Quantum algorithms without initializing the auxiliary qubits

Details Quantum algorithms without initializing the auxiliary qubits Quantum algorithms without initializing the auxiliary qubits

2005-04-25

arxiv.org/abs/quant-ph/0504173v3

Phys. Rev. Lett. 95, 080504 (2005)

Physics

Quantum Physics

4 pages, typos corrected, references added, accepted for publication in Physical Review Letters

Scientific paper

In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the original algorithms. In these quantum algorithms, one can use any arbitrarily mixed state as the auxiliary qubits, and furthermore can recover the state of the auxiliary qubits to the original one after completing the computations. Since the recovered state can be employed in any other computations, we obtain that a single preparation of the auxiliary qubits in an arbitrarily mixed state is sufficient to implement the iterative procedure in the Simon algorithm or the period-finding algorithm.

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