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Quantum Electronics and Laser Science Conference

Kerr-induced phase noise in quantum parity gates

Mohsen Razavi, Jeffrey H. Shapiro

Published May 1, 2007• 0 citations
Publisher

Abstract

Quantum parity gates that use weak nonlinearity between single photons and intense coherent pulses are analyzed using a continuous-time model for cross-phase modulation. An inevitable phase noise is shown to degrade gate fidelity.
DOI
10.1109/qels.2007.4431702

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Abstract. The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyze the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will degrade the performance of the parity gate proposed by Munro, Nemoto, and Spiller [1].Continuous-time cross-phase modulation and quantum computation 2 1.
The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyse the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will preclude satisfactory performance of the parity gate proposed by Munro et al (2005 New J. Phys. 7 137).
A possible two-qubit gate for optical quantum computing is the parity gate based on the weak Kerr effect. Two photonic qubits modulate the phase of a coherent state, and a quadrature measurement of the coherent state reveals the parity of the two qubits without destroying the photons. This can be used to create so-called cluster states, a universal resource for quantum computing. Here, the effect of self-phase modulation on the parity gate is studied, introducing generating functions for the Wigner function of a modulated coherent state. For materials with non-electromagnetically-induced-transparency-based Kerr nonlinearities, there is typically a self-phase modulation that is half the magnitude of the cross-phase modulation. Therefore, this effect cannot be ignored. It is shown that for a large class of physical implementations of the phase modulation, the quadrature measurement cannot distinguish between odd and even parity. Consequently, weak nonlinear parity gates must be implemented with physical systems where the self-phase modulation is negligible.
Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.