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Logical quantum processor based on reconfigurable atom arrays
Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim, Sophie H. Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, J. Pablo Bonilla Ataides, Nishad Maskara, Iris Cong, Xun Gao, Pedro Sales Rodriguez, Thomas Karolyshyn, Giulia Semeghini, Michael J. Gullans, Markus Greiner, Vladan Vuletic, Mikhail D. Lukin
TL;DR
Large-scale useful quantum algorithms require error correction, but controlling redundantly encoded logical qubits remains challenging. The paper realizes a programmable logical processor in reconfigurable neutral-atom arrays and demonstrates fault-tolerant operations and complex logical circuits. Error detection improves sampling performance in circuits reaching 48 logical qubits, while repetitive correction and fault-tolerant preparation remain important scope boundaries.
Problem
Controlling logical qubits encoded across many physical qubits remains a significant challenge for large-scale logical quantum computing.
Method
The authors implement logical-level control in reconfigurable neutral-atom arrays and use surface, color, and three-dimensional [[8,3,2]] encodings for programmable logical algorithms.
Results
Error detection improves cross-entropy benchmarking for entangled systems of up to 48 logical qubits, demonstrating improved sampling performance with logical qubits.
Takeaways & Limitations
The experiments demonstrate key ingredients of scalable error correction and practical utility for sampling and quantum simulations of complex scrambling circuits.
Takeaways & Limitations
State preparation is non-fault-tolerant for the d = 5, 7 surface codes and [[8,3,2]] codes, and deep circuits require repetitive error correction.
Abstract
from arXiv · showhide
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.
Improving entangling gates with code distance
The transversal CNOT between surface-code logical qubits improves with increasing code distance when errors propagated between blocks are decoded jointly. However, non-fault-tolerant state preparation limits the observed scaling under conventional decoding.
- ≈0.95 populations in the X_LX_L and Z_LZ_L bases demonstrate entanglement between the d = 7 logical qubits using correlated decoding.Correlated decoding adds edges and hyperedges between the two logical qubits’ decoding graphs to account for deterministic error propagation during the transversal CNOT.
- Correlated decoding uses stabilizer correlations caused by physical-error propagation between the two blocks during the transversal CNOT.The joint decoding graph connects the stabilizers of the two logical qubits with edges and hyperedges.
- Larger code distance improves the logical Bell pair, demonstrating improvement of the entangling operation.The experiment compares surface-code blocks across code sizes while keeping experimental conditions unchanged by removing selected atoms.
- Conventional decoding shows decreasing Bell-pair fidelity with increasing code distance, partly because state preparation is non-fault-tolerant.The nFT preparation effect is partially mitigated by correlated decoding.
- The experiment demonstrates surpassing an effective threshold for the entire circuit, including the transversal CNOT.The reported threshold is elevated by projective readout after the transversal CNOT.
- Repeated noisy syndrome extraction remains an important future requirement because the demonstrated transversal CNOT used projective readout after the gate.The authors expect repetitive syndrome extraction to have a somewhat lower threshold in practice.
Fault-tolerant logical algorithms
The processor demonstrates fault-tolerant logical algorithms using color-code encodings, scalable zoned operation, and mid-circuit feedforward. These experiments produce logical GHZ states, entanglement teleportation, and operation of 40 color code qubits.
- Color-code initialization: 99.91+0.04−0.09% |0L⟩ initialization fidelity exceeds the physical |0⟩ initialization and two-qubit gate fidelities.Fault-tolerant initialization postselects on an ancilla logical flag not detecting errors.
- Logical GHZ states: 72(2)% GHZ fidelity demonstrates genuine multipartite entanglement using a fault-tolerant logical algorithm.Postselecting on correct computation-logical stabilizers increases the fidelity to 99.85+0.1−1.0%, at the cost of postselection overhead.
- Logical GHZ states: Discarding 50% of experimental data improves GHZ fidelity to approximately 90% through partial postselection based on correlated matching weights.The procedure tunes the tradeoff between algorithm success probability and fidelity.
- Logical GHZ states: Fault-tolerantly measuring all 256 logical Pauli strings enables full GHZ state tomography.The tomography follows direct fidelity estimation using Pauli measurements.
- Scalable logical operation: 40 color codes are created and operated using 280 physical qubits, with approximately 1% logical decoherence per additional encoding step from storage idling errors.The zoned architecture scales circuits without increasing the number of controls by moving encoded qubits between entangling and storage zones.
- Entanglement teleportation: 77(2)% Bell-state fidelity is recovered after real-time feedforward in fault-tolerant entanglement teleportation.Repeating the experiment with postselection instead of mid-circuit readout gives a similar 75(2)% Bell fidelity, indicating high-fidelity readout and feedforward operations.
Complex logical circuits using 3D codes
Three-dimensional [[8,3,2]] codes enable transversal non-Clifford gates and complex logical sampling circuits. Across up to 48 logical qubits, error detection improves sampling quality and quantum-simulation measurements.
- Code architecture: [[8,3,2]] codes encode three logical qubits per block and transversally implement CCZ, CZ, Z, and CNOT operations.They support error detection in the Z basis, correction in the X basis, and transversal CNOTs between blocks.
- Sampling performance: 12-logical-qubit IQP sampling circuits improve from XEB 0.156(2) to 0.616(7) with error detection.The measured distribution increasingly approaches the ideal theoretical distribution as postselection becomes more stringent.
- Scaling: 48-logical-qubit circuits contain 228 logical two-qubit gates and 48 logical CCZ gates on hypercube connectivity, achieving XEB ≈0.1.Across 3, 6, 12, 24, and 48 logical qubits, XEB remains finite and improves with increased error detection.
- Logical versus physical performance: Error detection improves logical XEB beyond the estimated upper bound for optimized physical-qubit implementations in this system.Small physical instances also produced values well below that upper bound.
- Quantum simulation: Two-copy measurements reveal Page-curve entanglement, magic versus applied CCZ gates, and 412 Pauli-string expectations with zero-noise extrapolation.The measured final-state purity is 0.74(3), while extrapolated Pauli expectations reach approximately 10% relative precision of ideal theoretical values.
- Quantum simulation: Error detection significantly improves simulation signal-to-noise despite postselection overhead.Near-zero entropies are exponentially faster to measure under this procedure.
Outlook
The experiments establish ingredients for scalable logical processing and show that co-designed encodings can improve complex sampling and quantum simulations. Future scaling requires repetitive error correction, improved control and gate errors, atom reloading, and more efficient codes.
- Outlook: The experiments demonstrate key ingredients of scalable error correction and quantum information processing with logical qubits.The demonstrated circuits approach the edge of exact simulation methods and can be used to explore error-corrected quantum advantage.
- Future milestones: Repetitive error correction during logical algorithms is identified as a key future milestone for extending accessible computation depth.The authors state that repeating stabilizer measurements can directly realize this capability.
- Scaling requirements: The architecture and logical-level control are projected to scale beyond 10000 physical qubits by increasing laser power and optimizing control methods.The authors also identify continuous atom reloading as necessary for deep computation.
- Scaling requirements: Further improvements include reducing two-qubit gate errors to 0.1%, increasing encoding efficiency, and adopting alternatives such as qLDPC codes, erasure conversion, or noise bias.These changes are presented as ways to improve QEC efficiency and continued scaling.
METHODS
The methods combine logical-qubit control, error-detection protocols, fault-tolerance analysis, and efficient simulation strategies for encoded neutral-atom circuits. They also identify limits from calibration, non-fault-tolerant preparation, residual physical errors, and exponential classical simulation cost.
- Control and calibration: ∼7 × 10−4 error per π/2 pulse limits the Raman Z-rotation scheme when calibration is poor, particularly through row-position inhomogeneity.The authors suggest X(θ) gates as a faster and potentially more robust alternative.
- Error detection: Sliding-scale error detection selects measurement outcomes by a confidence threshold rather than discarding every result containing a stabilizer error.This protocol is explored for algorithmic circuits to balance error suppression against data retention.
- Fault-tolerant state preparation: The logical GHZ fidelity is limited to 72% by error accumulation and error spreading through transversal gates despite theoretical p2 failure scaling.Modeling with 99.4% two-qubit gate fidelity and roughly 4% data-qubit decoherence predicts 79%, indicating residual calibration or physical errors.
- Fault-tolerant state preparation: A single stabilizer-measurement round makes d = 5, 7 surface-code state preparation non-fault-tolerant because one ancilla error can induce multiple data-qubit errors.The d = 3 initialization is a special case that avoids this issue.
- Logical decoding: Joint correlated decoding uses stabilizer correlations propagated across a transversal CNOT to recover improved Bell-state performance with code distance.Independent decoding instead causes Bell-state quality to degrade substantially as distance increases.
- Classical simulation: Hypercube circuits exploit a final inter-partition CNOT layer to reduce tensor-contraction complexity, although the simulation still scales exponentially with qubit number.Adding l intra-partition CNOT layers yields an estimated execution-time scaling of roughly O(82l/2l).