In-situ mid-circuit qubit measurement and reset in a single-species trapped-ion quantum computing system

TL;DR

This work addresses mid-circuit measurement and reset in a trapped-ion quantum processor by using metastable states in $^{171}\mathrm{Yb}^+$ to isolate data qubits from measurement. It introduces and experimentally validates two MCMR strategies—hands-off and shelving—within a single-species two-ion system, avoiding shuttling or extra addressing optics. The authors demonstrate selective metastable-state access via dressing or qubit-rotation, achieving data-qubit errors around $2\%$ while maintaining high measurement fidelity, with laser-noise reductions capable of pushing errors below $0.1\%$. The results imply a scalable, simplified architectural path for MCMR in long ion chains, with further gains possible through longer-lived metastable states and improved laser control. Overall, the paper provides practical, high-fidelity MCMR protocols compatible with single-species trapped-ion platforms.

Abstract

We implement in-situ mid-circuit measurement and reset (MCMR) operations on a trapped-ion quantum computing system by using metastable qubit states in $^{171}\textrm{Yb}^+$ ions. We introduce and compare two methods for isolating data qubits from measured qubits: one shelves the data qubit into the metastable state and the other drives the measured qubit to the metastable state without disturbing the other qubits. We experimentally demonstrate both methods on a crystal of two $^{171}\textrm{Yb}^+$ ions using both the $S_{1/2}$ ground state hyperfine clock qubit and the $S_{1/2}$-$D_{3/2}$ optical qubit. These MCMR methods result in errors on the data qubit of about $2\%$ without degrading the measurement fidelity. With straightforward reductions in laser noise, these errors can be suppressed to less than $0.1\%$. The demonstrated method allows MCMR to be performed in a single-species ion chain without shuttling or additional qubit-addressing optics, greatly simplifying the architecture.

Figures (7)

• Figure 1: MCMR sequences via metastable intermediate states. The energy levels here are abstract and may be applicable to different ion types. Most of the qubit operations in circuits are done on the two ground states $|g_1\rangle$ and $|g_2\rangle$. The metastable $|m\rangle$ state has a long enough lifetime such that its decay can be ignored during the sequence. Finally, a short-lived excited state $|e\rangle$ can be used for photon scattering. Depending on the type of the sequence, different $|e\rangle$ may be chosen for either a cycling or non-cycling transition. (a) The hands-off method does not disturb the data qubit and drives the auxiliary ion to $|m\rangle$ as an intermediate state for photon scattering on $|e\rangle$. (b) The shelving method hides the data qubit in state $|m\rangle$ and measures the auxiliary qubit.
• Figure 2: Example individual metastable state control sequence implemented with qubit rotation. This sequence achieves the same final state as the one in Fig. \ref{['fig:mcmr-methods']}b while only requiring individual qubit gates and global shelving operations.
• Figure 3: Overview of the experiment. (a) Relevant energy levels and supported operations on the $^{171}\mathrm{Yb}^+$ ions. The normal reset and measurement operation is done on the $370\ \mathrm{nm}$ transition between $S_{1/2}$ and $P_{1/2}$ with population leakage into the $D_{3/2}$ repumped back with the $935\ \mathrm{nm}$ transition via the $[3/2]_{1/2}$ state. The metastable $D_{3/2}$ state can also be directly populated using the $435\ \mathrm{nm}$ transition. (b) Beam geometry relative to the ion chain. The $370\ \mathrm{nm}$ and $435\ \mathrm{nm}$ beams are sent in $45^\circ$ relative to the ion chain parallel to the trap surface and the $935\ \mathrm{nm}$ beam is sent in along the chain. All of these are global beams that illuminate the whole chain. The Raman beam path consists of a global beam perpendicular to the chain and an array of counter-propagating individual beams to target each ions separately.
• Figure 4: Simultaneous $D_{3/2}$ spectrum on two ions with individual dressing on one ion. Inset: illustration of the measurement protocol.
• Figure 5: Mid-circuit measurement with shelving method (Fig. \ref{['fig:mcmr-methods']}b) to the $D_{3/2}$ manifold. (a) Experimental sequence. First, the data ions are shelved to the $|D\rangle$ state. The auxiliary ion is measured using the $370\ \mathrm{nm}$ transition with a pause for the global spin echo to improve data ion fidelity. After the measurement, the data ions are unshelved back to the ground states. The shelving and unshelving of the data ions may use either the dressing implementation or a simplified qubit rotation sequence. (b) Ramsey phase scan demonstrating that the mid-circuit measurement of the auxiliary ion using the qubit rotation implementation preserves the coherence of the data ion coherence. The contrast of the Ramsey fringe shows a data ion fidelity of $98.8(6)\ \%$ ($98.2(7)\ \%$) when the auxiliary ion was in the $|0\rangle$ ($|1\rangle$) state. (c) Mid-circuit measurement on the auxiliary ion which is initialized in a superposition of $|0\rangle$ and $|1\rangle$ with a single qubit rotation $R_x(\theta)$ with variable rotation angle $\theta$. The result shows a measurement fidelity of $99.6(2)\ \%$ which is identical to that of a normal measurement.