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Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm
Hongye 泓烨 Yu 余, Yuliang 宇亮 Huang 黄, Biao 飙 Wu 吴·June 23, 2017·DOI: 10.1088/0256-307X/35/11/110303
Physics
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Abstract
We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of L gates we can construct a quantum adiabatic algorithm with time complexity of O(L). Additionally, our construction shows that one may exponentially speed up some quantum adiabatic algorithms by properly choosing an evolution path.