Related papers: The Quantum Eigenvalue Problem and Z-Eigenvalues o…
Let A be an n x n symmetric random matrix whose upper-triangular entries are independent and follow possibly non-identical subgaussian distributions. This paper investigates the spectral properties of A, including its eigenvalues and…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using…
By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in…
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin chains with an improvement on the conventional notation. The rest of this thesis is divided into two parts. The first part is devoted to…
A symmetry of a state $\vert \psi \rangle$ is a unitary operator of which $\vert \psi \rangle$ is an eigenvector. When $\vert \psi \rangle$ is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical…
Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical problems. However, quantum machine learning itself is limited by low effective dimensions achievable in state-of-the-art…
One of the best systems for the study of quantum chaos is the atomic nucleus. A confined particle with general boundary conditions can present chaos and the eigenvalue problem can exhibit this fact. We study a toy model in which the…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
The purpose of quantum private comparison (QPC) is to solve "Tierce problem" using quantum mechanics laws, where the "Tierce problem" is to judge whether the secret data of two participants are equal under the condition of protecting data…
A technique for constructing an infinite tower of pairs of PT-symmetric Hamiltonians, $\hat{H}_n$ and $\hat{K}_n$ (n=2,3,4,...), that have exactly the same eigenvalues is described. The eigenvalue problem for the first Hamiltonian…
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor…
Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing a parameter. In the canonical…
Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…
We introduce a purely geometric formulation for two different measures addressed to quantify the entanglement between different parts of a tripartite qubit system. Our approach considers the entanglement-polytope defined by the smallest…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for…
Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the…