A major goal in quantum computation is the implementation of error correction to produce a logical qubit with an error rate lower than that of the underlying physical qubits. Recent experimental progress demonstrates physical qubits can achieve error rates sufficiently low for error correction, particularly for codes with relatively high thresholds such as the surface code and color code. Motivated by experimental capabilities of neutral atom systems, we use numerical simulation to investigate whether coherent error correction can be effectively used with the 7-qubit color code. The results indicate that coherent error correction does not work at the 10-qubit level in neutral atom array quantum computers.
By adding more qubits there is a possibility of making the encoding circuits fault-tolerant which could improve performance.
A major goal in quantum computation is the implementation of error correction to produce a logical qubit with an error rate lower than that of the underlying physical qubits. Recent experimental progress demonstrates physical qubits can achieve error rates sufficiently low for error correction, particularly for codes with relatively high thresholds such as the surface code and color code. Motivated by experimental capabilities of neutral atom systems, we use numerical simulation to investigate whether coherent error correction can be effectively used with the 7-qubit color code. The results indicate that coherent error correction does not work at the 10-qubit level in neutral atom array quantum computers.
By adding more qubits there is a possibility of making the encoding circuits fault-tolerant which could improve performance.
Quantum computing has reached a pivotal inflection point with the recent demonstration ofbelow-threshold quantum error correction and the emergence of logical qubits that outperformtheir physical counterparts. This review synthesizes the remarkable progress achieved between2024 and 2026 across multiple quantum hardware platforms, including superconducting circuits,trapped ions, and neutral atom arrays. We examine the theoretical foundations of quantumerror correction codes, with particular emphasis on surface codes and the rapidly advancingquantum low-density parity-check (qLDPC) codes. Key experimental milestones are analyzed,including Google’s Willow chip demonstration of exponential error suppression, IBM’s modularfault-tolerant roadmap culminating in the Starling system, IonQ’s achievement of 48 logicalqubits with a 2:1 encoding ratio, and QuEra’s record-efficiency neutral atom error correctionapproaching the Teraquop regime. The review further explores critical enabling technologiessuch as real-time decoding architectures, magic state distillation protocols, and fault-tolerant gateimplementations. We discuss the remaining challenges in scaling to hundreds of logical qubits,achieving practical logical error rates of 10−10 to 10−15, and realizing end-to-end fault-tolerantalgorithms. By synthesizing these developments, this article provides a comprehensive assessmentof the field’s trajectory toward practical fault-tolerant quantum computing and identifies the keymilestones that will define the next phase of progress.
Abstract Surface codes are building blocks of quantum computing platforms based on 2D arrays of qubits responsible for detecting and correcting errors. The error suppression achieved by the surface code is usually estimated by simulating toy noise models describing random Pauli errors. However, Pauli noise models fail to capture coherent processes such as systematic unitary errors caused by imperfect control pulses. Here we report the first large-scale simulation of quantum error correction protocols based on the surface code in the presence of coherent noise. We observe that the standard Pauli approximation provides an accurate estimate of the error threshold but underestimates the logical error rate in the sub-threshold regime. We find that for large code size the logical-level noise is well approximated by random Pauli errors even though the physical-level noise is coherent. Our work demonstrates that coherent effects do not significantly change the error correcting threshold of surface codes. This gives more confidence in the viability of the fault-tolerance architecture pursued by several experimental groups.
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information, giving our procedure extra fault tolerance and eliminating the need for ancilla verification. The procedure is particularly favorable when multiqubit gates are available for the correction step. Simulations of the bit-flip, Bacon-Shor, and Steane codes indicate that coherent error correction can produce threshold error rates that are on the order of 10^{-3} to 10^{-4}-comparable with or better than measurement-based values, and much better than previous results for other coherent error correction schemes. This indicates that coherent error correction is worthy of serious consideration for achieving protected logical qubits.
Quantum computing platforms based on arrays of tweezer-confined neutral atoms have recently emerged as a competitive modality thanks to a direct path toward high qubit count, rapidly advancing operation fidelities, and their ability to execute circuits with arbitrary qubit connectivity. These features will enable the use of efficient error correction schemes with high encoding-rates, time-efficient decoding, and resource-efficient architectures based on transversal gates. With these goals in mind, recent state of the art neutral atom demonstrations focus on the transition from the use of physical qubits to error-corrected logical qubits, but to date there has been no demonstration of repeated error correction scalable to arbitrary depth. Here, we demonstrate many cycles of syndrome extraction in a toric quantum error correcting code, using mid-circuit measurement and replacement of lost qubits, including reloading of a qubit reservoir for indefinite coherent operation. We characterize the logical error rate after up to 90 cycles, showing that logical information can be preserved through multiple rounds of qubit reloading. Comparing two distances of the code up to 8 rounds of syndrome extraction shows a lower absolute logical error rate for the larger distance code.
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, mid-circuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a ten qubit QCCD trapped-ion quantum computer to encode a single logical qubit using the [[7,1,3]] color code, first proposed by Steane~\cite{steane1996error}. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical SPAM error of 1.7(6)×10−3, compared to the average physical SPAM error 2.4(8)×10−3 of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a logical magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudo-threshold.
Quantum error correction enables scalable fault-tolerant quantum computation by suppressing logical errors exponentially with code distance once physical error rates fall below a critical threshold. Here we demonstrate below-threshold operation of triangular color codes with distances d=3,5, and 7 on Quantinuum's Helios trapped-ion quantum processor. Leveraging both circuit- and hardware- level leakage reduction schemes, we achieve logical error rates as low as 5−2+4×10−6, and demonstrate error suppression by over an order of magnitude, Λ=12−2+3, with each successive increase in code distance. Moreover, we demonstrate below threshold scaling of error rates for Clifford two-qubit randomized benchmarking circuits when encoded in d=3,5 color codes, achieving logical error rate of 7−3+3×10−5 per logical two-qubit Clifford at distance 5 with a suppression factor of Λ=9−3+8. We compare logical performance for existing near-optimal algorithmic decoders, and both convolutional neural network and transformer-based neural network decoders capable of real-time decoding an order of magnitude faster than the syndrome extraction rate. These results approach the logical error rates required for megaquop-scale quantum computation and indicate that scaled trapped-ion processors could reach application-relevant performance with substantially smaller code blocks than indicated by previous results in other qubit modalities.