Related papers: Complexity of geometrically local stoquastic Hamil…

The k-local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k<=2. It was known that the problem is QMA-complete for any…

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…

Despite having an unnatural definition, $\mathsf{StoqMA}$ plays a central role in Hamiltonian complexity, e.g., in the classification theorem of the complexity of Hamiltonians by Cubitt and Montanaro (SICOMP 2016). Moreover, it lies between…

The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…

We study several problems related to properties of non-negative matrices that arise at the boundary between quantum and classical probabilistic computation. Our results are twofold. First, we identify a large class of quantum Hamiltonians…

We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is QMA-complete. We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using…

We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the…

We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete. We also prove similar results in 2D translation-invariant systems and for the 3D Heisenberg and…

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…

Here we present a problem related to the local Hamiltonian problem (identifying whether the ground state energy falls within one of two ranges) which is restricted to being translationally invariant. We prove that for problems with a fixed…

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)…

We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results. We show that the stoquastic local Hamiltonian problem is $\textbf{StoqMA}$-complete even for globally…

Although stoquastic Hamiltonians are known to be simulable via sign-problem-free quantum Monte Carlo (QMC) techniques, the non-stoquasticity of a Hamiltonian does not necessarily imply the existence of a QMC sign problem. We give a…

Estimation of the minimum eigenvalue of a quantum Hamiltonian can be formalised as the Local Hamiltonian problem. We study the natural special case of the Local Hamiltonian problem where the same 2-local interaction, with differing weights,…

Quantum many-body systems whose Hamiltonians are non-stoquastic, i.e., have positive off-diagonal matrix elements in a given basis, are known to pose severe limitations on the efficiency of Quantum Monte Carlo algorithms designed to…

We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN) in the special case when a Hamiltonian obeys conditions of the Perron-Frobenius theorem: all off-diagonal matrix elements in the standard basis are real and…

We prove that 2-Local Hamiltonian (2-LH) with Low Complexity problem is QCMA-complete by combining the results from the QMA-completeness[4] of 2-LH and QCMA-completeness of 3-LH with Low Complexity[6]. The idea is straightforward. It has…

StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as…

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo…

We examine the problem of determining whether a multi-qubit two-local Hamiltonian can be made stoquastic by single-qubit unitary transformations. We prove that when such a Hamiltonian contains one-local terms, then this task can be NP-hard.…