Phase-Noise Limitations on Nonlinear-Optical Quantum Computing

Abstract

Flying in the face of the long-sought-after goal of building optical quantum computers, we show that traditional approaches leveraging nonlinear-optical cross phase modulation (XPM) to construct the critical element, the cphase gate-a gate which seeks to impart a π-radian phase shift on a single photon pulse, conditioned on the presence of a second single photon pulse-are doomed to fail. The traditional story told in common textbooks fails to account for the continuous-time nature of the real world. Previous work addressing this fact-finding that that the proper continuous-time theory introduces fidelity-degrading phase noise that precludes such proposals-was limited in scope to the case of co-propagating pulses with equal group velocities. This left room for criticism that a high-fidelity cphase gate might be constructed using XPM with pulses that pass through each other. In our work, we build such a continuous-time quantum theory of XPM for pulses that pass through each other and evaluate its consequences. We find that fundamental aspects of the real world prevent one from constructing a perfect cphase gate, even in theory, and we show that the best we can do seems to fall far short of what is needed for quantum computation, even if we are extremely optimistic.