Scalable high-fidelity and near-deterministic preparation of large photon-number states

Chuanzhen Cao; Jinbin Li; Jize Han; Ming Xue; Mo Xiong; Zhiguo Huang

REVIEW 4 major objections 4 minor 82 references

Scalable high-fidelity and near-deterministic preparation of large photon-number states

T0 review · 4 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A sequence of alternating Jaynes–Cummings pulses and displacements can prepare Fock states with N up to about 200 at post-selected fidelity above 0.95 and success probability above 0.90, using shallow control circuits.

desk verdict Plausible and useful numerical protocol for Fock-state preparation, but the headline fidelities rest on a single optimizer run and the dissipation claim is extrapolated, so the scaling needs independent verification. read the letter →

arxiv 2601.10559 v3 pith:IA3IATVF submitted 2026-01-15 quant-ph

Mo Xiong , Jize Han , Chuanzhen Cao , Jinbin Li , Zhiguo Huang , Ming Xue This is my paper · ORCID

classification quant-ph

keywords Fockstateslargephoton-numberJaynes–Cummingsmodelcoherent-stateinterferencequantumcontrolcavityQEDvariationalpulseoptimizationnear-deterministicstatepreparation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that large photon-number (Fock) states can be prepared almost deterministically by interleaving resonant Jaynes–Cummings evolutions with phase-space displacements. The nonlinear photon-number-dependent phases accumulated during the spin–oscillator interaction are converted, by the displacements, into constructive interference that funnels a coherent seed state into a sharp photon-number peak. With optional final qubit projection, post-selected fidelities stay at or above 0.95 up to N=160 and only slightly below at N=180 and 200, with success probability above 0.90. The optimized sequences remain shallow, at most ten layers, and are shown to tolerate detuning, control noise, and dissipation at levels relevant for current platforms. If these numerical results hold, the protocol offers a concrete route to non-Gaussian states that previously required more resource-intensive or probabilistic methods.

What carries the argument

The central object is the composite pulse: one resonant Jaynes–Cummings evolution segment U(τ_k)=exp(−iHτ_k), governed by H=−Δa†a + Ω(aσ_+ + a†σ_−), followed by a phase-space displacement D(β_k). Repeating these layers p times, with the total time structured by the revival index ℓ through Ω T_R^(ℓ)≈(2ℓ+1)π/√N, imprints photon-number-dependent phases and converts them, via displacement-induced mixing, into constructive interference in Fock space. An optional final qubit projection removes residual qubit–field correlations and enhances the cavity-state purity.

What would settle it

Reoptimize the pulse sequences for N=160, 180, and 200 from many independent, non-transfer random initializations, or with a substantially larger optimization budget, and compare the best and median fidelities with the paper's reported values; if the best fidelity drops below 0.95 or scatters widely across seeds, the claimed scaling is not robust. Conversely, an experiment on a cavity-QED or circuit-QED platform that implements the optimized sequence and reconstructs the Wigner function or photon-number distribution at N≈100 should show a dominant peak at n=N with fidelity near the reported le

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a control sequence built from native spin–oscillator operations—alternating JC interaction segments U(τ_k) with displacement pulses D(β_k), starting from an excited qubit and a coherent field with mean photon number |α|²=N—can reshape that coherent state into a Fock state at large N. The optimized multi-pulse sequences (p≤10) achieve post-selected fidelity F≥0.95 for all targets up to N=160, with F only slightly below 0.95 at N=180 and 200, and success probability P_succ≳0.90 for the final qubit projection. The dynamics work by imprinting number-dependent phases through the nonlinear JC spectrum and then using displacements to convert t

Load-bearing premise

The result rests on the numerical assumption that the hybrid genetic-Adam search, run under a fixed optimization budget in a quasi-periodic loss landscape full of local minima, finds near-global optima; if it gets trapped, the reported 'only weak degradation with N' may not reflect the protocol's true capability.

