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Architectural mechanisms of a universal fault-tolerant quantum computer

Dolev Bluvstein, Alexandra A. Geim, Sophie H. Li, Simon J. Evered, J. Pablo Bonilla Ataides, Gefen Baranes, Andi Gu, Tom Manovitz, Muqing Xu, Marcin Kalinowski, Shayan Majidy, Christian Kokail, Nishad Maskara, Elias C. Trapp, Luke M. Stewart, Simon Hollerith, Hengyun Zhou, Michael J. Gullans, Susanne F. Yelin, Markus Greiner, Vladan Vuletic, Madelyn Cain, Mikhail D. Lukin

arXiv:2506.20661v1quant-phcond-mat.quant-gasphysics.atom-ph

TL;DR

The paper examines how to design efficient fault-tolerant quantum architectures by balancing logical operations, physical entanglement, and entropy removal. Experiments with neutral-atom arrays demonstrate below-threshold QEC and architectural principles supporting universal, deep-circuit processing.

  • Problem

    Efficient fault-tolerant encodings require generating logical entanglement while minimizing physical entanglement and coordinating it with entropy removal.

  • Method

    The experiments combine surface-code QEC, loss-aware machine-learning decoding, logical entanglement methods, teleportation, and mid-circuit qubit re-use in neutral-atom architectures.

  • Results

    The experiments demonstrate below-threshold repeated QEC and establish architectural principles linking quantum logic, entropy removal, physical entanglement, and teleportation.

  • Takeaways & Limitations

    Efficient fault-tolerant processing depends on applying syndrome extraction selectively, deploying physical entanglement judiciously, and using teleportation for universality and qubit reset.

  • Takeaways & Limitations

    Large-scale computation remains limited by physical errors, the scalability requirements of machine-learning decoding, and a depleting atomic reservoir.

Abstract

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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.

Neutral atom logical processor

The processor uses reconfigurable neutral-atom arrays with non-destructive readout, qubit re-use, and repeated stabilizer measurements to support logical computation.

  • Processor architecture: Up to 448 atoms are stored across storage, entangling, readout, and reservoir zones, with circuits programmed by shuttling qubits.Rydberg excitation provides entangling operations, while local single-qubit operations are programmable.
  • Readout and re-use: Spin-resolved lattice readout converts qubit state to position, enabling atom-loss detection and retention.This differs from conventional spin-to-loss conversion followed by camera readout.
  • Readout and re-use: Mid-circuit re-initialization enables qubit re-use and increases the experimental cycle rate by two orders of magnitude.The upgrade supports extended computation rather than requiring fresh physical qubits after every operation.
  • Repeated QEC: A distance-5 surface-code qubit undergoes up to five rounds of stabilizer measurement using movable ancilla blocks.Ancilla blocks shuttle between entangling and storage zones so stabilizer checks can be repeated.
  • Repeated QEC: Stabilizer products between rounds act as detectors, while loss-aware processing uses superchecks around lost atoms.Superchecks multiply stabilizers surrounding a lost atom to recover error information.

Below-threshold performance

Repeated surface-code QEC exhibits below-threshold behavior when atom-loss information is incorporated into decoding. Loss-aware decoding and machine learning substantially improve performance in the four-round characterization circuit.

  • Loss-aware decoding: Superchecks suppress detected error probability by multiplying stabilizers around lost atoms.Loss-aware decoding avoids treating a lost qubit as an erroneous |0⟩ assignment.
  • Below-threshold performance: 2.14(13)x lower error per round for d=5 than d=3 demonstrates below-threshold behavior in the four-round circuit.The d=5 error per round is 0.62(3)%, approaching 0.1% on shots without qubit loss.
  • Below-threshold performance: 1.73(13)x improvement over conventional methods results from combining loss information with machine-learning decoding.Both most-likely-error and machine-learning decoders were evaluated with and without loss information.
  • Error correlations: Error distributions are consistent with uncorrelated Pauli-type and loss-type errors, suggesting no large-scale correlated errors.Postselection on no qubit loss nearly eliminates time correlations, and more than 80% of leakage corresponds to atom loss.

Stabilizer measurement during logic operations

Transversal gates and lattice surgery realize logical entanglement with different roles for stabilizer measurements. Transversal operations are less sensitive to ancilla measurement errors, while repeated QEC removes entropy generated by the logic.

