Abstract
In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called controlled-path gate with which the realization of all possible bipartite positive-operator-value measurements of two-photon polarization states may be nearly deterministic. Following the same technique, the realization of quantum control gates, including the controlled-NOT gate, Fredkin gate, Toffoli gate, arbitrary controlled-U gate, and even arbitrary multicontrolled-U gate, are proposed. The corresponding probabilities are $1∕2$, $1∕8$, $2∕23$, etc., respectively. Only the coherent states are required but not any ancilla photons, and no coincidence measurement are required, which results in these gates being scalable. The structures of these gates are very simple, therefore we think they are feasible with the current experimental technology in optics.
Highlights
INTRODUCTIONQuantum control gates play a very important role. It was proven that two-qubit unitary gates and single-qubit gates are sufficient for universal quantum computation [1]
In the quantum computation, quantum control gates play a very important role
Before we outline our schemes of quantum control gates, we briefly review the useful weak cross-Kerr nonlinearity which has been used in Refs. [5, 6, 7, 8]
Summary
Quantum control gates play a very important role. It was proven that two-qubit unitary gates and single-qubit gates are sufficient for universal quantum computation [1]. Many schemes are provided for the realization of two-qubit unitary gates, for example, controlled-NOT (CNOT) gates [2] or controlled-phase gates [3] Some of these gates work on the coincidence basis which results in these gates are not scalable, i.e., these gates can not be used to realize multi-qubit gates and the universal computation. In sec.II, we first propose a scheme of a gate we call it controlled-path (C-path) gate with the weak cross-Kerr nonlinearities, and use this gate to realize all possible bipartite positive-operator-value measurements (POVMs) of twophoton polarization states.
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