English
Related papers

Related papers: Optimal scaling quantum linear systems solver via …

200 papers

In this report, we explore the use of a quantum optimization algorithm for obtaining low energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of…

We study the Hamiltonian-independent contribution to the complexity of quantum optimal control problems. The optimization of controls that steer quantum systems to desired objectives can itself be considered a classical dynamical system…

Quantum Physics · Physics 2007-08-28 Raj Chakrabarti , Rebing Wu , Herschel Rabitz

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…

Quantum Physics · Physics 2007-11-22 Dorit Aharonov , Wim van Dam , Julia Kempe , Zeph Landau , Seth Lloyd , Oded Regev

In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…

Atomic Physics · Physics 2009-11-11 Avner Fleischer , Nimrod Moiseyev

We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…

Quantum Physics · Physics 2022-01-17 Almudena Carrera Vazquez , Ralf Hiptmair , Stefan Woerner

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…

Quantum Physics · Physics 2019-03-15 Peng Qian , Wei-Cong Huang , Gui-Lu Long

Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…

Quantum Physics · Physics 2025-04-01 Titus D. Morris , Ananth Kaushik , Martin Roetteler , Phillip C. Lotshaw

We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…

Quantum Physics · Physics 2012-03-30 Edward Farhi , Jeffrey Goldstone , David Gosset , Sam Gutmann , Harvey B. Meyer , Peter Shor

Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…

Statistical Mechanics · Physics 2013-01-29 Victor Bapst , Laura Foini , Florent Krzakala , Guilhem Semerjian , Francesco Zamponi

In this paper,we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a non degenerate continuous spectrum. A new strategy is initiated by defining a kind of gap, "a virtual gap", for the…

Quantum Physics · Physics 2008-04-28 M. Maamache , Y. Saadi

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a…

Quantum Physics · Physics 2009-11-10 V. N. Smelyanskiy , S. Knysh , R. D. Morris

Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing…

Quantum Physics · Physics 2021-05-06 Veit Stooß , Martin Ulmke , Felix Govaers

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

Quantum Physics · Physics 2017-04-07 Michael Ben-Or , Lior Eldar

The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…

Quantum Physics · Physics 2022-11-10 David Headley , Thorge Müller , Ana Martin , Enrique Solano , Mikel Sanz , Frank K. Wilhelm

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g. in quantum annealing and in studies of topological properties of matter. In this setup,…

Mathematical Physics · Physics 2017-09-29 Sven Bachmann , Wojciech De Roeck , Martin Fraas

Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…

Quantum Physics · Physics 2024-04-12 Hari Krovi

Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard…

We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…

Quantum Physics · Physics 2019-02-04 Guillaume Verdon , Juan Miguel Arrazola , Kamil Brádler , Nathan Killoran

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…

Quantum Physics · Physics 2014-02-21 Dominic W. Berry