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We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems…

We study the computational complexity of 2-local Hamiltonian problems generated by a positive-weight symmetric interaction term, encompassing many canonical problems in statistical mechanics and optimization. We show these problems belong…

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…

The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…

We prove several new results concerning the pure quantum polynomial hierarchy (pureQPH). First, we show that QMA(2) is contained in pureQSigma2, that is, two unentangled existential provers can be simulated by competing existential and…

We present a new way of encoding a quantum computation into a 3-local Hamiltonian. Our construction is novel in that it does not include any terms that induce legal-illegal clock transitions. Therefore, the weights of the terms in the…

Understanding the entanglement structure of local Hamiltonian ground spaces is a physically motivated problem, with applications ranging from tensor network design to quantum error-correcting codes. To this end, we study the complexity of…

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…

We describe Kitaev's result from 1999, in which he defines the complexity class QMA, the quantum analog of the class NP, and shows that a natural extension of 3-SAT, namely local Hamiltonians, is QMA complete. The result builds upon the…

We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…

Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are ``consistent'' if there exists some global state…

The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA, see quant-ph/0406180. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local…

In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…

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…

Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…

$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers,…

The Local Hamiltonian problem is the problem of estimating the least eigenvalue of a local Hamiltonian, and is complete for the class QMA. The 1D problem on a chain of qubits has heuristics which work well, while the 13-state qudit case has…

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…

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 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.…