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Accuracy versus run time in an adiabatic quantum search
Rezakhani, A. T ; Sharif University of Technology | 2010
597
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- Type of Document: Article
- DOI: 10.1103/PhysRevA.82.052305
- Publisher: 2010
- Abstract:
- Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood.We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times.We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time
- Keywords:
- Adiabatic quantum search ; Algorithmic errors ; Continuous time ; Evolution paths ; Quadratic speedup ; Quantum algorithms ; Runtimes ; Quantum theory ; Algorithms
- Source: Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 82, Issue 5 , 2010 ; 10502947 (ISSN)
- URL: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.82.052305