相关论文: Combinational Logic Circuit Design with the Buchbe…

We consider the possibility of performing linear optical quantum computation making use of extra photonic degrees of freedom. In particular we focus on the case where we use photons as quadbits. The basic 2-quadbit cluster state is a…

We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gr\"obner…

Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…

We study in detail the algebraic structures underlying quantum circuits generated by CNOT gates. Our results allow us to propose polynomial-time heuristics to reduce the number of gates used in a given CNOT circuit and we also give…

Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…

An effective method for the quantitative description of the electronic excited states of polyatomic systems is developed by using computer technology. The proposed method allows calculating various properties of matter at the atomic level…

A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…

We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…

We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results we give an algorithm for the following problem: given a homogeneous polynomial of degree 3, decide whether it can be…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

We propose a scheme for solving mixed-integer programming problems in which the optimization problem is translated to a ground-state preparation problem on a set of bosonic quantum field modes (qumodes). We perform numerical demonstrations…

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs, and also simplify the task of making the…

A monotone Boolean circuit is composed of OR gates, AND gates and input gates corresponding to the input variables and the Boolean constants. It is $q$-multilinear if for each its output gate $o$ and for each prime implicant $s$ of the…

The detailed investigation of electronic and magnetic properties of polymeric coordination materials with accurate ab initio quantum mechanical methods is often computationally extremely demanding because of the large number of atoms in the…

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

We present an experimentally feasible scheme to implement holonomic quantum computation in the ultrastrong-coupling regime of light-matter interaction. The large anharmonicity and the Z2 symmetry of the quantum Rabi model allow us to build…

Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…

For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…