相关论文: Rigorous test of the Raleigh-Ritz method for Mexic…

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…

A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the…

We propose a heuristic method to obtain the approximate groundstate for a Hamiltonian in the qubit form, based on the stabilizer formalism. These states may serve as proper initial states for further refined computation. It would be…

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…

Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized…

Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this…

We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over a tensor train variety. The complex critical points of this…

By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by…

We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N=1 toy…

We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of…

Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…

The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum…

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…

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then…

We develop Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge- Higgs models and introduce a new observable for the constraint effective Higgs potential. We use an extension of the so-called Rattle algorithm to…

The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some…

We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a…

Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo…