Suppressing errors is the central challenge for useful quantum computing¹, requiring quantum error correction (QEC)²⁻⁶ for large-scale processing. However, the overhead in the realization of error-corrected 'logical' qubits, in which information is encoded across many physical qubits for redundancy²⁻⁴, poses substantial 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. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays⁷, our system combines high two-qubit gate fidelities⁸, arbitrary connectivity⁷,⁹, as well as fully programmable single-qubit rotations and mid-circuit readout¹⁰⁻¹⁵. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code⁶ distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities⁵, fault-tolerant creation of logical Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks¹⁶,¹⁷, we realize computationally complex sampling circuits¹⁸ with up to 48 logical qubits entangled with hypercube connectivity¹⁹ with 228 logical two-qubit gates and 48 logical CCZ gates²⁰. 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 scrambling²¹,²². These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.
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Bluvstein et al. (2023) studied this question.
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