相关论文: The 2-local Hamiltonian problem encompasses NP

We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we…

Complexity of a quantum analogue of the satisfiability problem is studied. Quantum k-SAT is a problem of verifying whether there exists n-qubit pure state such that its k-qubit reduced density matrices have support on prescribed subspaces.…

Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…

A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…

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…

In recent years, quantum annealing has gained the status of being a promising candidate for solving various optimization problems. Using a set of hard 2-satisfiabilty (2-SAT) problems, consisting of upto 18-variables problems, we analyze…

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

In this paper we quantize the $N$-dimensional classical Hamiltonian system $H= \frac{|q|}{2(\eta + |q|)} p^2-\frac{k}{\eta +|q|}$, that can be regarded as a deformation of the Coulomb problem with coupling constant $k$, that it is smoothly…

We investigate the computational complexity of the Local Hamiltonian (LH) problem and the approximation of the Quantum Partition Function (QPF), two central problems in quantum many-body physics and quantum complexity theory. Both problems…

In this paper, we introduce a so-called Multistage graph Simple Path (MSP) problem and show that the Hamilton Circuit (HC) problem can be polynomially reducible to the MSP problem. To solve the MSP problem, we propose a polynomial algorithm…

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…

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…

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…

A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in closed form. An entirely new class of QES Hamiltonians having sextic polynomial…

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas…

One of the main problems in quantum complexity theory is that our understanding of the theory of QMA-completeness is not as rich as its classical analogue, the NP- completeness. In this paper we consider the clique problem in graphs, which…

The Quantum k-SAT problem is the quantum generalization of the k-SAT problem. It is the problem whether a given local Hamiltonian is frustration-free. Frustration-free means that the ground state of the k-local Hamiltonian minimizes the…