Related papers: Quantum Algorithm for Low Energy Effective Hamilto…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
We present a simple algebraic procedure that can be applied to solve a range of quantum eigenvalue problems without the need to know the solution of the Schr\"odinger equation. The procedure, presented with a pedagogical purpose, is based…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
Quantum phase estimation is a cornerstone in quantum algorithm design, allowing for the inference of eigenvalues of exponentially-large sparse matrices.The maximum rate at which these eigenvalues may be learned, --known as the Heisenberg…
We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of the dynamic mode decomposition algorithm used in diverse fields such as fluid…
The Variational Quantum Eigensolver (VQE), as a hybrid quantum-classical algorithm, is an important tool for effective quantum computing in the current noisy intermediate-scale quantum (NISQ) era. However, the traditional hardware-efficient…
Quantum $k$-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem…
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…
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…
Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol…
In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for the…
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for…
In this work, we propose a quantum unitary downfolding formalism based on the driven similarity renormalization group (QDSRG) that may be combined with quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a classical…
We give a quantum algorithm for solving the Bounded Distance Decoding (BDD) problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm uses a well-known but challenging-to-use quantum state on…
The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a…
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…
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…