# 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…

## 1,484 Citations

### Quantum Adiabatic Evolution Algorithms with Different Paths

- 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…

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

- PhysicsArXiv
- 2012

### 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…

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

- Physics, Computer ScienceScientific 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

- 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, Computer SciencePhysical 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

- PhysicsRAIRO 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.

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

- Physics
- 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…

### Learning adiabatic quantum algorithms for solving optimization problems

- Computer Science, Physics
- 2019

A technique to learn the encoding of a given optimization problem into a problem Hamiltonian and the convergence of the algorithm is presented and the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.

### Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems

- Physics, Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to…

## References

SHOWING 1-10 OF 17 REFERENCES

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

- Computer Science, PhysicsArXiv
- 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

- 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

- 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 $|w〉$…

### A fast quantum mechanical algorithm for database search

- Computer ScienceSTOC '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 ScienceSIAM Rev.
- 1999

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

### Critical Behavior in the Satisfiability of Random Boolean Expressions

- Computer ScienceScience
- 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

- Computer ScienceSIAM 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 $o(2^{n/2})$.

### Sharp thresholds of graph properties, and the -sat problem

- Mathematics
- 1999

Consider G(n, p) to be the probability space of random graphs on n vertices with edge probability p. We will be considering subsets of this space defined by monotone graph properties. A monotone…