Related papers: Geometry and symmetry in quantum Boltzmann machine
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
In standard quantum theory, symmetry is defined in the spirit of Klein's Erlangen Program: the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the…
The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts…
Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state,…
Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot", vast computational…
Bosonic Bogoliubov de Gennes (BBdG) Hamiltonians describe the excitations of weakly interacting Bose condensates as well as photonic systems under parametric driving. Their topological features have been studied mainly by utilizing a…
Recently, quantum-state representation using artificial neural networks has started to be recognized as a powerful tool. However, due to the black-box nature of machine learning, it is difficult to analyze what machine learns or why it is…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…
Recent results have established dramatic advantages in learning properties of quantum states when a quantum computer is available to process or jointly measure multiple copies of the unknown quantum state. Learning tasks can be accomplished…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to…
Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra…
Quantum mechanics can produce correlations that are stronger than classically allowed. This stronger-than-classical correlation is the "fuel" for quantum computing. In 1991 Schumacher forwarded a beautiful geometric approach, analogous to…
We propose a Restricted Boltzmann Machine (RBM) neural network using a quantum thermodynamics formalism and the maximization of entropy as the cost function for the optimization problem. We verify the possibility of using an entropy…
We extend the semiclassical black hole microstate construction to include quantum corrections to the microscopic entropy using a doubly holographic model of black holes. Specifically, we consider a double-sided black hole on a JT brane with…
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to…
Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations…