entropy can be used to improve constraint-based methods such as the PC algorithm in the small-sample regime, where such methods are known to struggle. We propose modifying these constraint-based methods to assess if a separating set found by these algorithms is valid using common entropy. We finally evaluate our algorithms on synthetic and real data to establish their performance.

I will sketch the current state of play with classifying causal scenarios (aka DAGs with latent variables). Some are interesting: the classical correlations are constrained by non-trivial inequalities such as Bell’s. Some are boring: the classical correlations are constrained only by observable conditional independencies. Some we still don’t know. Along the way I will mention joint work with Joe Henson, Ray Lal, Shashaank Khanna, Marina Ansanelli and Elie Wolfe, and disjoint work by Robin Evans.