Editorial extensions

If this is right

If correct, the protocol removes the need for Kerr-type nonlinearities or measurement-based filtering when generating large Fock states: only linear displacements and the intrinsic Jaynes–Cummings interaction are required.
Because the total evolution time is set by ΩT≈(2ℓ+1)π/√N, the time cost grows only polynomially with N rather than linearly in the number of added photons, and the pulse count p grows slowly, staying at most ten over the explored range.
Post-selected preparation remains near-deterministic, with success probability above 0.90, so the final qubit measurement does not reintroduce the exponential overhead typical of heralded Fock-state sources.
The demonstrated robustness to sub-percent timing and displacement errors, as well as to detuning, suggests the sequences are compatible with existing cavity-QED, circuit-QED, and trapped-ion platforms without demanding error correction.
The same interference-engineering language is intended to extend to other non-Gaussian states, such as photon-number superpositions and grid-like states, as the paper states in its outlook.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the reported scaling trend may be influenced by the fixed optimization budget on a rugged quasi-periodic landscape; a natural check is to compare transfer-initialized searches with many random restarts at N≈200 under a much larger budget. If random restarts match the transfer-seeded results, the fidelity trend is a property of the protocol; if not, it is partly an optimizer pr
Editorial inference: the saturation of detuning tolerance with total evolution time, rather than with pulse segmentation, implies that increasing the coupling strength (for example through collective coupling of many emitters) should simultaneously shorten the sequence and widen the usable detuning window. The paper's dissipation estimate leans on collective enhancement, but the detuning-side bene
Editorial inference: because each JC segment redistributes population only locally while displacements perform the long-range envelope reshaping, one could combine this protocol with a weak continuous measurement or a second photon-number post-selection to trade a small success probability for additional fidelity gain; the paper does not discuss such hybrid strategies.
Editorial inference: the phase-texture alignment near n+m≈2N suggests that stopping one step earlier or changing the final displacement and projection should produce Fock-state superpositions rather than only pure Fock states. The paper mentions superpositions in outlook but does not quantify the achievable fidelity for them.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read the paper. The idea is simple and physically sensible: instead of one long JC interaction at revival time, use many short JC pulses interleaved with displacements. That gives you much more interference control, and the numbers are surprisingly good — post-selected fidelities above 0.95 out to N = 160, with success probability > 0.9. If that trend is real, it is a practical advance for Fock-state generation in cavity QED and trapped ions. The paper is also honest: it shows the loss landscape is rugged, describes the optimizer in detail, and discloses the overlapping Kerr-based preprint in a note added.

The main problem is that the scaling trend is produced by one optimizer run. The paper says the landscape is quasi-periodic and full of local minima; every point in Fig. 2(a) comes from a single GAdam run with transfer initialization. There is no multi-seed statistics, no released code, no parameter sets, and no convergence diagnostics. The authors say the results are conservative because of a fixed budget, but a fixed budget only makes results conservative if you are already near the global minimum — which is exactly what is not shown. This is a load-bearing reproducibility issue, not a style issue.

Two smaller overstatements. The abstract says F ≥ 0.95 for photon numbers in the few-hundred regime, but the plot shows that at N = 180, 200 the fidelity dips slightly below 0.95. And the abstract says the protocol already achieves high fidelity unconditionally, but no unconditional numbers are shown — all the quantitative results are post-selected. The dissipation robustness is also extrapolated from a cooperativity benchmark rather than simulated; the detuning and pulse-error plots are real simulations, but the master equation is never integrated for the optimized sequences.

None of this kills the paper. The physics is standard, the optimization strategy is thoughtful, and the protocol itself is a legitimate extension of Ref. [38] with different ingredients than the Kerr-based approach. For a reader working on bosonic state preparation, the paper is worth knowing about. I would send it to peer review, but a competent referee should ask for multi-seed optimization runs (or at least convergence diagnostics), a plot of unconditional fidelity, and a master-equation simulation at one representative N with realistic rates. With those additions, the central claim would be much more convincing.

Referee Report

4 major / 4 minor

Summary. The paper proposes a control protocol for preparing large photon-number (Fock) states by alternating Jaynes–Cummings (JC) evolutions with phase-space displacements, starting from a coherent state with mean photon number N and optionally post-selecting on a final qubit measurement. The control parameters (pulse durations, displacements, and projection angles) are optimized with a hybrid genetic–Adam routine. The central numerical claim is that post-selected fidelities F ≥ 0.95 are achieved for all targets up to N = 160, remain slightly below 0.95 at N = 180 and 200, and the post-selection success probability is ≳0.90. Robustness to detuning, pulse errors, and dissipation is also discussed. Appendices derive the revival-time condition, document the rugged loss landscape, and describe the GAdam optimizer.

