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arXiv:1711.06142

High Fidelity Quantum Gates beyond spectral selection

Kwok Chung Matthew Cheung, Florian Mintert

Published Nov 16, 2017• 0 citations
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Abstract

Driving a certain transition without including undesired transitions is an ubiquitous problem in quantum control and the implementation of quantum information processing. This problem gets the more challenging the weaker the desired transition couples to the control field, and the denser the system's spectrum is. With the explicit example of a trapped ion we show how temporally shaped driving helps to increase the fidelity of a gate operation beyond the regular spectral selection of resonantly driven transitions. We chose the explicit example of side-band transitions, since those couple more weakly to a control field than carrier transitions. Driving a sideband transition without carrier excitation thus allows us to test the limits of frequently employed control tools, and we discuss their potential and limitations.

DOI
10.48550/arxiv.1711.06142

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Driving a certain transition without including undesired transitions is an ubiquitous problem in quantum control and the implementation of quantum information processing. This problem gets the more challenging the weaker the desired transition couples to the control field, and the denser the system's spectrum is. With the explicit example of a trapped ion we show how temporally shaped driving helps to increase the fidelity of a gate operation beyond the regular spectral selection of resonantly driven transitions. We chose the explicit example of side-band transitions, since those couple more weakly to a control field than carrier transitions. Driving a sideband transition without carrier excitation thus allows us to test the limits of frequently employed control tools, and we discuss their potential and limitations.
Trapped ions driven by electromagnetic radiation constitute one of the most developed quantum technologies to date. The scenarios range from proof-of-principle experiments to on-chip integration for quantum information units. In most cases, these systems have operated in a regime where the magnitude of the ion-radiation coupling constant is much smaller than the trap and electronic transition frequencies. This regime allows the use of simple effective Hamiltonians based on the validity of the rotating-wave approximation. However, novel trap and cavity designs now permit regimes in which the trap frequency and the ion-radiation coupling constant are commensurate. This opens up new avenues for faster quantum gates and state transfers from the ion to a photon and other quantum operations. From the theoretical side, however, there is not yet much known in terms of models and applications that go beyond the weak-driving scenario. In this work, we present two main results in the scenario of stronger driving. First, we revisit a known protocol to reconstruct the motional Wigner function and expand it to stronger-driving lasers. This extension is not trivial because the original protocol makes use of effective Hamiltonians valid only for weak driving. The use of stronger fields or faster operations is desirable since experimental reconstruction methods of that kind are usually hindered by decoherence. We then present a model that allows the analytical treatment of stronger driving and that works well for nonresonant interactions, which are generally out of the reach of previous models.
High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\ensuremath{\pi}$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the M\o{}lmer-S\o{}rensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.
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