相关论文: Classical Algorithms for Constant Approximation of…

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 consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…

We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…

We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

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…

We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…

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…

Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…

The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…

Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…

Estimating the ground state energy of a multiparticle system with relative error $\e$ using deterministic classical algorithms has cost that grows exponentially with the number of particles. The problem depends on a number of state…

The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…

We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the…

We study the problems of state preparation, ground state preparation and quantum state preparation. We propose an analytic approach to a stochastic quantum algorithm which prepares the ground state for $n$-qubit Hamiltonian that is…

The DMRG method is very effective at finding ground states of 1D quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this paper we describe an efficient classical algorithm which…

The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian. First, we show the existence of a good product-state approximation for the ground-state energy of…

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…

Quantum chemistry calculations are important applications of quantum annealing. For practical applications in quantum chemistry, it is essential to estimate a ground state energy of the Hamiltonian with chemical accuracy. However, there are…

Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound…