Midcircuit Operations Using the omg Architecture in Neutral Atom Arrays

Midcircuit operations, such as qubit state measurement or reset, are central to many tasks in quantum information science, including quantum computing, entanglement generation, and metrology. For instance, in quantum error correction, the information gained from a measurement on a subset of qubits is used to influence the state of the remaining unmeasured qubits, rectifying inevitable errors that arise in a quantum circuit. Such partial projective operations pose a challenge for dense neutral atom arrays and trapped ions, where accidental exposure to resonant laser light during quantum state initialization and detection can spoil the state of untargeted qubits. In this work, we implement midcircuit operations in a 48-site array of neutral atoms, enabled by new methods for high-fidelity control of the omg (optical-metastable-ground-state qubit) architecture present in ${}^{171}\mathrm{Yb}$. Here, the quantum information is encoded in either of the three qubit manifolds and can be shuttled between them. With state-sensitive shelving between the ground and metastable states, we realize a nondestructive state detection for ${}^{171}\mathrm{Yb}$, incorporating global control and local feed-forward operations. Using new schemes for local addressing of the optical clock transition, we shelve a subset of qubits to the metastable state, hiding them from projective operations performed on the qubits remaining in the ground state, demonstrating midcircuit measurement, spin reset, and motional reset in the form of ground-state cooling.

Popular Summary

In quantum information processing, global measurement and reset destroy a system’s “quantumness,” and thus occur only at the beginning or end of a circuit. However, for certain applications such as error correction, it is advantageous to perform measurements midcircuit but on just a subset of the system while leaving the rest unperturbed. These midcircuit operations are particularly challenging in neutral atom arrays, where the quantum bits, or qubits, are encoded in atoms trapped in tightly focused beams of light, called tweezers. In this case, measurement and reset are performed by scattering photons, which means that the remaining atoms must be hidden from these photons. In this work, we realize these midcircuit operations on a tweezer array of ytterbium-171 atoms.

We take advantage of ytterbium-171’s “omg” architecture, where quantum information resides either in an optical (o), metastable-state (m), or ground-state (g) qubit. The ground- and metastable-state qubits are encoded in the nuclear spin of the atom, well isolated from the environment and with coherences surviving for seconds, while the optical qubit transition bridges between them. We manipulate these qubits with high fidelities and, in particular, transfer quantum information between the ground and metastable states. With imaging and reset laser light targeting only the ground-state atoms, we protect a subset of qubits by hiding them in the metastable state, all while preserving their coherence.

With midcircuit measurement and reset in hand, our work points the way toward implementing quantum error correction as well as metrological and entanglement generation protocols on a neutral-atom array platform.

Figure 1

Midcircuit operations using the omg architecture in ${}^{171}\mathrm{Yb}$. (a) The omg level structure in ${}^{171}\mathrm{Yb}$. The optical qubit $o$ is defined on the clock transition between the ${{}^1\mathrm{S}}_0$ and ${{}^{3}P}_0$ states; the metastable $m$ and ground $g$ state qubits are defined by the $|0⟩\equiv |m_F=+1/2⟩$ and $|1⟩\equiv |m_F=-1/2⟩$ Zeeman states of nuclear spin-$1/2$ within the respective manifolds. The optical Raman transitions through ${{}^{3}P}_1$ and ${{}^3\mathrm{D}}_1$ drive nuclear qubit rotations in $g$ and $m$. The insets show Rabi oscillations with $\{{\mathrm{\Omega }}_m/2\pi ,{\mathrm{\Omega }}_o/2\pi ,{\mathrm{\Omega }}_g/2\pi \}\approx \{0.26\mathrm{MHz},0.11\mathrm{MHz},0.33\mathrm{MHz}\}$ and $1/e$ damping of approximately $\{30,80,80\}$ cycles, respectively. (b) Local shelving operations and MCO. The array is divided into data qubit (DQ) and ancilla qubit (AQ) subsets. The light-shift operation $L$ hinders shelving for ancilla qubits, leaving them in $g$ and therefore in a bright state for an image. The data qubits are shelved into $m$ with the $S_0$ shelving operation—a rotation on the $\pi$-polarized clock transitions that addresses both $|0⟩$ and $|1⟩$ states. At the end of MCO, the data qubit is assessed for coherence (right inset). The complementary $S_1$ operation—a rotation on the ${\sigma }^{-}$-polarized clock transition—shelves only the $|0⟩$ spin state, realizing a nondestructive spin-sensitive detection. Atom images shown are averages of 600 shots. (c) Trapping, imaging, and local addressing apparatus. (d) Qubit addressing beam geometry. QB1 and QB2 control $R_X$ and $R_Z$ nuclear spin qubit rotations in ground $g$ (green) and metastable $m$ (blue) manifolds. The $S_{0,1}$ beam controls optical qubit and shelving operations between the two nuclear spin qubit manifolds. The 532-nm tweezers ($L$) site-selectively light shift the clock transition for local shelving operations.

Figure 2

Characterization of omg qubits and their control. (a) Clifford RB for $g$ (green) and $m$ (blue) qubit manifolds. The Clifford gates are compiled from $\sqrt{X}\equiv R_X(\pi /2)$ and $\sqrt{Z}\equiv R_Z(\pi /2)$ rotations, with typical pulse lengths $0.5-1.4\mathrm{\mu }\mathrm{s}$. The magnetic field during the nuclear spin qubit RB is 1.6 G. We measure average single-qubit gate fidelities of ${\mathcal{F}}_g=99.968(3)\%$ and ${\mathcal{F}}_m=99.12(4)\%$. Bottom: sitewise analysis of average single-qubit fidelities. (b) Coherence measurement for $|g⟩$ (green) and $|m⟩$ (blue). In a Ramsey-type experiment, contrast is recorded for dark times in $g$ and $m$ while scanning the phase $\varphi$ accumulated between $|0⟩$ and $|1⟩$ qubit states. We extract $T_{2,g}^{*}=12(2)\mathrm{s}$ and $T_{2,m}^{*}=7.2(6)\mathrm{s}$, respectively. (c) RB for optical qubit $o$, performed without a light-shifting beam (global) and in the presence of a light-shifting beam (local). In the former case, we measure average single-qubit gate fidelities of ${\mathcal{F}}_o=99.804(8)\%$, which decreases to ${\mathcal{F}}_o^L=99.53(4)\%$ in the presence of the light-shifting beam. Shown in green is the error in clock suppression as a function of the number of the Clifford gates applied. We extract an error of 0.27(2)% per Clifford gate. Bottom: sitewise analysis of average single-qubit fidelities (three tweezer sites not included due to insufficient statistics). For all panels, the error bars indicate a $1\sigma$ confidence interval.

Figure 3

Coherent shelving. (a) Motional effects in the ${\mathrm{\Omega }}_o\gg \omega$ regime. A single $\pi$ pulse addresses multiple sidebands heating up the atom while MPP leaves the original motional state unchanged after the operation is complete. (b) Pulse sequences for the MPP. The MPP comprises two CORPSEs, each realizing a target 90° rotation on the clock transition. One CORPSE consists of ${384.3}_{+x}^{°}$, ${318.6}_{-x}^{°}$, and ${24.3}_{+x}^{°}$ rotations, with $\pm x$ denoting 0° and 180° phases of the applied pulses [56]. (c) Population remaining in the ground state after an odd number of shelving operations. From the slope, we extract the error per shelving operation: ${\epsilon }_S=0.21(2)\%$ for a $\pi$ pulse and no wait time (gray); ${\epsilon }_S=1.33(4)\%$ for a $\pi$ pulse and 2-ms wait time (orange); and ${\epsilon }_S=0.28(3)\%$ for MPP and 2-ms wait time (yellow). The error bars (smaller than marker size) indicate a $1\sigma$ confidence interval. (d) Simulation of the motional-state evolution in the $⟨\widehat{x}⟩-⟨\widehat{p}⟩$ phase space of a harmonic oscillator under a $\pi$ pulse (left) and MPP (right) with the units of a zero-point motion. (e) Average number of motional quanta vs number of shelving operations. A $\pi$ pulse and MPP increase $\overline{n}$ by $9(1)\times {10}^{-2}$ and $4(2)\times {10}^{-3}$, respectively. Lines show a no-free-parameter simulation of the expected behavior for the two cases (see Appendix pp5-s2). The error bars indicate a $1\sigma$ confidence interval.