Significance. If the numerical results are reproducible and correctly interpreted, the protocol would be a meaningful step toward preparing few-hundred-photon Fock states with shallow circuits using native spin–oscillator operations. The revival-time insight and the explicit treatment of the non-convex landscape in Appendix B are useful, and the noise-averaged robustness study in Fig. 3(b) is a positive feature. However, the central scaling claim is entirely a product of a single non-convex optimization pipeline; no optimized parameter sets, no code, no multi-seed statistics, and no convergence diagnostics are provided. The paper also overstates the achieved N-range and the unconditional-fidelity claim. These issues are fixable but are load-bearing for the paper's main conclusion.

major comments (4)

[Abstract and Sec. II B (Fig. 2)] The abstract states that the protocol 'already achieves high preparation fidelity unconditionally' and that 'fidelities exceeding 0.95 is achieved for photon numbers in the few-hundred regime.' Both claims are stronger than what Sec. II B and Fig. 2(a) actually show. The reported F values are post-selected fidelities, and they satisfy F ≥ 0.95 only up to N = 160, with N = 180 and 200 'slightly below 0.95.' No unconditional (pre-projection) fidelity data are presented anywhere. Please revise the abstract to match the quantitative results and either add unconditional-fidelity data or explicitly frame the abstract claims as post-selected.
[Eq. (6) and Fig. 2(a)] The optimization minimizes the joint-state loss L = 1 − |⟨Ψ(τ,β)|Ψ_N(φ)⟩|², but the reported figure of merit is the reduced-state fidelity F in Eq. (5). These are not the same quantity: the joint overlap equals P_succ × F_cond only after conditioning on the qubit projection, so minimizing L can trade off success probability against conditional fidelity. The paper does not explain how the reported F values are computed from the optimized parameters or how the proxy relates to the reported F. Since the central quantitative claim is the fidelity, this connection must be made explicit and correct.
[Appendices B and C] The scalability trend in Fig. 2(a) rests entirely on the GAdam optimizer finding sufficiently good local minima. Appendix B explicitly shows a dense, quasi-periodic landscape with many competing minima (Fig. 5), and Appendix C states that results are obtained 'under a fixed optimization budget.' The claim that this makes the result 'conservative' is only valid if the search is close to the global minimum, which is not demonstrated. No multi-seed statistics, independent restart checks, convergence diagnostics, or released parameter sets are provided. Without such verification, a reader cannot distinguish a genuine scaling property of the protocol from a favorable single optimization trajectory. Please add multi-start/independent-verification data and release the optimized parameters or code.
[Sec. II C, Dissipation effects] The dissipation robustness conclusion is extrapolated from a cooperativity benchmark rather than from master-equation simulations. The paper introduces a Lindblad equation with κ and Γ, but no open-system simulation results are shown. The estimate F ≳ 0.8 for N = 100 is obtained by combining a unitary-optimized value with a collective cooperativity product N_atom C, which is not a substitute for solving the dissipative dynamics with the actual optimized pulse sequence. Moreover, the collective enhancement Ω_eff = Ω√N_atom is used in a context where multi-photon JC dynamics may not reduce to the single-excitation collective manifold. Please present actual master-equation results for at least one representative N and state the parameter assumptions explicitly.

minor comments (4)

[Sec. II B] Typo: 'Fig. 2 benchmarks the our protocol' should read 'benchmarks our protocol.'
[Sec. II C] Text contains 'and and' in the dissipation paragraph: 'Using an experimentally motivated collective cooperativity benchmark N_atom C ∼ 10^8 and and taking...' Please fix.
[Appendix A, Eq. (A4)] The definition of c_m is given with α^n in the text, but the index should be m (and n for c_n). The notation s_m' and the m≈n≈|α|² statement would be clearer if the approximation used for s_m were written out explicitly.
[Fig. 2(a)] The marker legend for the 'optimized multi-pulse protocol (p≤10)' is not self-explanatory; please indicate which point type corresponds to which N and define the staircase ℓ axis in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: reported fidelities are direct numerical optimization results, and no load-bearing self-citation or definitional reduction occurs.

full rationale

The paper's central quantitative claims are obtained by explicitly optimizing the control parameters θ={τ,β,φ} with respect to the loss Lθ = 1 − |⟨Ψ(τ,β)|Ψ_N(φ)⟩|² (Eq. 6) and then evaluating the resulting post-selected fidelity and success probability (Sec. II B, Appendix C). This is a numerical existence argument, not a prediction from a fitted model: the high-fidelity parameters are not built into the ansatz a priori, the p=1 baseline provides a nontrivial comparison, and the paper discloses the non-convex landscape and fixed optimization budget (Appendix B, Fig. 5; Sec. II B). No parameter is fitted to external data and then 'predicted' on the same data; no load-bearing result is justified exclusively by a self-citation; no uniqueness theorem or ansatz is imported from the authors' prior work. The acknowledged risk that GAdam may settle into local minima is a correctness/reproducibility concern about whether the optimizer found near-global minima, not a circularity, because the reported fidelities are the optimized values themselves rather than quantities defined in terms of those values. Therefore no circular step is identified.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its quantitative claims rest on a standard JC-plus-displacement model and on numerically optimized control parameters; the scaling trend is an interpolation of optimizer results. The dissipative estimate imports a cooperativity value from the literature.