  • Logical entanglement: Transversal gates entangle two surface-code blocks by transporting, interlacing, and pairwise entangling their data qubits.Lattice surgery instead uses ancillas between codes to perform a joint logical measurement.
  • Stabilizer measurement during logic operations: Lattice surgery is significantly more sensitive to injected ancilla measurement errors than transversal gates.The comparison uses logical Bell-state parity errors after preparing Bell states with either method.
  • Stabilizer measurement during logic operations: Approximately three CNOTs per QEC round is optimal at low error rates after postselection on decoding confidence.The optimum reflects a balance between logic operations and entropy removal.
  • Stabilizer measurement during logic operations: In transversal gates, data qubits directly implement logic while stabilizer measurements remove entropy; in lattice surgery, ancilla measurements directly perform the logic.This distinction explains why lattice-surgery measurements must be correct, whereas transversal operations use checks primarily for error removal.
  • Stabilizer measurement during logic operations: Logical-gate error depends on the number of gates applied per QEC round rather than a single physical-gate fidelity.The observed dependence connects decoding success with the physical entropy generated during computation.

Universality and synthesizing arbitrary unitaries

The experiments use teleportation with 3D Reed–Muller codes to implement non-Clifford operations and synthesize arbitrary rotations. Increasing the number of T gates exponentially refines the accessible angle spacing, while teleportation also supports constant-entropy computation.

  • Universal gate set: 3D Reed–Muller codes exhibit a 45-degree stabilizer plateau corresponding to the non-Clifford T gate.The plateau appears for codes with all positive stabilizer signs.
  • Universal gate set: Universal rotations are built from alternating H and T gates, with T supplied by state preparation and H implemented through quantum teleportation.The circuit uses transversal teleportation with logical CZ gates, X-basis measurements, and feedforward.
  • Angle synthesis: Generated logical states span Bloch-sphere angles consistent with theory, and angular spacing shrinks exponentially with the number of T gates.The experiment used entangled Reed–Muller codes and tomography with up to three T gates.
  • Angle synthesis: Arbitrary rotation angles can therefore be synthesized with a logarithmic number of steps.The observed scaling is consistent with the Solovay–Kitaev theorem.
  • Constant-entropy architecture: Teleportation preserves unitary logical information through measurement, decoding, and feedforward while physical dissipation corrects errors.The same mechanism connects universal processing with physical-level error removal.

Deep circuits at constant entropy

The experiments use transversal teleportation, repeated measurement, and qubit re-use to run deep logical circuits while maintaining constant internal entropy and suppressing physical-error correlations.

  • Teleportation and reset: The protocol alternated fresh encoded group-A blocks with entangled group-B blocks, followed by measurement and re-initialization of group B.This repeated the space-and-time entangling structure across circuit layers.
  • Steane-code circuits: Repeated state preparation of 32 [[7,1,3]] Steane-code blocks for up to 27 layers maintained a constant stabilizer expectation value.The experiment used 16 blocks in each of two alternating groups.
  • Cluster states: Logical correlations persisted in 1D and 2D cluster states, while stabilizer-error correlations rapidly decayed.The 2D data remained effective until the atomic reservoir began to run out.
  • Teleportation and reset: Transversal teleportation propagated logical information while leaving physical errors on the previous block for removal through measurement and reset.Decoding and logical feedforward preserve logical unitary evolution, while physical evolution is dissipative.
  • High-rate codes: High-rate [[16,6,4]] codes showed logical propagation and physical-error suppression at a rate similar to [[7,1,3]] Steane codes.Permutation CNOTs within blocks extended the correlation length relative to non-permuted qubits.
  • High-rate codes: In-block logical entanglement improved algorithm performance because overlapping logical operators share the same physically entangled qubits.The experiment entangled up to 16 [[16,6,4]] blocks in two dimensions.

Discussion and outlook

The discussion identifies architectural principles linking quantum logic, entropy removal, physical entanglement, and teleportation, while noting remaining error-reduction and scalability challenges.

  • Architectural principles: Efficient fault-tolerant architectures require coordinating coherent logical operations with dissipative physical-error removal.This coordination allows syndrome extraction to be applied only where necessary.
  • Architectural principles: Physical entanglement should be deployed selectively: transversal gates and high-rate codes reduce requirements, whereas magic states require precise entanglement structure.The discussion contrasts entanglement efficiency in logical operations with the demands of magic-state generation.
  • Architectural principles: Logical teleportation provides universality with fully transversal operations and a native route to physical-error removal and atom-loss-aware decoding.The authors connect these roles across universal processing and deep-circuit protocols.
  • Outlook and limitations: The experiments operate about 2x below key QEC thresholds, and further physical-error reduction would benefit large-scale computation.The authors estimate an additional 3–5-fold reduction may be achievable through hardware and calibration improvements.
  • Outlook and limitations: Machine-learning decoding is effective and fast, but additional work is needed to establish its scalability.The reported implementation runs at approximately 1 µs per shot when batched on a GPU.

