相关论文: Counting Abelian Squares for a Problem in Quantum …

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…

During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles…

This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…

Quasiprobabilistic cutting techniques allow us to partition large quantum circuits into smaller subcircuits by replacing non-local gates with probabilistic mixtures of local gates. The cost of this method is a sampling overhead that scales…

A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…

In this paper we propose an algorithm for enumerating diagonal Latin squares of small order. It relies on specific properties of diagonal Latin squares to employ symmetry breaking techniques, and on several heuristic optimizations and bit…

Quantum computing has become a promising computing approach because of its capability to solve certain problems, exponentially faster than classical computers. A $n$-qubit quantum system is capable of providing $2^{n}$ computational space…

Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…

Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…

This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…

I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: 1) XXZ model; 2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for…

We give an efficient algorithm to evaluate a certain class of exponential sums, namely the periodic, quadratic, multivariate half Gauss sums. We show that these exponential sums become $\#\mathsf{P}$-hard to compute when we omit either the…

Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…

Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…

Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an…

Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…

A new method for quantum computation in the presence of detected spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes $n$ logical qubits into…

We present a formulation of quantum circuit diagrams based on the exponential map which provides a new way to calculate graphically with circuits. We present a sound list of rewrite rules for this formulation and demonstrate a variety of…

We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for…