Related papers: Quasi-sparse eigenvector diagonalization and stoch…
This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagonalization (SQD) as near-term alternatives…
We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of $\hbar $. Considering $\hbar $ as a running parameter, a differential equation connecting two diagonalization processes for…
We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. This results in a rich class of systems which include the GUE and the fixed $q$ SYK theories. Our…
An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2x2) matrices. The method is based on the measurement of…
We experimentally demonstrate that a hybrid quantum-classical algorithm can outperform purely classical, off-the-shelf selected configuration interaction methods. First, we construct a class of local Hamiltonian problems with sparse ground…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by…
We present error mitigation (EM) techniques for noisy intermediate-scale quantum computers (QC) based on density matrix purification and perturbative corrections to the target energy. We incorporate this scheme into the variational quantum…
Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z_2 symmetry. Natural realizations of such…
A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to…
The estimation of low energies of many-body systems is a cornerstone of computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization…
The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum…
Given a matrix A \in R^{m x n}, we present a randomized algorithm that sparsifies A by retaining some of its elements by sampling them according to a distribution that depends on both the square and the absolute value of the entries. We…