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Quantum annealing aims to provide a faster method for finding the minima of complicated functions, compared to classical computing, so there is an increasing interest in the relaxation dynamics of quantum spin systems. Moreover, it is known…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
The quantum dynamics of a two state system coupled to a bosonic reservoir with sub-Ohmic spectral density is investigated for strong friction. Numerically exact path integral Monte Carlo methods reveal that in contrast to conventional…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Quantum Tunneling is ubiquitous across different fields, from quantum chemical reactions, and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
The role of AI-generated synthetic data has recently been expanded to support realistic Monte Carlo simulations. However, guidance is limited on generating data with multilevel structures and designing simulations based on such data. This…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in…
Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
Accounting for inaccuracies in Monte Carlo simulations is a crucial step in any high energy physics analysis. It becomes especially important when training machine learning models, which can amplify simulation inaccuracies and introduce…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
An emergent theory of quantum measurement arises directly by considering the particular subset of many body wavefunctions that can be associated with classical condensed matter and its interaction with delocalized wavefunctions. This…
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks…