High-fidelity entanglement of metastable trapped-ion qubits with integrated erasure conversion

Abstract

Today's most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors. We address both of these issues by establishing high-fidelity control of metastable qubits, a key component of \textit{omg} or dual-type architectures, which enables converting a significant fraction of gate errors to erasures. We first implement an erasure conversion scheme which enables detection of $\sim 94\%$ of spontaneous Raman scattering errors during logic gates and nearly all errors from qubit decay. Second, we perform a two-ion geometric phase gate using far-detuned (-44\,THz) stimulated Raman transitions to produce an entangled state with a raw Bell state fidelity of 97.73\% and a SPAM-corrected Bell state fidelity of 98.61\%. When subtracting erasure errors, this fidelity becomes 99.16\%. These results, along with projections based on our detailed error budget, demonstrate metastable trapped-ion qubits as a platform for low-overhead, fault-tolerant quantum computing.

Figures (9)

• Figure 1: a) A level diagram for $^{40}$Ca$^{+}$ showing relevant transitions and their associated wavelengths (in nm). b) Pulse sequence for a generic experiment in our m qubit, showing the optical pumping technique used for state preparation and the shelving technique used for state detection. c) A schematic of our injection-locked diode laser system for producing 976 nm beams for driving stimulated Raman transitions. Light from a 976 nm free-space seed laser (0.7 W) is injected into a pair of fiberized amplifier (amp) diodes (1.0 W each) via optical circulators that in turn output into fiberized acousto-optic modulators (AOMs), which modulate the frequency of the fiberized light before output into free space optics at the trap (with powers up to 220 mW per beam).
• Figure 2: a) Schematic illustration of our scheme for converting leakage errors to erasures used with a two-ion gate, showing how FCs are used both before an algorithm to ensure that optical pumping has shelved both ions in $D_{5/2}$ and after for erasure conversion. b) Leakage pathways in our experiment, with SRS producing detectable leakage errors (labelled "erasure errors"), undetected leakage errors, and Pauli errors. Decay (in orange) due to the natural lifetime of the $D_{5/2}$ always produces a detectable leakage error.
• Figure 3: a) Pulse sequence for carrying out the gate, with SDF phase (0, $\pi$) denoted by color (white, blue). b) A plot of qubit state population versus SDF detuning from the motional mode resonance, showing the crossing point in $\lvert\downarrow\downarrow\rangle$ and $\lvert\uparrow\uparrow\rangle$ populations at which the gate was performed. c) A sample parity fringe. Insets shows high-shot time series data at the gate operating point and parity fringe extrema.
• Figure 4: a) Motional Ramsey experiment, plotting the contrast between the $\lvert0\rangle$ and $\lvert1\rangle$ fock states as a function of the delay time between sideband $\pi/2$ pulses. b) Numerically simulated Bell state infidelity due to a white motional noise source as a function of the coherence to gate time ratio. Orange lines represent the infidelity expected for measured coherence and gate times used in this work. Dashed lines represent the $68\%$ confidence interval.
• Figure 5: a) Bell-state infidelity corresponding to a normally distributed relative $\pi$-time error characterized by standard deviation $\sigma_{t_\pi}$. b) Distribution of Bell-state infidelities corresponding to the measured $\sigma_{t_\pi}/t_\pi$ of $1\%$ in this work for a Walsh-1 gate. The solid orange line marks the average infidelity while the dashed orange lines represent the $68\%$ confidence interval.