Related papers: StoqMA meets distribution testing
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable…
The present era of quantum processors with hundreds to thousands of noisy qubits has sparked interest in understanding the computational power of these devices and how to leverage it to solve practically relevant problems. For applications…
We study the problem of recovering the latent ground truth labeling of a structured instance with categorical random variables in the presence of noisy observations. We present a new approximate algorithm for graphs with categorical…
A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few…
We study distribution testing in the standard access model and the conditional access model when the memory available to the testing algorithm is bounded. In both scenarios, the samples appear in an online fashion and the goal is to test…
The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…
There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example,…
New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the…
This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…
The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…
Identifying non-classicality unambiguously and inexpensively is a long-standing open challenge in physics. The No-Signalling-In-Time protocol was developed as an experimental test for macroscopic realism, and serves as a witness of quantum…
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations…
Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
We address the witnessing of quantum correlations beyond the limits imposed by an ensemble statistical average. By relying upon the continuous observation of a single quantum open system under the action of classical or quantum noise, we…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
Effective Hamiltonians, when used in tandem with statistical mechanics techniques, offer a rigorous connection between 0 Kelvin ab-initio predictions and finite temperature experimental observations. For alloys, cluster expansion…