The Calibration Loop as Fixed Point: Ontological Underdetermination of the Qubit by Its Own Metrology

In the paper's words

Every engineered qubit is certified by a closed calibration chain: drive pulses are calibrated by readout, readout is calibrated by states prepared with those drives, and tomography validates the whole loop using measurements calibrated within it. The physical referent of the qubit label — a collective circuit mode, an electronic transition, a spin — is therefore never fixed by any single external measurement. We formalize this chain as a self-consistent fixed-point problem, derive its contraction condition and iteration count explicitly, and exhibit two distinct physical ontologies of the same device — a strict two-level abstraction and a three-level anharmonic carrier with leakage amplitude c — that are observationally identical (total-variation distance exactly zero) under any measurement chain confined to the computational subspace. [...]

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Using the single-shot readout fidelity of $99.991(1)\%$ reported for trapped-ion qubits over $10^6$ trials, we compute the per-shot error scale $9\times10^{-5}$, the calibration iterations needed to reach it, and the shot budget ($N \ge 2500$ at one sigma for $|c|^2 = 0.01$) required to break the degeneracy once a leakage-resolving observable exists.

   from Abstract

2. It demonstrates single-shot qubit readout with fidelity sufficient for fault-tolerant quantum computation, for two types of qubit stored in single trapped calcium ions; for an optical qubit stored in the $(4S_{1/2}, 3D_{5/2})$ levels of $^{40}\mathrm{Ca}^+$ it achieves $99.991(1)\%$ average readout fidelity in one million trials using time-resolved photon counting, and an adaptive measurement technique allows $99.99\%$ fidelity.

   from 2. Background and Related Work

3. Input 1 (from [2]): average readout fidelity $f_{\mathrm{ro}} = 99.991\% = 0.99991$ for the optical qubit in $^{40}\mathrm{Ca}^+$, over $N_{\mathrm{trials}} = 10^6$ trials.

   from 4. Analysis

4. Input 2 (from [2]): the adaptive measurement technique allows fidelity $f_{\mathrm{ad}} = 99.99\% = 0.99999$.

   from 4. Analysis

5. Input 4 (model assumption, Section 3.1): loop gain–sensitivity product $g\,s = 0.5$, giving contraction factor $|1 - g\,s| = 0.5$; initial calibration error $e_0 = 0.1$ in units of the drive parameter.

   from 4. Analysis

6. Input 5 (model assumption, Section 3.2): weak-drive operating point $\Omega/\Delta = 0.1$; tomographic shot budget $N_{\mathrm{tom}} = 10^4$ shots per element.

   from 4. Analysis

How it is done

1. Using the single-shot readout fidelity of $99.991(1)\%$ reported for trapped-ion qubits over $10^6$ trials, we compute the per-shot error scale $9\times10^{-5}$, the calibration iterations needed to reach it, and the shot budget ($N \ge 2500$ at one sigma for $|c|^2 = 0.01$) required to break the degeneracy once a leakage-resolving observable exists.

   from Abstract

2. We do not claim that any real experiment is ontologically confused; we claim that the standard certification pipeline, taken on its own terms, cannot distinguish certain ontologies, and we quantify exactly how indistinguishable they are.

   from 1. Introduction

3. The literature bearing on this question falls into three groups: works that treat self-referential reasoning as a formal method, works on quantum readout, and control-theoretic treatments of systems whose working models are truncations of richer dynamics.

   from 2. Background and Related Work

4. We use this to relate the abstract leakage amplitude to an operating point in Section 4.6.

   from 3.2 Two ontologies, one loop

What would falsify it

1. Using the single-shot readout fidelity of $99.991(1)\%$ reported for trapped-ion qubits over $10^6$ trials, we compute the per-shot error scale $9\times10^{-5}$, the calibration iterations needed to reach it, and the shot budget ($N \ge 2500$ at one sigma for $|c|^2 = 0.01$) required to break the degeneracy once a leakage-resolving observable exists.

   from Abstract

2. Fourth, we identify the structural features — leakage-resolving spectroscopy and cross-platform consistency — that break the circularity, and we state explicitly what would falsify the thesis (Sections 4.5, 6).

   from 1. Introduction

3. Two further corpus entries, "Stabilization of Gottesman-Kitaev-Preskill States" [10] and "A Pre-Registered Falsification of Deterministic Measurement-Triggered Relaxation" [11], are supplied with summaries too thin to support substantive statements; we cite them only as adjacent corpus context and draw no claims from them, noting this as an explicit limitation in Section 6.

   from 2. Background and Related Work

Where the claim stops

1. What the result does and does not show.

   from 6. Discussion

2. It does not show that qubit ontology is unknowable, nor that all ontologies are equivalent.

   from 6. Discussion

3. The adiabatic-elimination step is a second-order approximation valid for $\Omega \ll \Delta$; it neglects counter-rotating terms, pulse-shape effects (a shaped pulse has a different leakage spectrum than a square pulse), and levels beyond $|2\rangle$.

   from 6. Discussion

Where to read

1. Abstract204 words · 1 min
2. 1. Introduction380 words · 2 min
3. 2. Background and Related Work963 words · 4 min
4. 3. Methods808 words · 4 min
5. 4. Analysis683 words · 3 min
6. 5. Results308 words · 1 min
7. 6. Discussion430 words · 2 min
8. 7. Conclusion205 words · 1 min