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Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…

Quantum Physics · Physics 2009-10-08 Aram W. Harrow , Avinatan Hassidim , Seth Lloyd

Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…

Computational Complexity · Computer Science 2024-09-13 Arash Vaezi , Ali Movaghar , Mohammad Ghodsi , Seyed Mohammad Hussein Kazemi , Negin Bagheri Noghrehy , Seyed Mohsen Kazemi

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…

Quantum Physics · Physics 2015-06-26 Sos S. Agaian , Andreas Klappenecker

Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or…

Computation · Statistics 2022-04-05 Anna Lopatnikova , Minh-Ngoc Tran , Scott A. Sisson

Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…

Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…

Quantum Physics · Physics 2020-04-03 Viv Kendon

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…

We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…

Quantum Physics · Physics 2007-05-23 Tad Hogg

We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…

Artificial Intelligence · Computer Science 2009-09-25 T. Hogg

Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…

Quantum Physics · Physics 2025-06-09 Chao Ding , Shi Wang , Yaonan Wang , Weibo Gao

We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…

Quantum Physics · Physics 2007-05-23 Christof Zalka

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.

Quantum Physics · Physics 2007-05-23 Michael Batty , Samuel L. Braunstein , Andrew J. Duncan , Sarah Rees

Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a…

We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…

Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…

Quantum Physics · Physics 2009-11-09 Alberto Politi , Jonathan C. F. Matthews , Jeremy L. O'Brien

This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…

Quantum Physics · Physics 2024-12-10 Sajad Fathi Hafshejani , Md Mohsin Uddin , David Neufeld , Daya Gaur , Robert Benkoczi

The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…

Quantum Physics · Physics 2009-11-10 Edward Gerjuoy

Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion…

Quantum Physics · Physics 2025-11-04 Hans Gundlach , Hrvoje Kukina , Jayson Lynch , Neil Thompson

Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…

Quantum Physics · Physics 2023-10-05 Jessie M. Henderson , John Kath , John K. Golden , Allon G. Percus , Daniel O'Malley