Logical quantum processor based on reconfigurable atom arrays

TL;DR

A programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits is described, in which improvement of algorithmic performance using a variety of error-correction codes is enabled.

Abstract

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Utilizing logical-level control and a zoned architecture in reconfigurable neutral atom arrays, our system combines high two-qubit gate fidelities, arbitrary connectivity, as well as fully programmable single-qubit rotations and mid-circuit readout. Operating this logical processor with various types of encodings, we demonstrate improvement of a two-qubit logic gate by scaling surface code distance from d=3 to d=7, preparation of color code qubits with break-even fidelities, fault-tolerant creation of logical GHZ states and feedforward entanglement teleportation, as well as operation of 40 color code qubits. Finally, using three-dimensional [[8,3,2]] code blocks, we realize computationally complex sampling circuits with up to 48 logical qubits entangled with hypercube connectivity with 228 logical two-qubit gates and 48 logical CCZ gates. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling. These results herald the advent of early error-corrected quantum computation and chart a path toward large-scale logical processors.

Figures (15)

• Figure 1: A programmable logical processor based on reconfigurable atom arrays.a, Schematic of the logical processor, segmented into three zones: storage, entangling, and readout (see ED Fig. 1 for detailed layout). Logical single-qubit and two-qubit operations are realized transversally with efficient, parallel operations. Transversal CNOTs are realized by interlacing two logical qubit grids and performing a single global entangling pulse that excites atoms to Rydberg states. Physical qubits are encoded in hyperfine ground states of $^{87}$Rb atoms trapped in optical tweezers. b, Fully programmable single-qubit rotations are implemented using Raman excitation through a 2D AOD; parallel grid illumination delivers the same instruction to multiple atomic qubits. c, Mid-circuit readout and feedforward. The imaging histogram shows high-fidelity state discrimination (500 $\mu$s imaging time, readout fidelity $\approx$ 99.8%, Methods), and the Ramsey fringe shows that qubit coherence is unaffected by measuring other qubits in the readout zone (error probability $p \sim 10^{-3}$, Methods). The FPGA performs real-time image processing, state decoding, and feedforward (Fig. 4).
• Figure 1: Neutral atom quantum computer architecture.a, Experimental layout, featuring optical tools including static SLM and 2D moving AOD traps, global and local Raman single-qubit laser beams, 420-nm and 1013-nm Rydberg beams, and imaging system for both global and local imaging. b, Level structure for $^{87}$Rb atoms, with the relevant atomic transitions employed in this work. c, Control infrastructure used for programming quantum circuits, featuring several arbitrary waveform generators (AWGs). In particular, the moving and Raman 2D AODs are each controlled by two waveforms (one for x axis and one for y axis). An additional AWG is used in first-in-first-out (FIFO) mode for rearrangement before the circuit begins, and then the moving AOD control is switched to the Moving AWG. See Ref. Ebadi2021 for additional SLM and pre-circuit rearrangement details, Ref. Evered2023a for additional Rydberg AWG details and Rydberg excitation details, Refs. Levine2021Bluvstein2022 for additional Raman laser and microwave control infrastructure details, and Ref. Bluvstein2022 for additional moving AWG details. All AWGs (other than rearrangement AWG) are synchronized to $<$ 10 ns jitter. During Rydberg gates the traps are briefly pulsed off by a TTL. The FPGA processes images from the camera real-time and in this work sends control signals to the Raman 2D AOD for local single-qubit control. d, Example array layout featuring entangling, storage, and readout zones. Zones can be directly reprogrammed and repositioned for different applications, as well as specific tweezer site locations. Tweezer beams and local Raman control are projected from out-of-plane. The entire objective field-of-view is 400-$\mu$m diameter, and consequently we do not expect or observe substantial tweezer deformation near the edges of our processor. During two-qubit Rydberg gates, we place atoms $\lesssim$ 2 $\mu$m apart within a gate site, and gate sites are separated such that atoms in different gate sites are no closer than 10 $\mu$m during the gate. At our present $n=53$ and two-photon Rabi frequency of 4.6 MHz, the blockade radius is roughly 4.3 $\mu$m, such that adjacent atoms are well-within blockade and distant atoms are well-outside blockade.
