Quantum Adiabatic Theorem Revisited

• URL: http://arxiv.org/abs/2003.03063v1
• Date: Fri, 6 Mar 2020 07:49:45 GMT
• Title: Quantum Adiabatic Theorem Revisited
• Authors: Runyao Duan
• Abstract summary: We show how to adiabatically prepare an arbitrary qubit state from an initial state. As applications, we show how to adiabatically prepare an arbitrary qubit state from an initial state.
• Score: 6.259224706032504
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In 2004 Ambainis and Regev formulated a certain form of quantum adiabatic theorem and provided an elementary proof which is especially accessible to computer scientists. Their result is achieved by discretizing the total adiabatic evolution into a sequence of unitary transformations acting on the quantum system. Here we continue this line of study by providing another elementary and shorter proof with improved bounds. Our key finding is a succinct integral representation of the difference between the target and the actual states, which yields an accurate estimation of the approximation error. Our proof can be regarded as a "continuous" version of the work by Ambainis and Regev. As applications, we show how to adiabatically prepare an arbitrary qubit state from an initial state.

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