Related papers: Linear time algorithm for quantum 2SAT
In the Max $r$-SAT problem, the input is a CNF formula with $n$ variables where each clause is a disjunction of at most $r$ literals. The objective is to compute an assignment which satisfies as many of the clauses as possible. While there…
Recently, Dunjko et al.(PRL, 2018) proposed an algorithm for accelerating the solution of 3-satisfiability problems using a small-scale quantum computer. In this paper, we design a distributed quantum-classical hybrid algorithm for solving…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
Optimization problems such as the NP-complete 3-SAT provide an important benchmark for the difficult task of finding ground-states in strongly correlated many-body systems with rugged energy landscapes. The study of random 3-SAT problems as…
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…
In the paper "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", TCS Volume 769 (2019), pages 63--74, the LHIT problem is proposed as follows: For a given set of non-intersecting line…
We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…
Many search-based quantum algorithms that achieve a theoretical speedup are not practically relevant since they require extraordinarily long coherence times, or lack the parallelizability of their classical counterparts.This raises the…
This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…
A 3-SAT problem is called positive and planar if all the literals are positive and the clause-variable incidence graph (i.e., SAT graph) is planar. The NAE 3-SAT and 1-in-3-SAT are two variants of 3-SAT that remain NP-complete even when…
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…
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 present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
We show that the NP complete problems MAX CUT and INDEPENDENT SET can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. He introduced the quantum complexity class BQNP as the quantum analog of NP, and showed that the…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
We report a cluster of results on k-QSAT, the problem of quantum satisfiability for k-qubit projectors which generalizes classical satisfiability with k-bit clauses to the quantum setting. First we define the NP-complete problem of product…
A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…
We demonstrate that any logical problem can be solved by Bayesian inference. In this approach, the distinction between complexity classes vanishes. The method is illustrated by solving the 3-SAT problem in polynomial time. Beyond this,…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…