Midcircuit Qubit Measurement and Rearrangement in a ${}^{171}\mathrm{Yb}$ Atomic Array

Measurement-based quantum error correction relies on the ability to determine the state of a subset of qubits (ancillas) within a processor without revealing or disturbing the state of the remaining qubits. Among neutral-atom-based platforms, a scalable, high-fidelity approach to midcircuit measurement that retains the ancilla qubits in a state suitable for future operations has not yet been demonstrated. In this work, we perform maging using a narrow-linewidth transition in an array of tweezer-confined ${}^{171}\mathrm{Yb}$ atoms to demonstrate nondestructive state-selective and site-selective detection. By applying site-specific light shifts, selected atoms within the array can be hidden from imaging light, which allows a subset of qubits to be measured while causing only percent-level errors on the remaining qubits. As a proof-of-principle demonstration of conditional operations based on the results of the midcircuit measurements, and of our ability to reuse ancilla qubits, we perform conditional refilling of ancilla sites to correct for occasional atom loss, while maintaining the coherence of data qubits. Looking toward true continuous operation, we demonstrate loading of a magneto-optical trap with a minimal degree of qubit decoherence.

Popular Summary

Many technologies are in the running for the realization of a useful quantum computer. One crucial requirement is the ability to determine the quantum state of part of the system without causing irreparable damage to the remainder. In neutral atom-based quantum processors, the state of individual atoms is typically determined by shining resonant light on the atoms and collecting the light that is scattered. Given the dense arrangement of atomic qubits, however, it is difficult to determine the state of a subset of atoms without decohering others, as even a single stray photon can cause decoherence. Here, we solve this problem by locally manipulating the energy levels of individual atoms so that specific atoms are insensitive to the light used to determine the state of other atoms.

In our experiments, we illuminate atoms that we do not wish to measure with light that dramatically shifts the energy of the excited state used for imaging. This pushes the atoms off resonance with the imaging light, hiding them from the image and preventing scattering. We show that this protocol can successfully hide selected atoms within a 2D array of ${}^{171}\mathrm{Yb}$ qubits, maintaining their coherence while others are measured. We then use this capability to repair defects created within the array due to occasional atom loss, all while maintaining coherence within the subset of hidden atoms.

These capabilities represent key steps toward implementing error correction in a neutral atom-based quantum computing platform.

Figure 1

(a) Experimental diagram. Individual ${}^{171}\mathrm{Yb}$ atoms are trapped in the sites of an optical tweezer array in the presence of a 500-G magnetic field. Two high-numerical-aperture objectives allow for site-resolved imaging, and the targeted application of trapping light (483-nm wavelength) and hiding light (460-nm wavelength). A movable tweezer (483-nm wavelength) rearranges atoms between trapping sites. A 556-nm laser incident through a hole in the imaging objective is used to drive global Raman transitions between the qubit states. (b) Laser beams with opposite circular polarization and different frequencies are applied along the direction of the magnetic field to selectively image the two qubit states ${}^1{\mathrm{S}}_0$ $m_f=1/2,-1/2$ (which we label $|1⟩$, $|0⟩$) by coupling them to either of ${}^3{\mathrm{P}}_1$ $m_f=3/2,-3/2$ (556-nm wavelength). The lower panels show two subsequent single-shot images of a fully filled ten-by-three array of atoms prepared in an equal superposition of $|1⟩$ and $|0⟩$ prior to the first image. This shows projection of the qubit state and state-resolved, nondestructive imaging. (c) Hiding light (purple arrows) applies up to 74-MHz differential light shift between the ${}^1{\mathrm{S}}_0$ and ${}^3{\mathrm{P}}_1$ manifolds of targeted sites, pushing the imaging light off resonance. The lower panel shows images of atoms prepared in $|1⟩$ averaged over many trials without hiding light (left), and with hiding light applied to a checkerboard pattern of sites within the array (right). Purple circles indicate hidden sites.

