Current quantum error correction (QEC) schemes require extensive classical processing overhead: ancilla measurement, syndrome decoding, and active feedback represent ~99% of the computational cost. We propose a fundamentally different approach: autonomous QEC via Fibonacci-Hopfield networks, in which error correction emerges from the natural dynamics of the system without external intervention. The key insight, formalized in the recently proven phinary framework (Harnessing the Phinary System, 2026), is that Fibonacci-structured quantum codes have error-detection properties that are logically necessary consequences of the non-adjacent-ones constraint — not engineering choices. We demonstrate that a quantum Hopfield network with Fibonacci-spaced energy levels realizes these properties naturally: the attractor states (logical codewords) correspond to stable harmonic modes, and errors (decoherence events) are automatically corrected by the system’s tendency to relax toward its Fibonacci attractors. We propose a concrete implementation on photonic qubits using time-bin encoding, where temporal modes |𝑡𝑛⟩ at Fibonacci time-delays Δ𝑡_𝑛 = 𝑇₀/𝜑^𝑛 constitute the physical register. This architecture achieves: (i) room-temperature operation (photons maintain coherence at 300 K); (ii) autonomous correction without classical feedback; (iii) content-addressable storage (robustness to partial errors); and (iv) natural integration with the Extended Integrated Information Theory (EIIT) framework, wherein a system achieving Φ_EIIT > Φ_threshold generates self-sustaining phase coherence. We provide threshold error rates, capacity bounds, and a 5-step experimental protocol toward a 10-logical-qubit proof-of-concept.
Current quantum error correction (QEC) schemes require extensive classical processing overhead: ancilla measurement, syndrome decoding, and active feedback represent ~99% of the computational cost. We propose a fundamentally different approach: autonomous QEC via Fibonacci-Hopfield networks, in which error correction emerges from the natural dynamics of the system without external intervention. The key insight, formalized in the recently proven phinary framework (Harnessing the Phinary System, 2026), is that Fibonacci-structured quantum codes have error-detection properties that are logically necessary consequences of the non-adjacent-ones constraint — not engineering choices. We demonstrate that a quantum Hopfield network with Fibonacci-spaced energy levels realizes these properties naturally: the attractor states (logical codewords) correspond to stable harmonic modes, and errors (decoherence events) are automatically corrected by the system’s tendency to relax toward its Fibonacci attractors. We propose a concrete implementation on photonic qubits using time-bin encoding, where temporal modes |𝑡𝑛⟩ at Fibonacci time-delays Δ𝑡_𝑛 = 𝑇₀/𝜑^𝑛 constitute the physical register. This architecture achieves: (i) room-temperature operation (photons maintain coherence at 300 K); (ii) autonomous correction without classical feedback; (iii) content-addressable storage (robustness to partial errors); and (iv) natural integration with the Extended Integrated Information Theory (EIIT) framework, wherein a system achieving Φ_EIIT > Φ_threshold generates self-sustaining phase coherence. We provide threshold error rates, capacity bounds, and a 5-step experimental protocol toward a 10-logical-qubit proof-of-concept.
Quantum computers hold immense promise for solving problems intractable for classical machines, yet their practical realization is hindered by the fragility of quantum states. Quantum Error Correction (QEC) is indispensable for protecting quantum information from environmental noise and operational imperfections. Traditional QEC schemes often rely on measurement-based feedback, which involves performing measurements, processing the classical outcomes, and then applying corrective operations. This process introduces latency, consumes significant resources, and can itself be a source of errors due to the invasive nature of quantum measurement and the classical-quantum interface. Coherent feedback control offers a compelling alternative by allowing the controller to directly interact with the quantum system using quantum fields, without intermediate measurement and classical processing. This maintains the coherence of the quantum information throughout the feedback loop, potentially leading to more robust and faster error correction. This paper explores the theoretical framework and potential advantages of employing coherent feedback control for autonomous QEC. We review existing QEC paradigms, delve into the principles of coherent feedback, and propose how this approach can be integrated into autonomous QEC architectures. Specifically, we investigate its application to bosonic codes and stabilizer codes, discussing the engineering challenges and the prospects for achieving truly fault-tolerant quantum computation by minimizing the classical overhead and enhancing real-time error suppression.
