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arXiv:2609.26880

Bosonic Error Correction with Fluxonium

Shantanu R. Jha, Shoumik D. Chowdhury, Gabriele Rolleri, Anaida Ali, Lev-Arcady Sellem, Réouven Assouly, David Pahl, Lukas Pahl, Junyoung An, Farid Hassani, Hung-Yu Tsao, Chia-Chin Tsai, Aranya Goswami, Jeremie Boudreault, Jeffrey M. Gertler, Michael A. Gingras, Bethany M. Niedzielski, Jeffrey M. Knecht, Mollie E. Schwartz, Kyle Serniak, Jeffrey A. Grover, Baptiste Royer, Max Hays, William D. Oliver

quant-phSubmitted Sep 22, 2026• Announced Sep 24, 2026• 0 citations
v1 · Sep 22, 2026v2 · Sep 30, 2026
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Abstract

Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose $451 \pm 70~μ\mathrm{s}$ bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of $1.59 \pm 0.05$. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.

Comments
40 pages, 17 figures, including supplementary material

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Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose 451±70 μs451 \pm 70~μ\mathrm{s}451±70 μs bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of 1.59±0.051.59 \pm 0.051.59±0.05. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.
Bosonic codes in superconducting resonators are a hardware-efficient avenue for quantum error correction and benefit from the inherent bias toward relaxation errors provided by long-lived cavities compared to typical superconducting qubits. The required coupling to an ancillary control qubit, however, can negate these benefits by inducing highly detrimental effects such as excess decoherence and undesired nonlinearities. This is exemplified by the typically employed transmon qubit that imposes limits on cavity operations due to its finite lifetime as well as the inevitably induced self-Kerr nonlinearity. An important question is thus whether a cavity-qubit coupling can be realized that offers readout and control capabilities without spoiling the cavity. Here, motivated by its long lifetime and design flexibility of its Hamiltonian, we experimentally investigate the fluxonium as a control qubit for superconducting cavities. We couple a fluxonium qubit to a superconducting resonator in the strong-dispersive regime and use it to measure the coherence and flux-tunable inherited nonlinearities of the resonator. We then demonstrate quantum control of the oscillator by preparing and characterizing resonator Fock states and their superpositions, with fidelities limited by resonator decay in our planar prototype device. Finally, we show that the fluxonium can realize cavity-couplings that eliminate undesirable cavity nonlinearities and reach regimes of suppressed self-Kerr that are inaccessible to transmon-based devices. Our results thus demonstrate the potential of the fluxonium as a high-performance bosonic control qubit for superconducting cavities that can outperform existing transmon-based architectures.
Bosonic quantum error correction encodes a logical qubit in an oscillator, avoiding the hardware overhead of large qubit arrays. Among such encodings, Gottesman-Kitaev-Preskill (GKP) states are paticularly powerful because their phase-space grid structure protects against small displacement errors simultaneously in both conjugate quadratures. Here we provide the first protocol for preparing magnonic GKP states, which involves an ellipsoidal magnetic crystal effectively coupled to a superconducting qubit via a microwave cavity. The geometric anisotropy intrinsically squeezes the magnon mode, while the cavity-mediated qubit control realizes an effective conditional-displacement interaction. We show that two rounds of a conditional-displacement interaction and a qubit projective measurement yield three- and four-component magnonic GKP-like states. We also show how to realize single logical qubit gate operations, such as Pauli, Hadamard and phase gates, completing the logical Pauli basis of the approximate GKP code. Our results establish hybrid magnon-qubit systems as a promising platform for preparing bosonic code states, with applications in magnonic fault-tolerant quantum computation and quantum sensing.
Quantum computers use the principles of quantum mechanics to store and manipulate information encoded in the quantized levels of physical systems. A goal of quantum computers is to accurately solve problems that are intractable for classical computers, such as simulating molecular dynamics and prime factorization of large integers. However, the failure probability is too high for quantum computers to solve useful problems. Fortunately, quantum error correction (QEC) provides a way to perform robust computations in the presence of errors by distributing information across multiple physical systems. Bosonic quantum error-correcting codes offer a hardware-efficient avenue for QEC where information is encoded in the continuous phase-space of a single harmonic