• Figure 2: Transversal entangling gates between two surface codes. a, Illustration of transversal CNOT between two $d=7$ surface codes based on parallel atom transport. b, The concept of correlated decoding. Physical errors propagate between physical qubit pairs during transversal CNOT gates, creating correlations that can be utilized for improved decoding. We account for these correlations, arising from deterministic error propagation (as opposed to correlated error events), by adding edges and hyperedges that connect the decoding graphs of the two logical qubits. c, Populations of entangled $d=7$ surface codes measured in the $XX$ and $ZZ$ basis. d, Measured Bell pair error as a function of code distance, for both conventional (top) and correlated (bottom) decoding. We estimate Bell error with the average of the $ZZ$ populations and the $XX$ parities (Methods). To reduce code distance we simply remove selected atoms the grid, as shown on the right, ensuring unchanged experimental conditions (for $d=3$, four logical Bell pairs are generated in parallel). Error bars represent standard error of the mean. See ED Figs. \ref{['fig:ED_surfacedata']}, \ref{['fig:ED_surfaceprep']} for additional surface code data.
• Figure 2: Single-qubit Raman addressing.a, 5S$_{1/2}$ hyperfine level diagram illustrating the two possible implementations of local single-qubit gates: resonant $X(\theta)$ (purple) and off-resonant $Z(\theta)$ (turquoise) rotations with two-photon Rabi frequencies $\Omega_{\textrm{Raman}}$. In this work, we use the $Z$ rotation scheme and are blue-detuned by 2 MHz from the two-photon resonance. Due to Clebsch-Gordan coefficients, $\widetilde{\Omega}_{\textrm{Raman}}^Z=-\sqrt{3}\Omega_{\textrm{Raman}}^Z$. b, Schematic showing the conversion of local $Z(\pi/2)$ into local $X(\pm \pi/2)$ gates, where the pulses before (after) the central $Y(\pi)$ have positive (negative) sign, while leaving non-addressed qubit states unchanged. The Gaussian-smoothed local pulses have duration 2.5 $\mu$s for $\pi/4$ pulses and 5 $\mu$s for $\pi/2$ pulses, and are performed on single rows at a time with a 3 $\mu$s gap between subsequent gates to allow the RF tones in the AODs to be changed (including this, duration is 5-8 $\mu$s per row). In this way, arbitrary patterns of qubits, such as the example drawn, can be addressed. c, Calibration procedure used to homogenize the Rabi frequency over a $220$$\mu$m $\times~ 35$$\mu$m array. The position calibration is illustrated for 80 sites: approximate $X(\pi/2)$ gates are locally performed and the horizontal/vertical position of all tones is scanned in parallel such that a Gaussian fit returns the optimal alignment. After this, powers are iteratively calibrated until the fitted scale factors for the individual RF tones converge to unity. d, Single-qubit randomized benchmarking of local $Z(\pi/2)$ gates. The local gates are interleaved with random global single-qubit Clifford gates and the final operation $C_f$ is chosen to return to the initial state. Each data point is the average of 100 random sets of Clifford gates, and fitting an exponential decay to the return probability quantifies the fidelity $\mathcal{F}$ per local gate. Note that we apply all 51 global Clifford gates for each data point, such that errors from the global Clifford gates (in addition to SPAM errors) do not contribute to the fitted value.
• Figure 3: Fault-tolerant logical algorithmsa, Circuit for preparation of logical GHZ state. Ten color codes are encoded non-fault-tolerantly (nFT), and then parallel transversal CNOTs between computation and ancilla logical qubits perform FT initialization. The ancilla logical qubits are moved to storage, and a 4-logical-qubit GHZ state is created between the computation qubits. Logical Clifford operations are applied before readout to probe the GHZ state. b, State-preparation-and-measurement (SPAM) infidelity of the logical qubits without (nFT) and with (FT) the transversal-CNOT-based flagged preparation, compared to physical qubit SPAM. c, Logical GHZ fidelity without postselecting on flags (nFT), postselecting on flags (FT), and postselecting on flags and stabilizers of the computation logical qubits, corresponding to error detection (EDFT). d, GHZ fidelity as a function of sliding-scale error detection threshold (converted into the probability of accepted repetitions) and of number of successful flags in the circuit. e, Density matrix of the 4-logical-qubit GHZ state (with at most 3 flag errors) measured via full state tomography involving all 256 logical Pauli strings.