System overview

The processor combines programmable neutral-atom arrays, synchronized control, spatially separated operating zones, and specialized imaging, cooling, and reconfiguration systems for fault-tolerant experiments.

  • Experimental platform: The platform loads and rearranges 87Rb atoms into programmable tweezer arrays, with qubits encoded in hyperfine clock states and controlled by Raman transitions.The system uses an SLM for static traps and AODs for moving traps.
  • Control system: Five synchronized arbitrary waveform generators control rearrangement, Rydberg entangling pulses, Raman operations, and local addressing.The control infrastructure is synchronized to less than 10 ns of jitter.
  • Control system: Circuit layers are looped through waveform memory segments, enabling experiments lasting up to 1.1 seconds.The Raman waveform is programmed directly to preserve phase continuity.
  • Calibration and limitations: The processor is highly programmable, but each new atomic layout requires configuration-specific characterization and calibration.The authors compare changing layouts to designing and printing a new chip.
  • Experimental platform: Up to 256 qubits can be entangled simultaneously in the deep-circuit entangling zone, while up to 128 atoms are measured and re-initialized in the readout zone.The zones are spatially organized to support repeated processing.
  • Calibration and limitations: Initial deep-circuit fidelity was affected by suboptimal re-initialization, echoing, trap transport, trap homogeneity, and Rydberg-beam uniformity.The authors state these choices have no fundamental limitation and can be improved.
  • Readout and cooling: Spin-to-position conversion enables non-destructive state readout and atom-loss detection using a one-dimensional optical lattice.State-dependent transport separates dark- and bright-state atoms before camera imaging.
  • Readout and cooling: Focused counterpropagating beams provide local cooling and imaging while preserving qubit control in a finite magnetic field.This adapts imaging and cooling to the conditions required for mid-circuit operation.

1529-nm shielding beam

A 1529-nm shielding beam protects storage-zone qubits from readout light by inducing a large Stark shift, while its detuning-dependent dephasing is characterized experimentally.

  • Shielding mechanism: A 1529-nm beam shifts the storage-zone transition off resonance with readout light while preserving hyperfine qubit information.The reported operating power is approximately 1.2 W, producing an estimated 6 GHz lightshift on the 5P3/2 state.
  • Dephasing characterization: The experiment measures storage-qubit dephasing as a function of detuning while readout-zone qubits receive local probe and repumper light.A simple model relates the added dephasing to probe-beam parameters, illumination time, and the calculated lightshift.
  • Dephasing characterization: The simple dephasing model does not capture more complex on-resonance or multilevel features, which are especially sensitive between 4D-level resonances.These features define an important operating constraint for the shielding scheme.
  • System integration: The 1529-nm beam must cover the storage zone homogeneously while avoiding illumination of the readout zone.This beam-profile requirement reflects the need to protect stored qubits without perturbing local imaging.

AOD intermodulation effects

AOD intermodulation can degrade performance for specific moves, making frequency planning important along both individual axes and their relative spacing.

  • Exact frequency combs are important because intermodulation can create interference and beating near trap frequencies.
  • Relative X- and Y-frequency spacing also matters when their beat notes approach trap frequencies.

Analysis of error correlations

The experiments examine spatial and temporal error correlations and show how measurement, error correction, and teleportation shape their persistence. Several mechanisms suppress or reveal correlations, while Rydberg-state decay can create long-lived cross-site effects.

  • Global coherent errors can be de-correlated by projective measurement because error correction natively de-correlates errors introduced by global control.
  • For small global rotations, stabilizer measurements convert coherent effects into probabilistic Pauli errors, while higher-weight logical terms are suppressed with code distance.
  • Stabilizer signs can be engineered to control coherent-error interference in Clifford circuits, but transversal non-Clifford gates require deterministic stabilizer eigenvalues.
  • 0.07% of the error budget comes from Rydberg P-state decay, whose over-100 µs lifetimes can corrupt gates at distant sites across many layers.
  • 99.3% to 99.5% CZ fidelity is observed when the interval between gates is increased to 100 µs, consistent with decay or ejection of residual Rydberg atoms.
  • Surface-code detector-error distributions are closely consistent with simulations assuming uncorrelated one- and two-qubit errors across approximately 10^5 detector rounds.
  • Logical teleportation rapidly removes errors and prevents their persistence as correlations in either time or space when atomic qubits are properly re-initialized.Without cooling and sorting, correlations do not rapidly decay.

