Related papers: A Quantifier Elimination Algorithm for Linear Real…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
We propose new quantum algorithms to solve the regulator and the principal ideal problem in a real-quadratic number field. We improve the algorithms proposed by Hallgren by using two different techniques. The first improvement is the usage…
We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It…
We investigate practical algorithms to find or disprove the existence of small subsets of a dataset which, when removed, reverse the sign of a coefficient in an ordinary least squares regression involving that dataset. We empirically study…
Toda's Theorem is a fundamental result in computational complexity theory, whose proof relies on a reduction from a QBF problem with a constant number of quantifiers to a model counting problem. While this reduction, henceforth called…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket…
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
Minimal annihilating polynomials are very useful in a wide variety of algorithms in exact linear algebra. A new efficient method is proposed for calculating the minimal annihilating polynomials for all the unit vectors, for a square matrix…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and…
We consider the problem of existential quantifier elimination for Boolean formulas in Conjunctive Normal Form (CNF). We present a new method for solving this problem called Derivation of Dependency-Sequents (DDS). A Dependency-sequent…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…