High-fidelity entanglement and coherent multi-qubit mapping in an atom array

Abstract

Neutral atoms in optical tweezer arrays possess broad applicability for quantum information science, in computing, simulation, and metrology. Among atomic species, Ytterbium-171 is unique as it hosts multiple qubits, each of which is impactful for these distinct applications. Consequently, this atom is an ideal candidate to bridge multiple disciplines, which, more broadly, has been an increasingly effective strategy within the field of quantum science. Realizing the full potential of this synergy requires high-fidelity generation and transfer of many-particle entanglement between these distinct qubit degrees of freedom, and thus between these distinct applications. Here we demonstrate the creation and coherent mapping of entangled quantum states across multiple qubits in Ytterbium-171 tweezer arrays. We map entangled states onto the optical clock qubit from the nuclear spin qubit or the Rydberg qubit. We coherently transfer up to 20 atoms of a $Z_2$-ordered Greenberger-Horne-Zeilinger (GHZ) state from the interacting Rydberg manifold to the metastable nuclear spin manifold. The many-body state is generated via a novel disorder-robust pulse in a two-dimensional ladder geometry. We further find that clock-qubit-based spin detection applied to Rydberg and nuclear spin qubits facilitates atom-loss-detectable qubit measurements and $>90\%$ Rydberg decay detection. This enables mid-circuit and delayed erasure detection, yielding an error-detected two-qubit gate fidelity of $99.78(4)\%$ in the metastable qubits. This error detection also enables Rydberg qubit evolution with an effective lifetime of $1.2(2)$ ms, enhancing the fidelity of the observed many-body dynamics. These results establish a versatile architecture that advances multiple fields of quantum information science while also establishing bridges between them.

Figures (14)