free parameters (3)

Pulse/detection parameter set θ = {τ_k, β_k, φ} (3p+2 numbers, p ≤ 10) = not listed; optimized per N,p,ℓ
These parameters are directly optimized to maximize the fidelity proxy (Eq. 6), so all reported fidelities are fitted values.
Circuit depth p(N) and revival index ℓ(N) = chosen per target N (colored markers and grey staircase in Fig. 2(a))
The optimal depth and global timing index are selected per N from the optimization results, adding freedom to the scaling curve.
GAdam hyperparameters (generations G, elite size E, mutation rate, tolerance ε_T) = not specified
Not given in the paper; the fidelity results depend on the optimization budget and are described as conservative due to fixed budget.

assumptions (6)

domain assumption The Jaynes–Cummings Hamiltonian (Eq. 1) describes the spin–oscillator system on resonance (Δ = 0)
Standard model for cavity/circuit QED and trapped ions; the protocol's phase engineering relies on the nonlinear √(n+1) ladder spectrum.
domain assumption The oscillator can be initialized in a coherent state |α⟩ with mean photon number |α|² = N, and the qubit in |e⟩
Seed state and initial qubit state define the protocol; displacements and projections are assumed ideal.
standard math The revival-time relation ΩT_R^(ℓ) ≈ (2ℓ+1)π/√N provides a valid global timing scale
Follows from JC collapse–revival analysis (Refs. 61,62) and is used to set the total evolution time for all depths.
domain assumption For large N the two semiclassical qubit branches evolve independently (Eq. B3)
Needed for the qubit near-purity and the concentration of optimal projection angles near the equator; cited to Gea-Banacloche (Refs. 61,80).
ad hoc to paper Transfer-initialized GAdam optimization reaches sufficiently good local minima for every N
The reported fidelities are outputs of this numerical procedure; the paper provides no guarantee of global optimality and notes the landscape is densely multi-extremal (Fig. 5).
domain assumption Dissipative feasibility can be estimated from a collective cooperativity benchmark N_atom C ~ 10^8
Used in Sec. II C to convert unitary fidelity F ≈ 0.97 into F ≳ 0.8 under photon loss and atomic decay; this is an extrapolation from literature values (Refs. 65-68), not a simulation.

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Pith. "Pith review of Scalable high-fidelity and near-deterministic preparation of large photon-number states." pith.science (2026). https://pith.science/paper/IA3IATVF

@misc{pith2026260110559,
  author       = {Pith},
  title        = {Pith review of: Scalable high-fidelity and near-deterministic preparation of large photon-number states},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IA3IATVF}},
  note         = {Machine review of arXiv:2601.10559}
}

abstract

The scalable preparation of large photon-number (Fock) states is a long-standing frontier in quantum science, with direct implications for quantum metrology and bosonic quantum information processing. Despite substantial progress at small photon numbers, extending state generation to large photon numbers while maintaining high fidelity and operating deterministically remains a significant challenge. Here we demonstrate a scalable and experimentally accessible control protocol for generating large photon-number states using only native spin--oscillator operations. The protocol alternates Jaynes--Cummings interactions with phase-space displacements to imprint photon-number--dependent phases and convert them into selective interference in photon-number space. It already achieves high preparation fidelity unconditionally, while an optional final qubit projection removes residual qubit--field correlations and further enhances the fidelity. Conditioned on this final projection, photon-number state preparation with fidelities exceeding $0.95$ is achieved for photon numbers in the few-hundred regime, with a success probability exceeding $0.90$, placing the protocol in a near-deterministic operating regime. The resulting control sequences remain shallow and are robust against detuning, control noise, and experimentally relevant dissipation. Our results establish a practical route to scalable, high-fidelity photon-number state preparation at large photon numbers and provide a versatile interference-engineering toolbox for nonclassical bosonic state synthesis.

Figures

Figures reproduced from arXiv: 2601.10559 by the authors.

**Figure 1.** Multi-pulse JC–displacement protocol for Fock-state generation.The control sequence consists of p layers, each comprising a resonant JC evolution U(τk) acting on the joint qubit–oscillator system, followed by a phase-space displacement D(βk) applied to the bosonic mode. The qubit is initialized in the excited state and the oscillator in a coherent state. