Architectural mechanisms of a universal fault-tolerant quantum computer

TL;DR

Key principles for efficient architecture design are revealed, involving the interplay between quantum logic and entropy removal, and judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset.

Abstract

Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement all key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors, demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding. We then investigate logical entanglement using transversal gates and lattice surgery, and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes, enabling arbitrary-angle synthesis with logarithmic overhead. Finally, we develop mid-circuit qubit re-use, increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic and entropy removal, judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.

Figures (16)

• Figure 1: Architectures and mechanisms for fault-tolerant quantum computation.a, We study the key building blocks of fault-tolerant processing. We utilize an architecture based on reconfigurable atom arrays trapped in optical tweezers, where the logical processor is segmented into storage, entangling, readout, and reservoir zones. Underlying physical mechanisms are identified and characterized. b, Spin-to-position conversion for non-destructive, loss-resolved qubit readout is accomplished with a state-selective 1D lattice that converts the atom spin state into position. Plot shows measured Rabi oscillation. This non-destructive readout has 0.46(4)% bit-flip error and 0.24(2)% loss (Methods). c,d, Stabilizer measurement on a $d=5$ surface code is interspersed with global coherent errors injected on the data qubits. Each CZ layer corresponds to one time-step (Methods). Repeated correction reduces error build-up through both the Zeno effect and error tracking (right plot is at a fixed $\theta/2\pi = 0.016)$. For visual clarity, an acceptance fraction of 50% is used in this plot (Methods).
• Figure 1: Neutral-atom quantum computing architecture.a, Experimental layout illustrating key optical tools, similar to Ref. Bluvstein2023 with the addition of beams for local cooling, imaging and hiding to enable qubit re-use experiments. b, Control infrastructure for programming quantum circuits. The entire waveform for all AWGs (except for rearrangement) is uploaded at the start of each experimental run. For qubit re-use experiments, the Moving, Raman AOD and Rydberg AWGs loop the same memory segment each layer. The full waveform is programmed for the Raman AWG to ensure phase continuity. For mid-circuit rearrangement, waveforms are calculated on-the-fly using a desktop computer and sent to the Rearrangement AWG operated in first-in first-out (FIFO) mode. c, Level diagram of the relevant atomic transitions of $^{87}$Rb. d, Processor layout used for qubit re-use experiments and relevant laser beams. Atoms are arranged into storage, entangling and readout zones, with an additional reservoir for refilling lost atoms mid-computation. The 1529-nm hiding beam illuminates the storage zone to preserve coherence of active qubits during imaging in the readout zone. Parallel two-qubit gates are performed in the entangling zone with global Rydberg beams, and local detunings are optionally applied to selected gate sites using an SLM. The readout zone is illuminated with local beams for 1D PGC imaging and EIT cooling, as well as two counter-propagating lattice beams to form a spin-dependent potential for readout via spin-to-position conversion. The entire array is addressed with global Raman control for dynamical decoupling. The same Raman light is directed through a pair of crossed AODs for local single-qubit gates. Global imaging and lambda-enhanced gray molasses cooling light are used for the initial loading.
• Figure 2: Below-threshold repeated quantum error correction leveraging loss detection.a, Results of repeated rounds of $d=5$ surface code using loss detection, showing a snapshot of the data block and multiple ancilla blocks (see ED Fig. \ref{['fig:ED_ExtraSurface']}). b, c, Products of stabilizer measurement results between rounds are used to detect qubit errors, which we refer to as 'detectors'. 'Bare' counts loss as state $\ket{0}$, 'detect loss' does not make this erroneous assignment, 'supercheck' multiplies detectors around lost atoms, and 'post.' postselects on all atoms of a detector being present. b, Detector error probability as a function of data qubit loss in each shot, analyzed by partitioning the total dataset. c, Average over all data. d, Logical error per round for a surface code after 4 QEC rounds in both bases, decoded using most-likely error methods ('bare MLE'), machine learning ('bare ML'), MLE with loss information, and ML with loss information. ML with loss renders the error per round for $d=5$ as $2.14(13)$x lower than $d=3$. No postselection is used. Small points are the four d=3 quadrants. Results are averaged between $\ket{+_L}$ and $\ket{0_L}$ initialization bases. See Methods and ED Fig. \ref{['fig:ED_ExtraSurface']} for more details. e, Logical error per round as a function of the mean qubit loss, plotted as a cumulative density function. f, Relative physical error contribution to overall error budget (see Methods). g, Distribution of detector errors per shot, suggesting the absence of large-scale correlated errors.
• Figure 2: Spin-to-position conversion.a, Level diagram showing the $^{87}$Rb hyperfine levels used to engineer a spin-selective one-dimensional optical lattice. b, Trapping potentials for the bright and dark states. The dark state only experiences a lightshift from the optical tweezers - allowing the atom to be moved around freely - while the bright state is additionally confined by the optical lattice potential. By using a blue-detuned lattice, atoms are trapped in intensity antinodes and so scattering of the lattice light is reduced. c, Schematic timeline of spin-to-position conversion. The time to transfer the clock qubit to the bright and dark states for readout is typically on the order of roughly $20\,\mu s$, but for some of our measurements is several milliseconds due to using a slow global rotation of the magnetic field (panel e). See Methods text for additional information. d, Transfer of qubit state $\ket{1}$ to the dark state via resonant optical pumping. e, Transfer of qubit state $\ket{0}$ towards into $m_F = +1,+2$ states. This is achieved with either a coherent Raman transfer to $F=2,m_F=+2$ or incoherent pumping with $\sigma^+$-polarized repumper. Both approaches achieve the same bright state readout fidelity, but in the specific implementation we use here the Raman transfer takes several milliseconds owing to the rotation of the external magnetic field for driving $\sigma$ transitions (2 and 3). f, Quadratic suppression of readout error due to scattering. The bright state transfer ensures that at least two lattice-induced scattering events are required to cause a readout error, which occurs if the AOD tweezer has not yet moved away as the bright state becomes unpinned. Scattering further causes diabatic changes in the depth of the lattice potential and may contribute to atom loss.
• Figure 3: Exploring the interplay of logic gates and entropy removal.a, Atom images illustrating two-qubit logic gates and stabilizer measurement. Lattice surgery is realized using ancillas to measure the logical product $Z^1_L Z^2_L$, and transversal gates are realized via atomic motion. b, Quantum circuits for realizing transversal gates and lattice surgery operations. CZ gates are realized as transversal CNOTs and Hadamards. c, Dependence of error of the logic operation on the ancilla measurement error. Lattice surgery errors rapidly worsen with increasing ancilla measurement errors (injected in post-processing). d, N repeated logic operations are interspersed with rounds of QEC stabilizer measurement. Transversal CNOT has a lower error than lattice surgery (left), and has an optimum of roughly 3 CNOTs per round, as seen most clearly when modest postselection, characterized by acceptance fractions (AF) are used (right). Error detection is used for lattice surgery in d to compensate for having $<d$ rounds (Methods).