A new quantum-computing design could preserve a useful imbalance between two kinds of errors during controlled operations, according to a mathematical and numerical study. Its 0–n Fock qubit is modeled to make logical bit flips exponentially rarer as the chosen level n increases, even when the gate is controlled by a qubit without the same error bias. The model says a logical flip requires O(⌈n/2⌉) sequential intrinsic decay events.
The proposal stores the two logical states in the oscillator’s ground state, |0⟩, and n-th excited Fock level, |n⟩. In ordinary terms, the encoding uses the lowest state and a much higher state of a nonlinear oscillator. That separation means a modeled logical flip has to build up through multiple decay events.
The trade-off is equally important. In the stated single-photon coherence model, phase-flip probability rises linearly with n and is not changed by the engineered dissipation. The proposed scheme therefore does not reduce every error at once; it aims to make bit flips exceptionally rare while accepting a slower, linear growth in phase flips.
A filter designed to favor the desired transitions
To create the needed stabilization, the authors model a frequency-selective filter made from a lossy chain of linear LC resonators. Beam-splitter couplings provide selective decay, while two-mode-squeezing couplings provide selective gain. The reported design says strong spectral selectivity can be obtained with fewer than 10 filter modes under realistic modeled parameters.
That engineered gain and decay is then used around Fock–controlled-X (CX) gates with a cat qubit. The simulation includes intrinsic single-photon transitions during ancilla stabilization and the gates. Under those assumptions, the modeled CX bit-flip probability falls below 10−8 once N reaches at least 10 levels. The N-scaling run used a 200 ns gate, a pulse-error probability of 10−3 and |α|² = 10.
The result depends on stabilization. Without engineered stabilization, the modeled CX bit-flip probability grows linearly, to first order, with both n and the pulse-error probability. That contrast makes engineered dissipation a central assumption of the reported gate result.
From gate errors to a code-level estimate
To connect those gate estimates to error correction, the study simulates a distance-d repetition code. It uses a phenomenological noise model, meaning an abstracted error model, with ancilla and data Z errors inserted at the beginning of each round before the CX gates.
Within that setup, the modeled logical error rate reaches p∗L = 10−6 at code distance d = 9. This is a result of the specified repetition-code simulation, not a measured device result; the study’s computational sample consists of analytical models and numerical simulations.
The paper also maps the modeled operating regime behind that target. For d = 9, it places p∗L = 10−6 near κ1 Tcycle ∼ 10−3 and a lifetime of about 2 ms when Tcycle ∼ 2 μs. At d ∼ 17, it reports the same target with κ1 Tcycle ∼ 4 × 10−3 and a lifetime of about 500 μs.
When a modeled dephasing budget is added, the parameter boundary for a given logical-error rate shifts toward smaller κ1 Tcycle, but not by an order of magnitude. In the paper’s calculation, the effect is moderate rather than a wholesale change to the headline estimate.
A result still confined to the model
The preprint’s status is central to how these numbers should be read. Its headline values are modeled rather than measured, and the evidence is limited to analytical derivations and numerical simulations under stated circuit, noise and code assumptions. No statistical uncertainty or confidence interval is reported.
The proposed 0–n device is aimed at serving as a compact, bias-preserving ancilla for hybrid cat–Fock error correction. On the evidence presented, it is a modeled route to low CX bit-flip and repetition-code error rates, not a demonstrated hardware component.
Paper data and sources
Original title: Dissipatively Stabilized 0-n Fock Qubits for Noise-Biased Quantum Computing
Authors: Su Direkci, Simon Lieu, Kyungjoo Noh, Connor T. Hann
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text