Figure 4

Nondestructive state-sensitive detection. (a) Overview of the protocol. Note that $S_1$ turns spin $|g,0⟩$ dark, shelving it to the $m$ manifold, while $|g,1⟩$ remains and appears bright for the image. The spins are then reset back to the $g$ manifold. A final image checks for atom loss at the end of the procedure. (b,c) Two reset approaches employed. In panel (d), image 1 (yellow) is spin sensitive, resolving $|0⟩$ and $|1⟩$ populations of a $|\psi ⟩=\cos (\theta /2)|0⟩-i\sin (\theta /2)|1⟩$ input state in $g$. Image 2 shows that the atoms can be reinitialized in $g$ following spin detection via global control. No correction was applied to the data shown. The error bars indicate a $1\sigma$ confidence interval. (e) Two-dimensional histogram showing counts recorded in both images for atoms initially prepared in $|0⟩$ (orange) and $|1⟩$ (yellow) 2-ms wait time. Reinitialization in $g$, for this data set, was performed via a global control and repumping step before image 2.

Figure 5

Midcircuit operations. (a) Overview of the protocol. With local light shifts $L$ acting on ancilla qubits (AQ), $S_0$ shelves data qubits (DQ) to the metastable state, dark to MCOs. After the MCO is completed, the DQ is brought back to the ground state and assessed for coherence loss. For reset operations, a final measurement is performed on AQ to check whether the operation was successful. (b) Midcircuit measurement results. In a Ramsey-type experiment, the contrast for AQ is measured midcircuit with ${\mathcal{C}}_{\mathrm{MCM}}^{\mathrm{AQ}}=98.2(6)\%$. After the MCO, the contrast for the DQ is ${\mathcal{C}}_{\mathrm{MCM}}^{\mathrm{DQ}}=95.5(1.0)\%$. The atom image shown is an average of 600 shots. (c) Midcircuit reset results. Prior to reset, we apply the pulse of a 399-nm heating beam, which increases $\overline{n}$ and mixes the spin state. The GMC and Raman sideband cooling (SB cool) then reset the motional state, while optical pumping (OP) and an $\sqrt{X}$ gate reset the spin state of AQ. Left: sideband spectroscopy (SB spec), showing a decrease in $\overline{n}$ after reset. Right: Ramsey-type experiment, showing contrast reset for AQ to ${\mathcal{C}}_{\mathrm{MCR}}^{\mathrm{AQ}}=97.7(5)\%$. The DQ contrast after the MCO is ${\mathcal{C}}_{\mathrm{MCR}}^{\mathrm{DQ}}=95.2(8)\%$. Starting from qubits stored in the $m$ manifold, a Rabi oscillation of a ${\mathcal{C}}_{\mathrm{MCM},m}^{\mathrm{AQ}}=96.2(8)\%$ contrast and a Ramsey-type experiment with a ${\mathcal{C}}_{\mathrm{MCM},m}^{\mathrm{DQ}}=90(1)\%$ contrast are performed for AQ and DQ, respectively, as shown in panel (d). The state readout for AQ and DQ is nondestructive, retaining approximately 94% of atoms at the end of the sequence. For all panels, no corrections are applied to the data nor to the reported contrasts (see text for an explanation of SPAM and errors), and the error bars indicate a $1\sigma$ confidence interval.

Figure 6

Magic angle and fast imaging. (a) Magic angle condition for the ${}^1{\mathrm{S}}_0\leftrightarrow |{}^3{P}_1,F^{\prime }=3/2,m_{F^{\prime }}=-1/2⟩$ transition. Purple points are measured with the magnetic field (B) parallel to the tweezer polarization (E), and red points, with B tilted by 17° with respect to E (near the magic angle condition for our configuration). The tweezer-induced light shift has a linear sensitivity to the trap intensity that is about 50 times smaller for the magic angle condition than for the parallel case. The error bars (smaller than marker size) indicate a $1\sigma$ confidence interval. (b) Histogram for high-fidelity fast imaging. The imaging has a duration of 3.5 ms and a discrimination fidelity of 99.80(5)%. The dashed line is the photon count threshold—events with photon counts below (above) the threshold are identified as dark (bright). (c) Survival rate after a variable number of images, yielding an average loss of 0.19(2)% per image after accounting for the vacuum loss. The error bars (smaller than marker size) indicate a $1\sigma$ confidence interval.

Figure 7

Gray-molasses cooling and Raman sideband cooling. (a) Temperature of tweezer-trapped atoms as a function of gray-molasses cooling time. The temperature is determined by comparing results of a release-and-recapture experiment and a Monte Carlo simulation for an atom of a certain temperature [100]. The black line is an exponential fit, yielding a cooling time constant of 0.4(2) ms and a final temperature of $3\mathrm{\mu }\mathrm{K}$. In the inset, we show that the magnetic field splits excited states of ${{}^{3}P}_1$, realizing a lambda configuration employed for the gray-molasses cooling. (b) Top: pulse sequence for Raman sideband cooling in the radial direction. The two axes of the radial direction are cooled alternately, each typically for 15 cooling cycles. One cooling cycle consists of a Gaussian-shaped Raman pulse and a rectangular optical pumping pulse. Bottom: Raman sideband spectroscopy for a probing time corresponding to a $\pi$ pulse on the sideband ($\approx 3\pi$ pulse on the carrier). The average motional state $\overline{n}$ is estimated to be about 0.05 from the ratio of the blue and red sidebands. The error bars indicate a $1\sigma$ confidence interval.