oscillator. The linear harmonic oscillator realised as the microwave modes of a superconducting resonator is controlled via a nonlinear superconducting control qubit. Experiments on bosonic QEC are limited by bit flip errors in the control qubit, leading to low logical lifetimes of the storage resonator. Our idea is to replace the transmon with a heavy fluxonium qubit that has intrinsic protection against bit-flips. With this architecture in mind, we investigate the performance of a universal gateset comprising of Echoed Conditional Displacement gates and single qubit rotations. Wenumerically solve the Schrödinger equation for a closed resonator- fluxonium device and use a combination of quantum and semiclassical approaches to simulate the system exactly. We adopt a pulse-level implementation of quantum gates where we realize target gates by applying tailored drives on the resonator. We develop a resonator frame-tracking technique that allows us to simulate the dynamics of the driven resonator exactly with less than five fock levels while retaining all the physics of the problem. This technique allowed us to accurately simulate the device up to a few 10000s of photons, matching experimental results, that otherwise would not be possible even using high-performance computers due to excessive memory and simulation time required.
Quantum information is vulnerable to environmental noise and experimental imperfections, hindering the reliability of practical quantum information processors. Therefore, quantum error correction (QEC) that can protect quantum information against noise is vital for universal and scalable quantum computation. Among many different experimental platforms, superconducting quantum circuits and bosonic encodings in superconducting microwave modes are appealing for their unprecedented potential in QEC. During the last few years, bosonic QEC is demonstrated to reach the break-even point, i.e. the lifetime of a logical qubit is enhanced to exceed that of any individual components composing the experimental system. Beyond that, universal gate sets and fault-tolerant operations on the bosonic codes are also realized, pushing quantum information processing towards the QEC era. In this article, we review the recent progress of the bosonic codes, including the Gottesman-Kitaev-Preskill codes, cat codes, and binomial codes, and discuss the opportunities of bosonic codes in various quantum applications, ranging from fault-tolerant quantum computation to quantum metrology. We also summarize the challenges associated with the bosonic codes and provide an outlook for the potential research directions in the long terms.
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes, particularly grid state encodings, offer a pathway to scalable fault-tolerant quantum computing in superconducting circuits. By leveraging the large Hilbert space of bosonic modes, quantum error correction can operate at the single physical unit level, therefore reducing drastically the hardware requirements to bring fault-tolerant quantum computing to scale. Going beyond the well-known Gottesman-Kitaev-Preskill (GKP) code, we discuss how using multiple bosonic modes to encode a single qubit offers increased protection against control errors and enhances its overall error-correcting capabilities. Given recent successful demonstrations of critical components of this architecture, we argue that it offers the shortest path to achieving fault tolerance in gate-based quantum computing processors with a MHz logical clock rate.
Quantum error correction of a grid-state qubit with state preparation and measurement errors below 10−310^{-3}10−3
Grid state qubits offer a hardware-efficient approach to large-scale fault-tolerant quantum computing. They access the information redundancy required for quantum error correction by exploiting the large Hilbert space naturally available in harmonic oscillators. Superconducting architectures are particularly suitable to implement grid state qubits due to their fast and high-fidelity operations. Grid states in superconducting circuits enable quantum error correction (QEC) with performance beyond break-even. However, the state preparation and measurements (SPAM) errors of grid states has been a significant limitation to computational performances. In this work, we leverage high-performance QEC to enable repeat-until-success state preparation of both cardinal and magic states of the single-mode grid-state qubit. We combine this with an improved measurement protocol that corrects for both finite-energy envelope and auxiliary qubit readout errors, and increases robustness to photon loss. Our experiments, using both techniques, achieve a combined state-preparation and measurement error below 10−310^{-3}10−3. This represents two orders-of-magnitude improvement over the state of the art, bringing this platform on par with standard SPAM error levels measured in transmon qubits.