Photonic scheme of quantum phase estimation for quantum algorithms via cross-Kerr nonlinearities under decoherence effect.

Quantum phase estimation (QPE) is the key procedure in various quantum algorithms. The main aim of the QPE scheme is to estimate the phase of an unknown eigenvalue, corresponding to an eigenstate of an arbitrary unitary operation. The QPE scheme can be applied as a subroutine to design many quantum algorithms. In this paper, we propose the basic structure of a QPE scheme that could be applied in quantum algorithms, with feasibility by utilizing cross-Kerr nonlinearities (controlled-unitary gates) and linearly optical devices. Subsequently, we analyze the efficiency and the performance of the controlled-unitary gate. This gate consists of a controlled-path gate and a merging-path gate via cross-Kerr nonlinearities under the decoherence effect. Also shown in this paper is a method by which to enhance robustness against the decoherence effect to provide a reliable QPE scheme based on controlled-unitary gates.