Related papers: Physically-Motivated Guiding States for Local Hami…
Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC…
We show that the Guided Local Hamiltonian problem for stoquastic Hamiltonians is (promise) BPP-hard. The Guided Local Hamiltonian problem extends the Local Hamiltonian problem by incorporating an additional input known as a guiding state,…
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have…
We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem, which we call 'Guidable Local Hamiltonian' problems. Unlike their guided counterparts, these problems do not have a guiding state provided as a part of…
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary $k$-local Hamiltonian acting on $n$ qubits. We first consider the setting where a good ``guiding state'' is available, which is the main…
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…
Finding the ground energy of a quantum system is a fundamental problem in condensed matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical…
We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a class which we call #BQP, which is the…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
The study of ground state energies of local Hamiltonians has played a fundamental role in quantum complexity theory. In this paper, we take a new direction by introducing the physically motivated notion of "ground state connectivity" of…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
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…
In this work we consider the ground space connectivity problem for commuting local Hamiltonians. The ground space connectivity problem asks whether it is possible to go from one (efficiently preparable) state to another by applying a…
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…
We study the computational complexity of the Local Hamiltonian problem under the promise that its ground state is succinctly represented. We show that the Succinct State 2-Local Hamiltonian problem, for qubit Hamiltonians, is (promise)…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known…
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…
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…
For any local Hamiltonian H, I construct a local CPT map and stopping condition which converges to the ground state subspace of H. Like any ground state preparation algorithm, this algorithm necessarily has exponential run-time in general…