Abstract To build a universal quantum computer from fragile physical qubits, effective implementation of quantum error correction (QEC)1 is an essential requirement and a central challenge. Existing demonstrations of QEC are based on an active schedule of error-syndrome measurements and adaptive recovery operations2, 3, 4, 5, 6, 7 that are hardware intensive and prone to introducing and propagating errors. In principle, QEC can be realized autonomously and continuously by tailoring dissipation within the quantum system1, 8, 9, 10, 11, 12, 13, 14, but so far it has remained challenging to achieve the specific form of dissipation required to counter the most prominent errors in a physical platform. Here we encode a logical qubit in Schrödinger cat-like multiphoton states15 of a superconducting cavity, and demonstrate a corrective dissipation process that stabilizes an error-syndrome operator: the photon number parity. Implemented with continuous-wave control fields only, this passive protocol protects the quantum information by autonomously correcting single-photon-loss errors and boosts the coherence time of the bosonic qubit by over a factor of two. Notably, QEC is realized in a modest hardware setup with neither high-fidelity readout nor fast digital feedback, in contrast to the technological sophistication required for prior QEC demonstrations. Compatible with additional phase-stabilization and fault-tolerant techniques16, 17, 18, our experiment suggests quantum dissipation engineering as a resource-efficient alternative or supplement to active QEC in future quantum computing architectures.
Protecting quantum information through quantum error correction (QEC) is a cornerstone of future fault-tolerant quantum computation. However, current QEC-protected logical qubits have only achieved coherence times about twice those of their best physical constituents. Here, we show that the primary barrier to higher QEC gains is ancilla-induced operational errors rather than intrinsic cavity coherence. To overcome this bottleneck, we introduce error-detectable universal control of bosonic modes, wherein ancilla relaxation events are detected and the corresponding trajectories discarded, thereby suppressing operational errors on logical qubits. For binomial codes, we demonstrate universal gates with fidelities exceeding 99.6% and QEC gains of 8.33× beyond break-even. Our results establish that gains beyond 10× are achievable with state-of-the-art devices, establishing a path toward fault-tolerant bosonic quantum computing.
This work explores the integration of Quantum Error Correction (QEC) techniques within energy-efficient green communication networks, emphasizing their pivotal role in achieving sustainability in next-generation Information and Communication Technology (ICT) systems. Quantum technologies, particularly error correction protocols like surface codes are indispensable for reliable quantum information processing. However, their implementation often incurs substantial energy overhead due to the extensive physical qubit resources required. This research proposes a framework for adapting scalable QEC algorithms, leveraging innovations such as reconfigurable atom arrays, to optimize energy consumption while preserving high fidelity in quantum operations. Surface codes, a cornerstone of QEC, encode logical qubits in two-dimensional lattices of physical qubits, utilizing stabilizer measurements to detect and correct bit-flip and phase-flip errors. The performance of surface codes is influenced by critical parameters such as code distance, which determines fault tolerance, and gate fidelity, which impacts logical error rates. Through a comprehensive analysis of these parameters, this work evaluates the interplay between code distance, qubit array size, and gate fidelity to highlight their collective impact on fault tolerance and computational accuracy. These insights align with global efforts to reduce the environmental footprint of emerging quantum technologies, advancing the principles of green ICT and environmentally conscious innovation.
Building fault-tolerant quantum computers with large numbers of logical qubits requires both scalable hardware architectures and error-correcting codes that make efficient use of physical qubits. Photonic interconnects address both of these challenges by allowing the physical qubits to be distributed across multiple processors while providing the non-local connectivity necessary to implement resource-efficient codes such as high-rate quantum low-density parity-check (qLDPC) codes. A key requirement for realising this architecture is the ability to perform stabiliser measurements between remote processors, which has not previously been demonstrated experimentally. Here we report the first experimental demonstration of distributed quantum error detection and correction. We generate entanglement between network qubits in two separate trapped-ion processors and use it to perform remote syndrome measurements on data qubits. We first realise a distributed [[2, 1, 1]] repetition code, detecting phase-flip errors on a logical qubit encoded across the two modules in real time and suppressing logical errors. We then combine these mid-circuit syndrome measurements with real-time feedforward to actively correct arbitrary single-qubit Pauli errors on a distributed Bell state. These results provide an experimental foundation for quantum error correction (QEC) across modular quantum architectures.
In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome measurements and feedback. Here, we propose a nullifier-based digital autonomous QEC enabled by conditional Gaussian operations. By designing jump operators for target nullifiers and compiling the resulting Lindbladian into a Trotterized sequence of elementary conditional Gaussian operations, we demonstrate two use cases: (i) deterministic preparation of non-Gaussian resource states for universal computation, including finitely squeezed cubic phase states and approximate trisqueezed states, and (ii) autonomous suppression of dephasing error for cat and squeezed cat states. We provide explicit gate decompositions for the required conditional Gaussian operations and numerically evaluate the performance under realistic imperfections, including photon loss in the bosonic mode and ancillary-qubit decoherence. Our results clarify the resource requirements and trade-offs, such as circuit depth, time-step choices, and the required set of conditional Gaussian operations, for scalable, gate-level implementations of autonomous state preparation and error suppression.