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We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as Quantum…
Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. A quantum advantage arises due to the intractability of…
The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive. In this…
Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state,…
We investigate how machine learning models acquire the ability to compose music and how musical information is internally represented within such models. We develop a composition algorithm based on a restricted Boltzmann machine (RBM), a…
Exploiting the fact that samples drawn from a quantum annealer inherently follow a Boltzmann-like distribution, annealing-based Quantum Boltzmann Machines (QBMs) have gained increasing popularity in the quantum research community. While…
Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…
Quantum neuromorphic computing (QNC) is a sub-field of quantum machine learning (QML) that capitalizes on inherent system dynamics. As a result, QNC can run on contemporary, noisy quantum hardware and is poised to realize challenging…
Stochastic gradient descent based algorithms are typically used as the general optimization tools for most deep learning models. A Restricted Boltzmann Machine (RBM) is a probabilistic generative model that can be stacked to construct deep…
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial…
Within context of quantum logic, it is possible to assign dispersion-free probabilities to experimental propositions pertaining to qubits. This makes qubits distinct from the rest of quantum systems since the latter do not admit…
We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training objective function. Our algorithm is…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
Existing Score-Based Models (SBMs) can be categorized into constrained SBMs (CSBMs) or unconstrained SBMs (USBMs) according to their parameterization approaches. CSBMs model probability density functions as Boltzmann distributions, and…
We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of…
Geometric frustration gives rise to emergent quantum phenomena and exotic phases of matter. While Monte Carlo methods are traditionally used to simulate such systems, their sampling efficiency is limited by the complexity of interactions…
Lattice Boltzmann (LB) on quantum devices must reconcile unitary gate evolution with the dissipative \emph{collision} step. In the multiple-relaxation-time (MRT) class, we work in the common setting of \emph{modewise diagonal} moment…
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models…