Quantum error correction (QEC) is a crucial step towards long coherence times required for efficient quantum information processing. One major challenge in this direction concerns the fast real-time analysis of error syndrome measurements and the associated feedback control. Recent proposals on autonomous QEC (AQEC) have opened new perspectives to overcome this difficulty. Here, we design an AQEC scheme based on quantum reservoir engineering adapted to superconducting qubits. We focus on a three-qubit bit-flip code, where three transmon qubits are dispersively coupled to a few low-$Q$ resonator modes. By applying only continuous-wave drives of fixed but well-chosen frequencies and amplitudes, we engineer an effective interaction Hamiltonian to evacuate the entropy created by eventual bit-flip errors. We provide a full analytical and numerical study of the protocol while introducing the main limitations on the achievable error correction rates.
Quantum error correction (QEC) is a crucial step towards long coherence times required for efficient quantum information processing. One major challenge in this direction concerns the fast real-time analysis of error syndrome measurements and the associated feedback control. Recent proposals on autonomous QEC (AQEC) have opened new perspectives to overcome this difficulty. Here, we design an AQEC scheme based on quantum reservoir engineering adapted to superconducting qubits. We focus on a three-qubit bit-flip code, where three transmon qubits are dispersively coupled to a few low-Q resonator modes. By applying only continuous-wave drives of fixed but well-chosen frequencies and amplitudes, we engineer an effective interaction Hamiltonian to evacuate the entropy created by eventual bit-flip errors. We provide a full analytical and numerical study of the protocol while introducing the main limitations on the achievable error correction rates.
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.
Dissipative quantum error correction (QEC) autonomously protects quantum information using engineered dissipation and offers a promising alternative to error correction via measurement and feedback. However, scalability remains a challenge, as correcting high-weight errors typically requires increasing dissipation rates and exponentially many correction operators. Here, we present a scalable dissipative QEC protocol for discrete-variable codes, correcting multi-qubit errors via a trickle-down mechanism that sequentially reduces errors weight. Our construction exploits redundancy in the Knill-Laflamme conditions to design correction operators that act on multiple error subspaces simultaneously, thereby reducing the overhead from exponential to polynomial in the number of required operators. We illustrate our approach with repetition codes under biased noise, showing a fourfold improvement in the exponential suppression factor at realistic physical error rates. Our approach connects autonomous QEC for discrete-variable codes with demonstrated dissipative protocols for bosonic codes and opens up new avenues for traditional measurement-feedback QEC and fault-tolerant quantum operations.
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.
Quantum error correction (QEC) is essential for practical quantum computation, but conventional approaches require large numbers of physical qubits per logical qubit, imposing severe hardware overhead. Noise-biased qubits, in which one error type dominates over the others, offer a route to reducing this overhead by enabling tailored QEC codes that exploit the error asymmetry. This work demonstrates, through two separate experiments, that combining Hamiltonian and dissipation engineering provides a versatile framework for enhancing the noise-bias of superconducting qubits. In the first experiment, we focus on the Kerr-cat qubit (KCQ), a noise-biased qubit encoded in the degenerate eigenstates of a two-photon driven Kerr oscillator, and study leakage outside the KCQ manifold, a key limitation of this system. We apply microwave pulses to selectively address the leakage states and to perform the first direct measurement of their population. We find a leakage population exceeding 9 %, consistent with substantial quantum heating and twelve times larger than the thermal excited-state population of the undriven oscillator. To reduce it, we introduce frequency-selective engineered single-photon dissipation. We show that this suppresses the leakage and extends the bit-flip time to 3.6 ms, while leaving the phase-flip time unchanged and reaching a qubit noise bias of 1400. In the second experiment, we introduce the gain-engineered transmon: a qubit encoded in the |g⟩ and |f⟩ levels of a standard transmon, in which a frequency-selective engineered single-photon-gain channel on the |e⟩ ↔ |f⟩ transition autonomously corrects single-photon loss errors. We demonstrate a factor-of-17 enhancement of the relaxation time, at the cost of only a 2.1 reduction in echo coherence time, while maintaining single-qubit gate errors below 0.5 %. Numerical simulations further show that the gain-engineered transmon can serve as a noisebiased ancilla for fault-tolerant error detection, suppressing both the ancilla detection infidelity and the error backaction below those of a standard |g⟩ ↔ |e⟩ ancilla qubit. These results establish the combination of Hamiltonian and dissipation engineering as a practical strategy for protecting quantum information. Because our architectures build on standard superconducting circuits, they integrate easily into existing platforms. We envision that steady improvements to noise-biased qubits, such as those developed in this thesis, could allow them to replace the transmon as the building block of superconducting quantum processors, lowering the hardware overhead of fault-tolerant quantum computation. Beyond quantum information processing, the driven nonlinear oscillators discussed in this thesis may serve as analog simulators of complex quantum dynamics, and as platforms for studying fundamental effects in driven-dissipative systems.
Autonomous quantum error correction (QEC) stabilizes a logical manifold through dissipative events that emit into output channels, which are typically accessible to measurement. These signals are often discarded, and whether they contain useful information about logical failures remains generally unclear. Using quantum trajectories, we show that in dissipatively stabilized cat qubits bit flips are not silent logical errors: each flip is accompanied by a strong, time-localized photon burst from the dissipative buffer. Photon counting and homodyne monitoring can therefore herald the loss of logical information without interrupting the autonomous stabilization: bit flips in dissipative cat qubits are erasures. More broadly, our results show that the emitted signals of engineered reservoirs can act as built-in failure monitors for autonomous QEC, turning rare logical faults into erasures available to a decoder and reducing fault-tolerance overhead. To this end, we develop a general framework, based on past quantum states and number-resolved master equations, to quantify the detectability of such logical failures in autonomous QEC from the emitted signal.
Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction (AQEC) instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. We realize an AQEC scheme, implemented with only two transmon qubits in a 2D scalable architecture, that actively corrects single-photon loss and passively suppresses low-frequency dephasing using six microwave drives. Compared to uncorrected encoding, factors of 2.0, 5.1, and 1.4 improvements are experimentally witnessed for the logical zero, one, and superposition states. Our results show the potential of implementing hardware-efficient AQEC to enhance the reliability of a transmon-based quantum information processor.