# Adiabatic quantum computation is equivalent to standard quantum computation

@article{Aharonov2004AdiabaticQC, title={Adiabatic quantum computation is equivalent to standard quantum computation}, author={Dorit Aharonov and Wim van Dam and Julia Kempe and Zeph Landau and Seth Lloyd and Oded Regev}, journal={45th Annual IEEE Symposium on Foundations of Computer Science}, year={2004}, pages={42-51} }

The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm. This implies that the adiabatic computation model and the standard quantum circuit model are polynomially equivalent. We also describe an extension of this result with implications to physical implementations of…

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## References

SHOWING 1-10 OF 68 REFERENCES

### From quantum circuits to adiabatic algorithms

- Physics, Computer Science
- 2005

This paper shows a way that directly maps any arbitrary circuit in the standard quantum-computing model to an adiabatic algorithm of the same depth and looks for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state.

### 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.

### How powerful is adiabatic quantum computation?

- Physics, Computer ScienceProceedings 2001 IEEE International Conference on Cluster Computing
- 2001

It is argued that the adiabatic approach may be thought of as a kind of 'quantum local search', and a family of minimization problems that is hard for such local search heuristics are designed, and an exponential lower bound is established for the ad iabatic algorithm for these problems.

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

- Physics, Computer ScienceScience
- 2001

For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.

### Noise resistance of adiabatic quantum computation using random matrix theory

- Physics, Computer Science
- 2005

A fully analytical study of the resistance to noise of quantum algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian orthogonal ensemble, whose elements vary in time and form a stationary random process.

### Adiabatic quantum computation in open systems.

- Physics, Computer SciencePhysical review letters
- 2005

An inherently open-systems approach is introduced, based on a recent generalization of the adiabatic approximation, that shows that a system may initially be in an adiAbatic regime, but then undergo a transition to a regime where adiABaticity breaks down.

### 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…

### Geometric quantum computation

- Physics
- 2000

Abstract We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for…

### 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…

### The quantum adiabatic optimization algorithm and local minima

- PhysicsSTOC '04
- 2004

It is proved that for a constant range of values for the transverse field, the spectral gap is exponentially small in the sector length, and there are exponentially many eigenvalues all exponentially close to the ground state energy.