Related papers: Resolvent-based quantum phase estimation: Towards …
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in…
We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
We propose an approach to measure the quantum phase of an electron in a non-Abelian system using the algorithm of Quantum Phase Estimation (QPE). The discrete-path systems were previously studied in the context of square or rectangular…
Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation…
Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
The learning process for multi layered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow-Hoff formula, do not change the eigenvectors of…
When estimating the eigenvalues of a given observable, even fault-tolerant quantum computers will be subject to errors, namely algorithmic errors. These stem from approximations in the algorithms implementing the unitary passed to phase…
Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
Quantum phase estimation is fundamental to advancing quantum science and technology. While much of the research has concentrated on estimating a single phase, the simultaneous estimation of multiple phases can yield significantly enhanced…
Quantum multiparameter estimation offers a framework for the simultaneous estimation of multiple parameters, pertaining to possibly noncommutating observables. While the optimal probe for estimating a single unitary phase is well understood…