Bounds for the adiabatic approximation with applications to quantum computation

Abstract

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

15 pages, one figure. Two comments added in Secs. 2 and 5

References in corpus (7)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Quantum Search by Local Adiabatic Evolution
• Adiabatic Theorem without a Gap Condition
• Inconsistency in the application of the adiabatic theorem
• Quantitative conditions do not guarantee the validity of the adiabatic approximation
• General error estimate for adiabatic quantum computing
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