• Figure 1: Architecture based on multi-level qubit mapping.a, Schematic of the ${}^\text{171}\text{Yb}$ atomic structure (top panel). Coherent spin-1/2 nuclear spin qubit in both the ground state ($g$-qubit, green) and the metastable state ($m$-qubit, blue). An optical transition connects the ground and metastable states, defining the clock qubit ($o$-qubit, yellow). The $m_F=+1/2$ metastable state can be excited to a Rydberg level via a single photon transition at $302\,\mathrm{nm}$ ($r$-qubit, red). In this system, $>90\%$ of Rydberg decay events are detected as atom loss. The bottom panel shows single-shot images after rearrangement for experiments involving two-qubit gates and experiments using analog many-body Hamiltonian evolutions. b, Bell state generation and mapping sequence. The Bell state generated by a high-fidelity two-qubit gate in the $m$-qubit manifold is subsequently mapped onto the $o$-qubit and detected by loss-detectable spin-measurements represented by a box with three dots. c, Measured $m$-qubit Bell state population (left) and the parity oscillation (right) with loss detection. d, Analogous measurement for $o$-qubit. e, The sequence of the GHZ-state mapping from $r$-qubit to $m$-qubit. The GHZ state is generated by an adiabatic many-body Hamiltonian sweep in the $r$-qubit and mapped to $m$-qubit. f, Measured $Z_2$-order of the GHZ state. The staggered magnetism is defined as a sum of the magnetism with flipped signs for the nearest neighbor atoms (Methods). Three spin detection methods are compared. Yellow (left) shows the data of direct $r$-qubit spin detection with erasure detection to suppress preparation errors (Methods). Light blue (center) includes additional error detection through erasures revealed after the sequence, which identifies Rydberg-state decay events. Finally, dark blue (right) applies qubit mapping and loss detection, as shown in e. The observed $Z_2$ population is $53(3)\%$, $57(4)\%$, and $78(3)\%$ respectively, showing two-fold improvement of population error in the loss detected case. (Inset) Single-shot loss-detected measurement result; images for two spins are combined with blue (red) color for $\ket{m_0}$ ($\ket{m_1}$).
• Figure 1: Beam geometry, atomic structure, tweezer polarizability, resource-efficient rearrangement, and state preparation.a, Beam and magnetic field geometry relative to the atom array. $B_1$ is used during initial optical pumping and Raman cooling, followed by $B_2$ for the qubit manipulations. The X-rotation beams for both the ground and metastable states propagate perpendicular to $B_2$. The Rydberg and clock beams are aligned parallel to the magnetic field and use circular polarization to drive the $\sigma^+$ transition. The ionization beam is co-aligned with the UV beam. b, Atomic structure of ${}^\text{171}\text{Yb}$ showing the transitions relevant to the experiment. The ${}^\text{1}\text{P}_1$ transition is used for fast destructive imaging, while ${}^\text{3}\text{P}_1$ serves as both the non-destructive imaging transition and the intermediate state for Raman transitions. The metastable state is coupled to the Rydberg state via a single-photon transition. The ionization beam is resonant with an inner-shell transition. c, Polarizability of excited states compared to the ground state ${}^\text{1}\text{S}_0$. At the operational tweezer wavelength $767\,\mathrm{nm}$, the ${}^\text{3}\text{P}_0$ state is nearly magic, and the ${}^\text{1}\text{P}_1$ state used for destructive imaging remains trapped. For ${}^\text{1}\text{P}_1$, only the scalar polarizability is considered due to scattering from both magnetic sublevels. d, Enhanced loading and rearrangement. We use single-atom loading at an efficiency of $\sim90\%$ followed by rearrangement to prepare defect-free arrays, as illustrated in the top graphic. The data show the full-array success rate as a function of target array size. e,State preparation sequence to the metastable state. After preparing the radial motional ground state via Raman sideband cooling, we flip the spin in the ground-state manifold using a $\pi$-pulse. Motional-state-preserving pulses (MPPs) are used to coherently excite the atoms to the ${}^\text{3}\text{P}_0$ state without adding motional excitationlis2023midcircuit. f, Measurement of atomic temperature. Inset: sideband spectroscopy indicating $\bar{n} = 0.05\xspace{}$. Main panel: release-and-recapture comparison between ground and metastable states. The agreement shows that the clock excitation does not introduce additional motional heating. The solid line shows the Monte-Carlo simulation best agrees with the experiment. We extract the atomic temperature of 0.28(4)$\,\upmu \mathrm{K}$. g, Simulation results for motional-state-preserving pulses at varying wavelengths. The upper panel shows the population transfer infidelity; the lower panel shows the motional excitation added by the pulse, indicating heating.
• Figure 2: Qubit mapping and loss-detectable spin measurement.a, Sequence of the loss-detectable spin measurements for the $m$-qubit (top) and the $o$-qubit (bottom). A clock $\pi$-pulse is used to selectively de-excite one of the spin components. Each spin component is destructively imaged via fast fluorescence imaging (see Methods). b, Distribution of the camera counts of the spin measurement. We apply the measurement to distinguish the three outcomes $\ket{m_1}$, $\ket{m_0}$, and atom loss, for the case of preparing each of these states (red, blue, and black dots). c, Loss-detectable spin measurement of $r$-qubit. The left schematic shows the sequence of mapping the $r$-qubit onto the $m$-qubit. (Right) Rabi oscillations of the Rydberg state observed by this spin-measurement method with loss detection. Both $\ket{r_0}$ population (red) and $\ket{m_1}$ population (blue) are observed simultaneously. d, Measured branching ratio of the decay for $\ket{r_0}$ Rydberg state (see Extended Data Fig. \ref{['SMfig4_5']}). Decays are registered as atom loss unless the atom decays back into the qubit manifold in use. e, Observation of population decay dynamics consistent with the non-Hermitian state evolution via qubit mapping and loss detection. The loss-detected probability of Rydberg state, $P_r(t)$ is plotted, where each marker represents different initial Rydberg populations, $\{16(1)\%, 53(2)\%, 84(1)\%, 99.7(3)\%\}$. The inset compares the fitted decay time constant and the curve derived from non-Hermitian dynamics without free parameters (see Methods). We use $P_r(t)=P_r(0)e^{-t/\tau}$ for the fitting function. f, Proof-of-concept demonstration combining analog quantum simulation and digital quantum operations to generate a metrologically valuable state. After evolving two atoms under the PXP-Hamiltonian, a Bell state in the Rydberg qubit is generated and mapped onto the $m$-qubit (lower left). A $\pi/2$-pulse on the $m$-qubit then converts the $(\ket{01}+\ket{10})/\sqrt{2}$ Bell state into a $(\ket{00}+\ket{11})/\sqrt{2}$ Bell state (top), which is subsequently mapped onto the clock $o$-qubit (lower right).
• Figure 2: Blue imaging and experimental sequence for the three-outcome measurement.a, Beam geometry and sequence of the destructive imaging. Counter-propagating beams resonant with the ${}^\text{1}\text{S}_0$ to ${}^\text{1}\text{P}_1$ transition are alternately applied on the atoms at a frequency of $3 \,\mathrm{MHz}$. b, Two methods of fast imaging. We use either $250 \,\mathrm{kHz}$-deep tweezers ("shallow") or $9.6 \,\mathrm{MHz}$-deep tweezers ("deep") in the experiment. The shallow tweezers are used for erasure detection, while the deep tweezers are used for spin detection. Bottom: typical single-shot images from both methods. The deep tweezers confine the atom position more tightly. c, Photon count histogram from shallow-tweezer imaging using a $7 \times 7$ pixel region of interest (ROI). A two-Gaussian fit infers a spin-readout infidelity below $<0.5 \%$. d, Comparison of photon count histograms from deep and shallow tweezers using a small ROI. The deep tweezers result in reduced overlap due to better confinement. e, Optimization of imaging time in a tightly spaced array matching the GHZ experiment geometry (Top). As imaging time increases, infidelity initially decreases due to improved fluorescence collection, then increases beyond $15 \,\upmu \mathrm{s}$ due to cross-talk from neighboring atoms. A similar trend is observed in the geometry for the gate experiment, which uses even smaller atom spacing ($2.4\,\upmu \mathrm{m}$). f, Three-outcome imaging sequence. "Meta" represents the $\pi$-pulse on the $m$-qubit subspace. The $\pi$-pulse on the $o$-qubit is indicated as "Clock". "Blue" indicates application of the resonant beam to the ${}^\text{1}\text{S}_0$$\longleftrightarrow$${}^\text{1}\text{P}_1$ transition, used for both, imaging and blow-away of ground-state atoms. (Top) Actual experimental sequence, with wait times inserted for camera readout. (Bottom) Projected sequence duration, totaling less than $3$$\,\mathrm{ms}$.
• Figure 3: High-fidelity two-qubit gate enhanced by loss detection.a, Global randomized benchmarking (gRB) sequence. To compare to the loss detection, ground state erasure detection is implemented. Preparation errors in the metastable state are detected by observing the ground state population at the beginning of the gRB sequence, while some of the qubit leakage errors are continuously monitored by observing the ground state population during the sequence. The erasure detection beam is off only during the two-qubit gate operations. b, gRB results. We observe an increase in the gate fidelity by partially detecting the decayed population by erasure decay detection (triangle) compared to the case only with preparation erasure detection (square). With loss detection, the fidelity increases to $99.78(4)\%$ (circle). c, Atom loss in the gRB experiment after preparation erasure detection. Here, the loss includes auto-ionized population due to the remaining population in the Rydberg state after a gate. d, Histogram of measured loss per CZ gate. The dashed line shows the simulation result (Methods).