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We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
In many practical applications, signals and environments are time- varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify…
Thompson sampling is an efficient algorithm for sequential decision making, which exploits the posterior uncertainty to address the exploration-exploitation dilemma. There has been significant recent interest in integrating Bayesian neural…
Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for…
Quantum dynamics compilation is an important task for improving quantum simulation efficiency: It aims to synthesize multi-qubit target dynamics into a circuit consisting of as few elementary gates as possible. Compared to deterministic…
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
Stochastic embedding transitions introduce a probabilistic mechanism for adjusting token representations dynamically during inference, mitigating the constraints imposed through static or deterministic embeddings. A transition framework was…
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
Compiling shallow and accurate quantum circuits for Hamiltonian simulation remains challenging due to hardware constraints and the combinatorial complexity of minimizing gate count and circuit depth. Existing optimization method pipelines…
A general but simple method is proposed to eliminate the quantum fluctuations generated by selected one-body operators in the excitation spectrum of a discrete RPA Hamiltonian. This method provides an outstanding tool for the removal of the…
Environmental fluctuations degrade the performance of solid-state qubits but can in principle be mitigated by real-time Hamiltonian estimation down to time scales set by the estimation efficiency. We implement a physics-informed and an…
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…