Talks

Certifying that an n-qubit state synthesized in the lab is close to the target state is a fundamental task in quantum information science. However, existing rigorous protocols either require deep quantum circuits or exponentially many single-qubit measurements. In this work, we prove that almost all n-qubit target states, including those with exponential circuit complexity, can be certified from only O(n^2) single-qubit measurements. This result is established by a new technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state, and for learning and verifying neural networks, tensor networks, and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties that would otherwise require an exponential number of measurements. We demonstrate these applications in numerical experiments with up to 120 qubits, and observe advantage over existing methods such as cross-entropy benchmarking (XEB).

I will discuss recent progress in understanding entanglement-based probes of 2D topological phases of matter. These probes are supposed to extract universal topological information from a many-body ground state. Specifically, I will discuss (1) the topological entanglement entropy, which is supposed to give information about the number of anyon excitations, and (2) the modular commutator, which is supposed to tell us the chiral central charge.

Consider a system described by a multi-dimensional state vector X. The evolution of x is governed by a set of equations in the form of dx/dt=F(X(t)). x is a component of X. F(X(t)), the differential forcing of x, is a deterministic function of X. The solution of such a system often exhibits randomness, where the solution at one time is independent of the solution at another time. This study investigates the mechanism responsible for such randomness. We do so by exploring the integral forcing of x, G_T (t), a definite integral of F over the time span extending from t to t+T, which links the solution at two times, t and t+T.

We show that, for a system in equilibrium, G_T (t) can be expressed as G_T (t)=c_T+d_T x(t)+f_T (t), which consists of (apart from constant c_T) a dissipating component with strength d_T and a fluctuating component f_T (t), in line with the fluctuation-dissipation theorem that for a system in equilibrium, anything that generates fluctuations must also damp the flu...

Consider a system described by a multi-dimensional state vector X. The evolution of x is governed by a set of equations in the form of dx/dt=F(X(t)). x is a component of X. F(X(t)), the differential forcing of x, is a deterministic function of X. The solution of such a system often exhibits randomness, where the solution at one time is independent of the solution at another time. This study investigates the mechanism responsible for such randomness. We do so by exploring the integral forcing of x, G_T (t), a definite integral of F over the time span extending from t to t+T, which links the solution at two times, t and t+T.

We show that, for a system in equilibrium, G_T (t) can be expressed as G_T (t)=c_T+d_T x(t)+f_T (t), which consists of (apart from constant c_T) a dissipating component with strength d_T and a fluctuating component f_T (t), in line with the fluctuation-dissipation theorem that for a system in equilibrium, anything that generates fluctuations must also damp the flu...

We present a data-driven framework for dimensionality reduction and causal inference in climate fields. Given a high-dimensional climate field, the methodology first reduces its dimensionality into a set of regionally constrained patterns. Causal relations among such patterns are then inferred in the interventional sense through the fluctuation-response formalism. To distinguish between true and spurious responses, we propose an analytical null model for the fluctuation-dissipation relation, therefore allowing us for uncertainty estimation at a given confidence level. The framework is then applied to understand the relation between sea surface temperature warming patterns and changes in the net radiative flux at the top of the atmosphere, the so-called "pattern effect". We present a set of new results on the pattern effect and discuss the role of different processes, active at different spatiotemporal scales, in establishing the causal linkages between warming at the surface and radiat...

Horizontal and vertical distributions of mesoscale eddy kinetic energy (EKE), the dominant reservoir of ocean kinetic energy, are influenced by both environmental and dynamical factors. Compared to partitioning across horizontal scales, distributions of EKE in the vertical have been relatively under-observed and under-studied. Using newly collected full-depth observations of horizontal velocity from four unique mooring sites and output from the NOAA GFDL CM2.6 suite, this work presents a characterization of eddy vertical structure and investigates the factorings controlling its spatio-temporal variability. Time series analysis and application of clustering tools reveal geographic patterns in vertical structure. These patterns indicate the role of latitude and bathymetry in moderating the vertical partitioning of EKE. These relationships are interpreted through the lens of theoretical expectation and considered in the context of techniques used to infer or impose vertical structure.

It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here we show that this belief may or may not be true depending on a particular code. To this end, we characterize a tradeoff between the code distance d quantifying the number of correctable errors, and geometric entanglement of logical states quantifying their maximal overlap with product states or more general ``topologically trivial" states. The maximum overlap is shown to be exponentially small in d for three families of codes: (1) low-density parity check (LDPC) codes with commuting check operators, (2) stabilizer codes, and (3) codes with a constant encoding rate. Equivalently, the geometric entanglement of any logical state of these codes grows at least linearly with d. On the opposite side, we also show that this distance-entanglement tradeoff does not hold in general. For any constant d and k (number of logical qubits), we show there exists a family of codes such that the geometric entanglement of some logical states approaches zero in the limit of large code length.

Entanglement in many-body quantum systems is notoriously hard to characterize due to the exponentially many parameters involved to describe the state. On the other hand, we are usually not interested in all the microscopic details of the entanglement attern but only some of its global features. It turns out, quantum circuits of different levels of complexity provide a useful way to establish a hierarchy among many-body entanglement structures. A circuit of a finite depth generates only short range entanglement which is in the same gapped phase as an unentangled product state. A linear depth circuit on the other hand can lead to chaos beyond thermal equilibrium. In this talk, we discuss how to reach the interesting regime in between that contains nontrivial gapped orders. This is achieved using the Sequential Quantum Circuit — a circuit of linear depth but with each layer acting only on one subregion in the system. We discuss how the Sequential Quantum Circuit can be used to generate nontrivial gapped states with long range correlation or long range entanglement, perform renormalization group transformation in foliated fracton order, and create defect excitations inside the bulk of a higher dimensional topological state.

Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.

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