Related papers: A linear time quantum algorithm for 3SAT using irr…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid…
This paper presents an algorithm for 3-SAT problems. First, logical formulas are transformed into elementary algebraic formulas. Second, complex trigonometric functions are assigned to the variables in the elementary algebraic formulas, and…
The aim of the paper is to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard…
The classical 3SUM conjecture states that the class of 3SUM-hard problems does not admit a truly subquadratic $O(n^{2-\delta})$-time algorithm, where $\delta >0$, in classical computing. The geometric 3SUM-hard problems have widely been…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a…
We construct a tensor network that delivers an unnormalized quantum state whose coefficients are the solutions to a given instance of 3SAT, an NP-complete problem. The tensor network contraction that corresponds to the norm of the state…
The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and…
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…
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…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
An algorithm is given for finding the solutions to 3SAT problems. The algorithm uses Bienstock's reduction from 3SAT to existence of induced odd cycle of length greater than three, passing through a prescribed node in the constructed graph.…
Quantum algorithm design plays a crucial role in exploiting the computational advantage of quantum devices. Here we develop a deep-reinforcement-learning based approach for quantum adiabatic algorithm design. Our approach is generically…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
This paper outlines a mathematical framework of quantum probability in which the time asymmetry in describing measuring processes is avoided. The main objects of the framework are hyperfinite operations, which are constructed by using…
Landauer's limit on heat dissipation during information erasure is critical as devices shrink, requiring optimal pure-state preparation to minimise errors. However, Nernst's third law states this demands infinite resources in energy, time,…
In signed k-SAT problems, one fixes a set M and a set $\mathcal S$ of subsets of M, and is given a formula consisting of a disjunction of m clauses, each of which is a conjunction of k literals. Each literal is of the form "$x \in S$",…