Loss detection for improved QEC

Loss detection supplies direct error-location information and enables superchecks, improving decoding and repeated-QEC performance. Machine-learning and maximum-likelihood methods exploit these signals, while deeper circuits and current hardware errors remain practical constraints.

  • Loss errors include physical atom loss, undetected leakage to other hyperfine states, and leakage to Rydberg states that can create correlated errors.
  • At least 80% of leakage is observed as loss when several hundred microseconds separate gates, and Rydberg-leakage effects are not apparent in repeated-QEC data.
  • Superchecks multiply stabilizers around a lost atom so the resulting checks commute and recover usable error information.
  • The delayed-erasure MLE decoder combines stabilizer measurements with physical error probabilities to infer the most likely error pattern.
  • 1.69(8) versus 1.24(5) is the measured d=3/d=5 error ratio with loss information versus bare MLE decoding.
  • A fully connected neural network performs supervised binary classification of logical |0L⟩ versus |1L⟩ from experimental measurement outcomes.
  • 9.04% mean detector error is comparable to the 8.5-8.7% mean detector error reported in Ref. [7], although the comparison is not one-to-one because of loss information.

Physical entropy removal

The paper treats entropy removal as a central architectural function of QEC, using syndrome extraction, decoding, teleportation, and feedforward to manage diverse physical errors while preserving logical computation.

  • Entropy-removal mechanisms: QEC removes entropy by mapping generic quantum errors into incoherent bit- and phase-flip errors, then detecting and tracking them.The paper also identifies loss, leakage, and atomic motion as entropy-bearing physical degrees of freedom.
  • Entropy-removal mechanisms: Ancilla-based stabilizer extraction maps stabilizer information onto measured ancillas, while Shor- and Steane-style methods provide alternative extraction architectures.These methods differ in how ancillas encode or collect syndrome information before measurement.
  • Logical teleportation: Logical teleportation leaves Pauli and non-Pauli physical errors behind while propagating the logical information to a fresh block.With transversal gates requiring only O(1) QEC rounds per logical gate, teleportation can remove errors without additional overhead.
  • Physical teleportation: Physical-level teleportation can implement leakage reduction, but dedicated ancilla pairing becomes impractical for high-rate codes with many encoded qubits.The number of unpaired data qubits is lower bounded by k, the number of encoded qubits.
  • Feedforward: For conventional transversal or planar Clifford computation, detected Pauli errors need not be physically corrected; logical feedforward suffices for teleportation-based operations.Transversal non-Cliffords such as T require deterministic stabilizer eigenvalues, although the paper uses deterministic initialization to support constant-entropy operation.

Methods of universality

Universality is obtained by combining transversal gates, logical measurement, teleportation, and code-specific resources while controlling the physical entanglement required by logical operations and magic states.

  • Transversal gates: The [[15,1,3]] 3D color code supports transversal {CZ, CCZ, CNOT, T}, whereas 2D topological codes cannot transversally implement T.A universal gate set can be formed from {H, T, CNOT}.
  • Logical measurement: Logical measurement breaks unitarity and enables universality: CZ with |+L⟩, followed by measurement and feedforward, teleports H onto |ψL⟩.This uses X-basis preparation and measurement together with transversal CZ gates.
  • Entanglement bounds: For any [[n, k, d]] code with k < 2d, logical operator entanglement cannot exceed the physical entanglement available in any region of size d −1.The paper frames efficient encodings as generating target logical entanglement with minimal physical entanglement.
  • Entanglement-efficient logic: In the [[16,6,4]] code, transversal CNOT uses 16 physical CNOTs and yields 6 logical CNOTs, while in-block permutations add 8 logical CNOTs for 14 total.The resulting 14 logical CNOTs are close to the 16-physical-CNOT entanglement resource.
  • Logical magic: Logical magic states require more in-block entanglement than non-magic logical states because they involve macroscopic superpositions of code-spanning operators.The paper contrasts product-form logical Pauli states with entangled states such as |TL⟩.
  • Output-dependent protection: Remote Bell-pair witnesses can require little entanglement within individual code blocks, whereas error-corrected Bell-inequality tests demand stronger internal protection.The required protection depends on which logical output is being produced.
  • Gate characterization: Logical gate characterization uses both FL(pdet) and Δpdet to capture fidelity versus internal error density and the gate’s increase in local error density.The per-step decoding error is described as PL ∝ (p/pth)^((d+1)/2).
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