# Algorithms for Quantum Computers

@inproceedings{Smith2012AlgorithmsFQ, title={Algorithms for Quantum Computers}, author={Jamie Smith and Michele Mosca}, booktitle={Handbook of Natural Computing}, year={2012} }

This paper surveys the field of quantum computer algorithms. It gives a taste of both the breadth and the depth of the known algorithms for quantum computers, focusing on some of the more recent results. It begins with a brief review of quantum Fourier transform based algorithms, followed by quantum searching and some of its early generalizations. It continues with a more in-depth description of two more recent developments: algorithms developed in the quantum walk paradigm, followed by tensor… Expand

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An efficient formalism for simulating families of quantum circuits, that are non-universal but comprise important quantum gates such as QFT or CNOT, is developed and used to design new algorithms that provide quantum speedups. Expand

Application of quantum walks on graph structures to quantum computing

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The Computational Structure of the Quantum Computer Simulator and Its Performance Evaluation

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The computational structure of the quantum computer simulator has been derived, taking into account all the available features of constructing a simulator of a quantum computing device, and a software implementation of the derived universal computational structure is implemented. Expand

Quantum search with prior knowledge

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The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods… Expand

On the study of the Potts model, Tutte and Chromatic Polynomials, and the Connections with Computation Complexity and Quantum Computing

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Marina von Steinkirch∗ Institute of Physics and Astronomy, State University of New York at Stony Brook, USA (Dated: May 1, 2012) Abstract The Tutte polynomial of a graph is revised and the chromatic… Expand

The computational power of normalizer circuits over black-box groups

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- ArXiv
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This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems, and finds that normalizer circuits are powerful enough to factorize and solve classically-hard problems in the black-box setting. Expand

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By applying a quantum search algorithm to various heuristic and provable sieve algorithms from the literature, we obtain improved asymptotic quantum results for solving the shortest vector problem on… Expand

#### References

SHOWING 1-10 OF 74 REFERENCES

Quantum algorithms for algebraic problems

- Physics
- 2010

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas… Expand

A framework for fast quantum mechanical algorithms

- Computer Science, Physics
- STOC '98
- 1998

The sqrt(N) step quantum search algorithm is an immediate consequence of a framework for the design and analysis of quantum mechanical algorithms, and several other search-type applications are presented. Expand

Quantum Computing

- Natural Computing Series
- 2004

This second edition of Mika Hirvensalo's quantum computing book differs from most of the previous ones which are mainly physics-oriented because the special style of presentation makes the theory of quantum computing accessible to a larger audience. Expand

Quantum computation and quantum information

- Mathematics, Computer Science
- Mathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal… Expand

Colloquium : Quantum annealing and analog quantum computation

- Physics
- 2008

The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive… Expand

Quantum Computation and the Evaluation of Tensor Networks

- Mathematics, Physics
- SIAM J. Comput.
- 2010

A quantum algorithm is presented that additively approximates the value of a tensor network to a certain scale and is used to derive new quantum algorithms that approximate the partition function of a variety of classical statistical mechanical models, including the Potts model. Expand

Quantum algorithms revisited

- Mathematics, Physics
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1998

Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum… Expand

Quantum measurements and the Abelian Stabilizer Problem

- Computer Science, Mathematics
- Electron. Colloquium Comput. Complex.
- 1996

A polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm is presented, based on a procedure for measuring an eigenvalue of a unitary operator. Expand

Quantum speed-up of Markov chain based algorithms

- Mathematics, Computer Science
- 45th Annual IEEE Symposium on Foundations of Computer Science
- 2004

It is shown that under certain conditions, the quantum version of the Markov chain gives rise to a quadratic speed-up, and that the quantum escape time, just like its classical version, depends on the spectral properties of the transition matrix with the marked rows and columns deleted. Expand

Exponential algorithmic speedup by a quantum walk

- Mathematics, Computer Science
- STOC '03
- 2003

A black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer is constructed and it is proved that no classical algorithm can solve the problem in subexponential time. Expand