# Quantum Computation by Adiabatic Evolution

@article{Farhi2000QuantumCB, title={Quantum Computation by Adiabatic Evolution}, author={Edward Farhi and Jeffrey Goldstone and Sam Gutmann and Michael Sipser}, journal={arXiv: Quantum Physics}, year={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 interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on…

## 1,107 Citations

### Quantum Adiabatic Evolution Algorithms with Different Paths

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- 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…

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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…

### Adiabatic Quantum Computing : An Overview

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- 2012

Quantum computations can be implemented not only by the action of quantum circuits, but by the adiabatic evolution of a system’s Hamiltonian. This can be done by initializing the system into the…

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

- Computer Science, PhysicsArXiv
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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.

### Approximability of Optimization Problems through Adiabatic Quantum Computation

- Physics, Computer ScienceApproximability of Optimization Problems through Adiabatic Quantum Computation
- 2014

This book investigates the computational simulation of AQC algorithms applied to the MAX-SAT problem and shows that every monadic second-order logic (MSOL) expression has associated pseudo-Boolean maps that can be obtained by expanding the given expression, and also can be reduced to quadratic forms.

### Path Independence in Adiabatic Quantum Computing for Hadamard Gate

- Physics, Computer Science
- 2014

The variational method is used to find an optimized path for the simplest case involving a single qubit and for the most general path involving one or more independent interpolating functions, which shows that in these two scenarios the authors can choose an arbitrary path provided that it satisfies the boundary conditions.

### Entangling Problem Hamiltonian for Adiabatic Quantum Computation

- PhysicsLobachevskii Journal of Mathematics
- 2022

Adiabatic quantum computation starts from embedding a computational problem into a Hamiltonian whose ground state encodes the solution to the problem. This problem Hamiltonian is normally chosen to…

### 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.

### 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.

### Quantum Adiabatic Evolution with a Special Kind of Interpolating Paths

- PhysicsAdvances in Intelligent Systems and Computing
- 2018

We study a special kind of interpolating paths in quantum adiabatic search algorithms. With this special kind of adiabatic paths, notably we find that even when the parameter n within it tends to…

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