Single-photon Kerr nonlinearities help quantum computation

Nobuyuki Matsuda, Ryōsuke Shimizu, Yasuyoshi Mitsumori +2 more

Muhammed Ashefas, T. M. Manosh, R. B. Thayyullathil

Jeffrey H. Shapiro

By embedding an atom capable of electromagnetically induced transparency inside an appropriate photonic-crystal microcavity it may become possible to realize an optical nonlinearity that can impart a $\ensuremath{\pi}$-rad-peak phase shift in response to a single-photon excitation. Such a device, if it operated at high fidelity, would then complete a universal gate set for all-optical quantum computation. It is shown here that the causal, noninstantaneous behavior of any ${\ensuremath{\chi}}^{(3)}$ nonlinearity is enough to preclude such a high-fidelity operation. In particular, when a single-photon-sensitive ${\ensuremath{\chi}}^{(3)}$ nonlinearity has a response time that is much shorter than the duration of the quantum computer's single-photon pulses, essentially no overall phase shift is imparted to these pulses by cross-phase modulation. Conversely, when this nonlinearity has a response time that is much longer than this pulse duration a single-photon pulse can induce a $\ensuremath{\pi}$-rad overall phase shift through cross-phase modulation, but the phase noise injected by the causal, noninstantaneous response function precludes this from being a high-fidelity operation.

Hayato Goto

Qi Guo, Liu‐Yong Cheng, Hong‐Fu Wang +1 more

By employing displacement operations, single-photon subtractions, and weak cross-Kerr nonlinearity, we propose an alternative way of implementing several universal quantum logical gates for all-optical hybrid qubits encoded in both single-photon polarization state and coherent state. Since these schemes can be straightforwardly implemented only using local operations without teleportation procedure, therefore, less physical resources and simpler operations are required than the existing schemes. With the help of displacement operations, a large phase shift of the coherent state can be obtained via currently available tiny cross-Kerr nonlinearity. Thus, all of these schemes are nearly deterministic and feasible under current technology conditions, which makes them suitable for large-scale quantum computing.

A. S. Parkins, Daniel F. Walls, Ataç İmamoğlu