English
Related papers

Related papers: On Euclidean Methods for Cubic and Quartic Jacobi …

200 papers

We propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm…

Quantum Physics · Physics 2024-10-03 Pranav Chandarana , Koushik Paul , Mikel Garcia-de-Andoin , Yue Ban , Mikel Sanz , Xi Chen

Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…

Quantum Physics · Physics 2025-05-14 Yusei Mori , Hideaki Hakoshima , Kyohei Sudo , Toshio Mori , Kosuke Mitarai , Keisuke Fujii

To ensure a long-term quantum computational advantage, the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares. Here, we demonstrate a superconducting quantum…

In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…

Numerical Analysis · Mathematics 2025-03-25 Wenrui Hao , Sun Lee , Xiangxiong Zhang

Using the methodology of (rigorous) {\it experimental mathematics}, we give a simple and motivated solution to Zudilin's question concerning a $q$-analog of a problem posed by Asmus Schmidt about a certain binomial coefficients sum. Our…

Combinatorics · Mathematics 2014-03-21 Thotsaporn Aek Thanatipanonda

Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…

Quantum Physics · Physics 2025-03-26 John M. Martyn , Patrick Rall

We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to $\gcd(deg(P),deg(Q))\le 35$, and…

Commutative Algebra · Mathematics 2017-08-29 Jorge A. Guccione , Juan J. Guccione , Rodrigo Horruitiner , Christian Valqui

Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols…

Quantum Physics · Physics 2021-08-11 Roderick D. Cochran , Daniel J. Gauthier

We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The numerical study of the effect of static…

Quantum Physics · Physics 2007-05-23 Giuliano Benenti , Giulio Casati , Simone Montangero , Dima L. Shepelyansky

The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…

Quantum Physics · Physics 2023-08-28 Michele Dall'Arno , Francesco Buscemi , Takeshi Koshiba

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…

Quantum Physics · Physics 2007-05-23 Matthias Steffen , Wim van Dam , Tad Hogg , Greg Breyta , Isaac Chuang

In this paper, we present a generalized Cuppen's divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. We extend the Cuppen's work to the rank two modifications of the form $A =T +\beta_1\bw_1\bw_1^T +…

Numerical Analysis · Mathematics 2015-06-30 Do Young Kwak , Jaeyeon Kim

We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…

Number Theory · Mathematics 2020-06-15 Arseniy , Sheydvasser

Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. In this context, we propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits…

Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…

Quantum Physics · Physics 2019-06-07 Alwin Zulehner , Philipp Niemann , Rolf Drechsler , Robert Wille

The superpositional wave function oscillations for finite-time implementation of quantum algorithms modifies the desired interference required for quantum computing. We propose a scheme with trapped ultracold ion-pairs being qubits to…

Quantum Physics · Physics 2007-05-23 Feng Mang , Zhu Xiwen , Gao Kelin , Shi Lei

It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…

Quantum Physics · Physics 2013-04-16 Erich Novak

We introduce the Shifted Legendre Symbol Problem and some variants along with efficient quantum algorithms to solve them. The problems and their algorithms are different from previous work on quantum computation in that they do not appear…

Quantum Physics · Physics 2007-05-23 Wim van Dam , Sean Hallgren

Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in…

Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…

Quantum Physics · Physics 2014-06-19 Hussain Anwar , Benjamin J. Brown , Earl T. Campbell , Dan E. Browne