相关论文: A variational description of the ground state stru…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our…
The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…
We study a class of random 3-SAT instances having exactly one solution. The properties of this ensemble considerably differ from those of a random 3-SAT ensemble. It is numerically shown that the running time of several complete and…
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution…
Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process…
One of the most promising applications for near term quantum computers is the simulation of physical quantum systems, particularly many-electron systems in chemistry and condensed matter physics. In solid state physics, finding the correct…
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation. [S. Bravyi and D. Gosset, Comm. Math. Phys. 356, 451 (2017)]. It is…
Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond…
We propose a variational framework for solving ground-state problems of open quantum systems governed by quantum stochastic differential equations (QSDEs). This formulation naturally accommodates bosonic operators, as commonly encountered…
Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for…
An analysis of the average-case complexity of solving random 3-Satisfiability (SAT) instances with backtrack algorithms is presented. We first interpret previous rigorous works in a unifying framework based on the statistical physics…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. For this…
We employ quantum variational methods to investigate a single-site interacting fermion-boson system -- an example of a minimal supersymmetric model that can exhibit spontaneous supersymmetry breaking. Our study addresses the challenges…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
Given a 2-SAT formula $F$ consisting of $n$ variables and $\cn$ random clauses, what is the largest number of clauses $\max F$ satisfiable by a single assignment of the variables? We bound the answer away from the trivial bounds of…