Related papers: Quantum Measurement Statistics as Bayesian Uncerta…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression and neural operator learning (DeepONet). Specifically, we…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…
Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this…
Uncertainty Quantification (UQ) is an essential step in computational model validation because assessment of the model accuracy requires a concrete, quantifiable measure of uncertainty in the model predictions. The concept of UQ in the…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&E) applications where risk management is a core component,…
Measurement-based quantum computation (MBQC) is a model of quantum computation, in which computation proceeds via adaptive single qubit measurements on a multi-qubit quantum state. It is computationally equivalent to the circuit model.…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…
Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…
This work presents novel extensions for combining two frameworks for quantifying both aleatoric (i.e., irreducible) and epistemic (i.e., reducible) sources of uncertainties in the modeling of engineered systems. The data-consistent (DC)…
The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…
In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification…
Canonical discrete quantum error correction (DQEC) schemes use projective von Neumann measurements on stabilizers to discretize the error syndromes into a finite set, and fast unitary gates are applied to recover the corrupted information.…