Robustness of adiabatic quantum computation

Abstract

We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm.

11 pages, 5 figures, REVTeX

References in corpus (7)

• Fault-tolerant quantum computation by anyons
• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Holonomic Quantum Computation
• Quantum Search by Local Adiabatic Evolution
• Geometric Quantum Computation
• A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability

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