# A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

@article{Farhi2001AQA, title={A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem}, author={Edward Farhi and Jeffrey Goldstone and Sam Gutmann and Joshua M. Lapan and A Lundgren and Daniel Preda}, journal={Science}, year={2001}, volume={292}, pages={472 - 475} }

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We tested one such algorithm by applying it to randomly generated hard instances of an NP-complete problem. For the small examples that we could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built…

## Topics from this paper

## 1,325 Citations

Quantum Adiabatic Evolution Algorithms with Different Paths

- Mathematics, Physics
- 2002

In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground…

Measurement-driven analog of adiabatic quantum computation for frustration-free Hamiltonians

- PhysicsPhysical Review A
- 2019

The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems…

The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective

- Physics, Computer ScienceArXiv
- 2012

This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.

Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem

- Computer Science, MedicineScientific reports
- 2016

By applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact.

Scalable Architecture for Adiabatic Quantum Computing of Np-Hard Problems

- Mathematics, Physics
- 2004

We present a comprehensive review of past research into adiabatic quantum computation and then propose a scalable architecture for an adiabatic quantum computer that can treat NP-Hard Problems…

Experimental implementation of an adiabatic quantum optimization algorithm.

- Physics, MedicinePhysical review letters
- 2003

A nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm that agrees well with the prediction of a simple decoherence model is reported.

An introduction to quantum annealing

- Computer Science, MathematicsRAIRO Theor. Informatics Appl.
- 2011

This survey paper illustrates how hard combinatorial problems are tackled by quantum computation and presents some examples of the heuristics provided by quantum annealing.

Learning adiabatic quantum algorithms over optimization problems

- Computer ScienceQuantum Mach. Intell.
- 2021

This paper proposes a hybrid quantum-classical algorithm that, by solving optimization problems with an adiabatic machine, determines a problem Hamiltonian assuming restrictions on the class of available problem Hamiltonians.

A ug 2 00 2 Quantum Adiabatic Evolution Algorithms with Different Paths

- 2008

In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground…

On fixed-gap adiabatic quantum computation

- Physics
- 2010

Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum…

## References

SHOWING 1-10 OF 22 REFERENCES

A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability

- Mathematics, Computer ScienceArXiv
- 2000

Numerical results on randomly generated instances of an NP-complete problem and of a problem that can be solved classically in polynomial time are presented.

Quantum Computation by Adiabatic Evolution

- Mathematics, Physics
- 2000

We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that…

Finding cliques by quantum adiabatic evolution

- Mathematics, PhysicsQuantum Inf. Comput.
- 2002

The results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph, appear to require only a quadratic run time.

Quantum annealing in the transverse Ising model

- Physics
- 1998

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between…

Analog analogue of a digital quantum computation

- Physics, Mathematics
- 1996

We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system with a Hamiltonian of the form $E|w〉〈w|$ where $|w〉$…

Quantum annealing of a disordered magnet

- Chemistry, Materials ScienceScience
- 1999

Thermal and quantum annealing are compared in a model disordered magnet, where the effects of quantum mechanics can be tuned by varying an applied magnetic field, and the results indicate that quantumAnnealing hastens convergence to the optimum state.

A fast quantum mechanical algorithm for database search

- Computer Science, PhysicsSTOC '96
- 1996

In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

- Computer Science, MathematicsSIAM Rev.
- 1999

Efficient randomized algorithms are given for factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems.

Critical Behavior in the Satisfiability of Random Boolean Expressions

- Mathematics, MedicineScience
- 1994

Finite-size scaling, a method from statistical physics, can be used to characterize size-dependent effects near the threshold and a relationship can be drawn between thresholds and computational complexity.

Strengths and Weaknesses of Quantum Computing

- Mathematics, PhysicsSIAM J. Comput.
- 1997

It is proved that relative to an oracle chosen uniformly at random with probability 1 the class $\NP$ cannot be solved on a quantum Turing machine (QTM) in time $o(2^{n/2})$.