Abstract
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
Highlights
Motivated by the recent experiments[30,31,32,33] and usefulness of different photonic DoFs34–46, in this paper, we consider the controlled gates on photonic system with two DoFs assisted by the weak cross-Kerr nonlinearity[22,23,46,47,48,49,50,51,52,53]
The present CNOT gates on photons with two DoFs may be nearly deterministically performed. These CNOT gates are different from CNOT gates on photonic systems with only one DoF11–15,22–29, where the latter is always applied in quantum applications using the polarization DoF while other DoFs such as the momentum and time-bin are not considered or only considered as auxiliary systems[11,15,22,23]
Our CNOT gates show that quantum tasks may be simulated using photonic systems with two DoFs assisted by the weak cross-Kerr nonlinearity
Summary
Motivated by the recent experiments[30,31,32,33] and usefulness of different photonic DoFs34–46, in this paper, we consider the controlled gates on photonic system with two DoFs assisted by the weak cross-Kerr nonlinearity[22,23,46,47,48,49,50,51,52,53]. Different from previous schemes on photonic systems with the polarization DoF11–15,22,23, where another DoF is used to assist quantum logic gates, we investigate the photonic quantum computation using two DoFs as simultaneous encoding qubits. To show the independence of two photonic DoFs in each quantum task, from the quantum circuit model the CNOT gate will be implemented on all the combinations of the polarization and spatial DoFs of the two-photon or one-photon system. This is beyond previous CNOT gates on the two-photon system with one DoF11–15,22,23. We present faithful teleportation of arbitrary n-photon and quantum superdense coding
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