Figure 2

Coherence-preserving midcircuit measurement of subarray. (a) Experimental sequence for characterizing midcircuit measurement, with operations performed on data sites indicated in the upper row and operations performed on ancilla sites in the lower row. Measurements are performed on ancilla sites during a Ramsey sequence. Data sites are shifted off resonance from imaging light, as indicated by red shading. Optical pumping (OP) allows for postselection of occupied sites based on a final image. Coherent global Raman transitions between the two qubit states are driven by a laser 280 MHz detuned from ${}^3{\mathrm{P}}_1$ $m_f=-1/2$ (red arrow), with two tones separated by the qubit frequency (388.9 kHz). (b) Ramsey fringes (see main text for details) for no imaging or hiding light applied (black), hiding light but not imaging light applied (gray), and both imaging and hiding light applied to the array for data (orange) and ancilla (blue) sites. (Hiding light is applied to alternating sites of the array and defines the data sites.) Imaging of ancilla qubits causes a 1.3(8)% loss of array-averaged contrast on data qubits, or 0.7(6)% average single-site contrast loss (see Appendix pp4) as well as a $\mathrm{\Phi }=1.59(2)\mathrm{rad}$ phase shift relative to the absence of imaging or hiding light. Unless otherwise stated, all quantities presented in this work are ensemble averages, and uncertainties are smaller than the markers when not visible. (c) Imaging count histograms (relative to the average camera background) for stochastically occupied sites with no hiding light (upper) and for the midcircuit measurement of ancilla sites from the dataset of (b) (lower), showing minimal perturbation of the ancilla imaging when hiding data qubits. The fitted peak separations are 31.3 and 33.0 photons, respectively. For the data shown, a threshold of nine signal photons enables a discrimination infidelity of 0.015% (0.017%) for the left (right) histograms, based on the overlap of a double-Gaussian fit.

Figure 3

Measured ensemble-averaged contrast loss (upper) and measured ensemble-averaged qubit phase shift $\mathrm{\Phi }$ (lower) on data qubits due to hiding light alone (red points) and both hiding and imaging light combined (black points), versus the magnitude of hiding shift ${\mathrm{\Delta }}_h$. The inset in the upper panel shows the three points with greatest light shift on a logarithmic scale. The solid black line in the lower panel represents an inverse relationship between hiding shift and measurement-induced phase shift, with a constant offset to account for far-off-resonant tones. Error bars correspond to those returned by a fit to the Ramsey fringe, and are smaller than markers when not visible.

Figure 4

Conditional reloading of ancilla qubits. (a) Experimental sequence. During repeated imaging and refilling of ancilla sites, data qubits are protected from decoherence by light shifts from hiding beams indicated by red boxes. (b) Data and ancilla sites (orange and blue, respectively) are defined within a three-by-four subarray surrounded by a reservoir region (green). Ancilla sites identified as empty in midcircuit images are refilled from occupied reservoir sites (red arrow). (c) Upper panel: ensemble-averaged fill fraction of ancilla sites with (blue diamonds) and without (white diamonds) conditional reloading. Lower panel: ensemble-averaged contrast on data sites relative to the $N=0$ case. Up to 16 cycles, ancilla filling remains above 98%, and contrast loss per cycle is 0.9(1)% with conditional reloading. Without reloading, ancilla filling drops by 1.1(1)% per cycle. Error bars correspond to those returned by a fit to the Ramsey fringe, and are smaller than markers when not visible.

Figure 5

Coherence during MOT loading. Main figure: remaining contrast after Ramsey sequence with (red points) and without (black points) simultaneous MOT operation. A single $\pi$ pulse in the middle of the hold time is used to eliminate dephasing from static detuning errors. Lines are Gaussian fits to guide the eye. Inset: relative contrast versus total hold time. Error bars represent the standard deviation on the fitted contrast. A linear fit indicates an additional contrast decay rate of rate of 0.03(2)/s in the presence of the MOT.

Figure 6

(a) Site-resolved data-qubit Ramsey contrast fringes in the presence of MCM on ancilla qubits (divided in a checkerboard pattern), with individual cosine fits. Where not visible, error bars are smaller than markers. Ancilla sites are omitted for clarity. Axis ranges for each subplot are 0 to 1 vertically and 0 to $2\pi$ horizontally. (b) Fitted amplitudes and phases for individual sites displayed according to their position in the array. (c) Histograms of contrast and phase from individual sites. (The overall offset to phase is arbitrary.).

Figure 7

Frequencies of imaging-laser tones within the ${}^3{\mathrm{P}}_1$ $F=3/2$ manifold. Atomic states are represented by thick black lines. The carrier tone is the thin black line. EOM sideband tones corresponding to imaging of the $m_f=-1/2$ ($|0⟩$) state and the $m_f=1/2$ ($|1⟩$) states are represented in red and blue, respectively. Solid lines indicate where states may couple to the qubit states via the dominant polarization component, and dashed lines indicate where coupling occurs through impure polarization. Second-order sidebands are indicated by lower color saturation than first order.