Real-time magnetic field noise correction using trapped-ion monitor qubits

TL;DR

The paper addresses drift in control parameters, notably magnetic-field fluctuations, that degrade coherence in quantum information processors. It introduces a real-time monitor-qubit protocol in a two-ion Ca+ system exploiting the optical-metastable-ground (omg) architecture to sense magnetic-field fluctuations via Ramsey interrogation and apply feedforward corrections to the data-qubit drive. Under a $1/f^2$ noise spectrum, the method preserves data-qubit coherence for long runs, extending usable probe times by up to $\sim\sqrt{2}$ and doubling the duty cycle relative to interleaved recalibration. These results demonstrate that monitor qubits are a scalable, in-situ recalibration tool for trapped-ion quantum processors, compatible with existing architectures and potentially extendable to track other drifting parameters.

Abstract

We demonstrate a trapped-ion protocol in which a nearby, dedicated "monitor" qubit tracks magnetic-field drifts in real time without interrupting data-qubit operations. Using two $^{40}\mathrm{Ca}^+$ ions and the optical--metastable--ground architecture, we encode the data qubit in the ground-state manifold and the monitor qubit in a metastable-state manifold to achieve spectral separation. The monitor qubit senses common magnetic fluctuations during data-qubit experiments, enabling feedforward corrections to the qubit-control drives. Under applied magnetic noise with a realistic spectrum ($1/f^{2}$), the protocol maintains coherence and, when compared with interleaved calibration, it extends usable data-qubit probe times by up to a factor of ${\sim}\sqrt{2}$ and doubles the experimental duty cycle. These results establish monitor qubits as a scalable tool for real-time recalibration in quantum information processors.

Figures (4)

• Figure 1: Monitor ion experiment overview. a) Energy levels used for the data ion, encoded as a $g$-type qubit and addressed with 13MHz RF radiation. b) Energy levels used for the monitor ion, encoded as an $m$-type qubit and addressed with 729nm laser light. c) Circuit diagram of one realization of the experiment, including the state preparation pulse, the monitor ion Ramsey sequence to measure the magnetic field, and the data ion's experiment (implemented here as a simple Ramsey sequence). Pulse durations are not drawn to scale. d) Circuit diagram showcasing the feedforward scheme, where the information obtained from the monitor ion's magnetic field measurement is used to inform the pulse sequence applied during the following data ion experiment realization. Prep: state preparation. e) Circuit diagram of the interleaved case used for comparison, where a single ion alternates between experiments and magnetic-field calibration measurements. Additional dead time is accrued in this case compared to the separate monitor qubit protocol due to the noise measurements occurring in series with the data qubit experiments, rather than in parallel (times not drawn to scale).
• Figure 2: Tracking drifting magnetic fields with a monitor ion. Top: Magnetic field noise (applied via in-chamber coils in a Helmholtz configuration) calculated from applied current, as described in the text, and the measurements made by a monitor ion's magnetic field tracking protocol, plotted over 45s. The applied noise strength is $\mathrm{ASD}_B(1Hz) = 18µ G \per \sqrt{Hz}$. Center: Calculated phase error accrued each realization by the data ion based on applied and measured magnetic field values. The orange trace is the estimated phase error the data ion would have accrued each realization if the monitor ion was not tracking the field, while the blue trace is the phase error with the monitor ion protocol active. These are calculated as described in the text. Bottom: Measured and estimated fidelities over the course of the run. Predicted fidelities are calculated as described in the text. The blue points are measured fidelities, calculated by binning the data-qubit measurements in groups of 100 realizations and taking the average probability of measuring the desired state. Error bars represent one standard deviation.
• Figure 3: Averaged fidelity of data-qubit ($g$-qubit) Ramsey experiments as a function of probe time when using the monitor ion for real-time recalibration and when using interleaved field noise measurements with only a single ion. A range of magnetic field noise strengths are demonstrated, labeled in the upper right corner of each subplot. The monitor ion data show a maximum useful probe time of up to a factor of ${\sim}\sqrt{2}$ longer than the interleaved field-tracking experiments because of the higher noise-tracking duty cycle. Phenomenological fits to $\tanh$ (hyperbolic tangent) functions are used to extract the coherence times. Error bars represent one standard error on the mean computed from 10 one-minute realizations. The corresponding interleaved experiments use the same total number of realizations as the monitor-ion experiments.
• Figure 4: Maximum usable probe time as a function of the applied noise strength. The maximum probe time is the 50% contrast (75% fidelity) point of the fits to individual noise strength measurements (\ref{['fig:probe-time-scan']}). The monitor-ion protocol demonstrates consistently better performance, with the gains highest at low noise strengths due to the smaller fractional contribution of dead time. Error bars are statistical standard deviations from probe time fits (shown in \ref{['fig:probe-time-scan']}), and lines are guides to the eye.