Figure 8

Control of the clock transition. (a) Schematic diagram of the clock-transition laser system. The 1156-nm seed laser light emitted from an external cavity diode laser (ECDL), locked to a high-finesse ultralow expansion (ULE) glass cavity, is preamplified by a semiconductor optical amplifier (SOA) and further amplified by an injection lock to a high-power DL in a butterfly package, using a free-space optical isolator (ISL). Electro-optic modulators (EOMs) and acousto-optical modulators (AOMs) are mainly used for modulating frequency, except for the second-to-last AOM used for intensity servo. The frequency doubler is a single-path waveguide. Phase noise between the seed laser and the 578-nm distribution is removed with phase noise cancellation (PNC). (b) Suppression of excitation on the clock transition using 532-nm light. The ordinate is the probability that atoms are excited into ${}^3{P}_0$ despite the presence of the 532-nm light, and the abscissa is the magnitude of the light shift from the 532-nm beam. A MPP is applied here. The solid line is the Lorentzian line shape for the corresponding Rabi frequency, with no free parameters. The error bars indicate a $1\sigma$ confidence interval. (c) Heating by the light-shift beam. The light-shift operation $L$ is applied repetitively, and the final average motional quanta are measured via Raman sideband spectroscopy. From the linear fit (solid line), we extract 0.056(5) quanta accumulated per iteration of $L$. The error bars indicate a $1\sigma$ confidence interval.

Figure 9

(a) Simulated randomized benchmarking in $g$ compared with measurements. We include measured intensity noise and site-to-site intensity variation, detuning errors, and scattering errors. We also include an error due to the $R_X$ and $R_Z$ beams propagating at an angle that is not perfectly orthogonal. Using the atoms as a probe, we measure the deviation from the orthogonal condition to be ${\theta }_X=0.9(8)°$. The total simulated error rate ranges from $r=1.2\times {10}^{-4}$ at ${\theta }_X=0.1°$ to $r=5.5\times {10}^{-4}$ at ${\theta }_X=1.7°$ (shaded purple region). The black points are the measured values, and the gray line is the fit to data. The success probability at zero gates in the simulation is fixed to the value given by the fit to data. (b) Simulated randomized benchmarking of the optical qubits $o$ compared with measurements. Here, we include only errors due to motional effects and plot the expected error as a function of initial $\overline{n}$. At the measured initial $\overline{n}=0.05(1)$, the calculated error rate $r=1.8\times {10}^{-3}$ due to motional effects is close to the measured value $r=2.0\times {10}^{-3}$. The black points are the measured values. For both panels, the error bars indicate a $1\sigma$ confidence interval.

Figure 10

Theoretical analysis of the MPP in a harmonic oscillator. The trap frequency is fixed to be 10 kHz. (a) Bloch sphere picture of the state evolution in a single MPP. (b) Theoretical state transfer infidelity after a single MPP for various initial average motional quanta, indicating a 2 orders-of-magnitude smaller infidelity, compared to a normal $\pi$ pulse. The dashed line is for the normal $\pi$ pulse, and the solid line is for the MPP. (c) Theoretical average motional state after a single MPP, assuming the initial state is in a motional ground state. A clear minimum can be observed at the Rabi frequency of approximately 80 kHz. We qualitatively confirm this feature is retained for another choice of initial temperature (not shown).

Figure 11

Experimental sequence of the MCOs, with the timing counted after the initial imaging and state preparation. For MCM, the green shaded region indicates imaging. (a) Sequence for the ground-state MCM and MC reset. Both share a similar experimental sequence, except for the spin detection, cooling, and spin reset. (b) Sequence for the metastable MCM. Here, an extra image is taken at the end to assess atom loss.

Figure 12

Quantum process tomography. Reconstructed $\chi$ process matrices for (a) ancilla qubits and (b) data qubits. Here, $\{I,X,Y,Z\}$ denote Pauli matrices, i.e., $\{I,R_X(\pi ),R_Y(\pi ),R_Z(\pi )\}$ rotations.