Adiabatic Deutsch-Jozsa Problem Solved by Modifying the Initial Hamiltonian

Zhaohui Wei, Mingsheng Ying

Shigeru Nakayama, Peng Gang

Jie Sun, Songfeng Lu, Fang Liu +1 more

Jie Sun, Songfeng Lu, Fang Liu +2 more

We present an alternate adiabatic evolution for the Deutsch—Jozsa problem. The biggest difference of our adiabatic evolution constructed here with those appearing before is that an alternate initial Hamiltonian is used for the adiabatic evolution, with which the evolution task can be finished in O(1) time complexity. Our construction mostly resembles the one discussed by Das et al. [ Phys. Rev. A 65 (2002) 062310 ], except for the initial system Hamiltonian of the adiabatic algorithm.

Avik Mitra, Arindam Ghosh, Ranabir Das +2 more

Quantum adiabatic algorithms is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. The adiabatic Deutsch-Jozsa algorithm given be Saurya Das, Randy Kobes and Gabor Kunstatter [Phys. Rev. A. 65, 062301 (2002)], shows how the Deutsch-Jozsa algorithm can be implemented in N^{1/2} steps, where N=2^n and n is the number of qubits, using local adiabatic evolution. In this paper we report the experimental implementation of the adiabatic Deutsch-Jozsa algorithm in a two qubit quantum information processor by Nuclear Magnetic Resonance.

Shigeru Nakayama, Peng Gang, Ichiro Iimura

Adiabatic quantum computation has been proposed as quantum parallel processing with adiabatic evolution by using a superposition state to solve combinatorial optimization problem, then it has been applied to many problems like satisfiability problem. Among them, Deutsch and Deutsch-Jozsa problems have been tried to be solved by using adiabatic quantum computation. In this paper, we modify the adiabatic quantum computation and propose to solve Simon problem more efficiently by a method with higher observation probability.