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arxiv: 2503.10436 · v2 · submitted 2025-03-13 · 🪐 quant-ph

Direct estimation of arbitrary observables of an oscillator

Tanjung Krisnanda , Fernando Valadares , Kyle Timothy Ng Chu , Pengtao Song , Adrian Copetudo , Clara Yun Fontaine , Lukas Lachman , Radim Filip
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Yvonne Y. Gao
This is my paper

Pith reviewed 2026-05-22 23:48 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum harmonic oscillatorobservable estimationbosonic cQEDnumerical optimizationancillary qubitphase-space quadraturesnon-Gaussianitycontinuous-variable quantum information
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The pith

A numerically optimized protocol maps the expectation value of any oscillator observable to an ancillary qubit.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces OREO, a protocol that uses numerical optimization to design a mapping from the expectation value of arbitrary observables on a quantum harmonic oscillator to the measurement outcome on a coupled qubit. Standard techniques either limit the accessible observables to a few analytical cases or require full tomography of the oscillator state. The method is shown to work for phase-space quadratures and their higher moments, for direct computation of non-Gaussianity ranks, and for preparing states without reference to the oscillator's initial condition. These capabilities are demonstrated in a bosonic circuit quantum electrodynamics platform. A reader would care because the approach replaces resource-heavy procedures with a single optimized routine for extracting information from continuous-variable systems.

Core claim

OREO is a numerically optimized protocol that maps the expectation value of arbitrary oscillator observables onto that of an ancillary qubit. In a bosonic cQED experiment it directly yields phase-space quadratures and higher moments, non-Gaussianity ranks, and state preparation that does not depend on the oscillator's starting state.

What carries the argument

OREO, the numerically optimized routine that finds control sequences mapping any chosen oscillator observable to an ancillary-qubit expectation value.

If this is right

  • Phase-space quadratures and their higher moments become directly measurable without predefined analytical sequences.
  • Non-Gaussianity ranks can be obtained without full state reconstruction.
  • State preparation routines can be made independent of the oscillator's initial condition.
  • Information extraction from bosonic states becomes more efficient, supporting measurement, control, and preparation tasks in continuous-variable systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same optimization strategy might lower overhead when checking stabilizer conditions in bosonic error-correcting codes.
  • If the mapping remains stable across different hardware noise profiles, OREO could support feedback loops for real-time oscillator control.
  • The approach could be tested on other oscillator platforms such as trapped-ion motional modes to check transferability.

Load-bearing premise

The numerical optimization produces a mapping that remains accurate under the noise and control limitations of the bosonic cQED hardware.

What would settle it

Apply OREO to a coherent state whose position quadrature is known analytically; a statistically significant mismatch between the OREO result and the known value would falsify the claim.

Figures

Figures reproduced from arXiv: 2503.10436 by Adrian Copetudo, Clara Yun Fontaine, Fernando Valadares, Kyle Timothy Ng Chu, Lukas Lachman, Pengtao Song, Radim Filip, Tanjung Krisnanda, Yvonne Y. Gao.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: b are considerably above the theoretically calcu￾lated threshold F3(λ) (lower boundary of the blue shaded region), indicating that the state has non-Gaussianity rank of 3. These results, obtained via a single measure￾ment for each value of λ, are consistent with the val￾ues extracted from the reconstruction of the full density matrix after Wigner tomography (dotted line), which is significantly more costly… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: , we observe significant deviations from the lossless case with typical coherence times in our devices, that is, Percengate Deviation (%) 0 8 16 -1.0 -0.5 0.0 0.5 1.0 0 9 18 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effect of potential differences between the estimated [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Real components of the reconstructed density matrix [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Reconstructed Wigner functions of the final cavity [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

Quantum harmonic oscillators serve as fundamental building blocks for quantum information processing, particularly in the context of the bosonic circuit quantum electrodynamics (cQED) platform. Conventional methods for extracting oscillator properties rely on predefined analytical gate sequences to access a restricted set of observables or resource-intensive tomography processes. Here, we introduce the Optimized Routine for Estimation of any Observable (OREO), a numerically optimized protocol that maps the expectation value of arbitrary oscillator observables onto that of an ancillary qubit. We demonstrate OREO in a bosonic cQED system as a means to efficiently measure phase-space quadratures and their higher moments, directly obtain faithful non-Gaussianity ranks, and effectively achieve state preparation independent of initial conditions in the oscillator. These results position OREO as a valuable tool for direct and efficient information extraction from bosonic quantum states, unlocking new possibilities for measurement, control, and state preparation in continuous-variable quantum information processing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces the Optimized Routine for Estimation of any Observable (OREO), a numerically optimized protocol that maps the expectation value of arbitrary oscillator observables onto that of an ancillary qubit. It claims demonstrations in a bosonic cQED system for efficient measurement of phase-space quadratures and higher moments, direct non-Gaussianity ranks, and state preparation independent of initial conditions.

Significance. If validated, OREO would offer a general, numerically optimized alternative to analytical gates or full tomography for bosonic systems, enabling more flexible extraction of information from continuous-variable states and potentially simplifying control and measurement tasks in cQED platforms.

major comments (1)
  1. Abstract: The central claim that the numerically optimized protocol produces a faithful mapping is presented without any quantitative validation details, error analysis, comparison baselines, or description of whether the optimization cost function incorporates hardware noise (e.g., photon loss, dephasing, or pulse distortion). This leaves the experimental fidelity as an untested extrapolation, directly bearing on whether the mapping remains accurate under realistic conditions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback. We address the major comment below and agree that the abstract requires enhancement for clarity on validation.

read point-by-point responses

  1. Referee: Abstract: The central claim that the numerically optimized protocol produces a faithful mapping is presented without any quantitative validation details, error analysis, comparison baselines, or description of whether the optimization cost function incorporates hardware noise (e.g., photon loss, dephasing, or pulse distortion). This leaves the experimental fidelity as an untested extrapolation, directly bearing on whether the mapping remains accurate under realistic conditions.

    Authors: We agree the abstract lacks these details. The full manuscript presents experimental results with measured fidelities, error bars, and comparisons to analytical methods and tomography in the Results and Discussion sections. The numerical optimization used an ideal cost function without hardware noise models (e.g., no explicit photon loss or dephasing terms), though experiments were performed on real hardware subject to those effects. We will revise the abstract to include key quantitative validation metrics, error analysis summary, and a note on the ideal optimization. revision: yes

Circularity Check

0 steps flagged

No significant circularity; OREO is an independent numerical construction

full rationale

The paper presents OREO as a numerically optimized protocol that constructs a mapping from oscillator observables to an ancilla qubit expectation value. No load-bearing steps reduce by definition or self-citation to the target quantities; the optimization is framed as a forward construction, followed by experimental demonstration. The central claim does not rely on renaming fitted parameters as predictions or importing uniqueness from prior self-work. This is a standard case of a self-contained numerical method with external validation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review limits visibility into specific parameters or axioms; standard quantum mechanics assumptions are implicit but not detailed.

pith-pipeline@v0.9.0 · 5711 in / 902 out tokens · 18873 ms · 2026-05-22T23:48:53.020170+00:00 · methodology

discussion (0)

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Reference graph

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