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We address the problem of estimating the phase phi given N copies of the phase rotation gate u(phi). We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by…

Quantum Physics · Physics 2015-06-26 W. van Dam , G. M. D'Ariano , A. Ekert , C. Macchiavello , M. Mosca

Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has…

Quantum Physics · Physics 2023-02-16 Marko J. Rančić

When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…

Mathematical Software · Computer Science 2007-05-23 Nicolas Brisebarre , Jean-Michel Muller

Retrieving classical information encoded in optical modes is at the heart of many quantum information processing tasks, especially in the field of quantum communication and sensing. Yet, despite its importance, the fundamental limits of…

Quantum Physics · Physics 2021-05-11 Ignatius William Primaatmaja , Asaph Ho , Valerio Scarani

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We…

Quantum Physics · Physics 2022-06-16 Ruslan Shaydulin , Yuri Alexeev

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…

Quantum Physics · Physics 2010-10-13 Cheng Lu , Jianxin Chen , Runyao Duan

Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…

Computational Geometry · Computer Science 2026-05-12 Timothy M. Chan , Hsien-Chih Chang , Jie Gao , Sándor Kisfaludi-Bak , Hung Le , Da Wei Zheng

Drug-drug interactions (DDIs) strongly affect the safety and efficacy of combination therapies. Despite the availability of large DDI databases, selecting optimal multi-drug combinations that balance safety, therapeutic benefit, and regimen…

Quantum Physics · Physics 2026-01-27 Mai Nguyen Phuong Nhi , Lan Nguyen Tran , Le Bin Ho

In this work, we propose a new way to (non-interactively, verifiably) demonstrate quantum advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) constant degree multivariate…

Quantum Physics · Physics 2025-09-10 Pierre Briaud , Itai Dinur , Riddhi Ghosal , Aayush Jain , Paul Lou , Amit Sahai

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…

Quantum Physics · Physics 2024-01-15 Yagnik Chatterjee , Eric Bourreau , Marko J. Rančić

Given a 0-dimensional affine K-algebra R=K[x_1,...,x_n]/I, where I is an ideal in a polynomial ring K[x_1,...,x_n] over a field K, or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether…

Commutative Algebra · Mathematics 2019-08-07 Martin Kreuzer , Le Ngoc Long , Lorenzo Robbiano

A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space,…

Optimization and Control · Mathematics 2022-10-26 Karl Kunisch , Donato Vásquez-Varas , Daniel Walter

We embed 1-layer QAOA circuits into the larger class of parameterized Instantaneous Quantum Polynomial circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The use of analytic…

Quantum Physics · Physics 2024-02-13 Sebastian Leontica , David Amaro

The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…

Quantum Physics · Physics 2013-10-04 Austin G. Fowler

Quantum-optical coherence tomography (Q-OCT) is an interferometric technique for axial imaging offering several advantages over conventional methods. Chirped-pulse interferometry (CPI) was recently demonstrated to exhibit all of the…

Quantum Physics · Physics 2009-09-07 Jonathan Lavoie , Rainer Kaltenbaek , Kevin J. Resch

We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…

Computational Complexity · Computer Science 2016-06-09 Gabor Ivanyos , Miklos Santha

In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial time and space if the given point is not in the convex hull of…

Optimization and Control · Mathematics 2023-10-09 Marius Costandin , Beniamin Costandin

We propose a new formulation of quadratic optimization problems. The objective function $F(f(x),g(x))$ is given as composition of a quadratic function $F(z)$ with two $n$-variate quadratic functions $z_1=f(x)$ and $z_2=g(x).$ In addition,…

Optimization and Control · Mathematics 2020-12-21 Huu-Quang Nguyen , Ruey-Lin Sheu , Yong Xia

Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…

Robotics · Computer Science 2024-05-15 Rudolf Reiter , Rien Quirynen , Moritz Diehl , Stefano Di Cairano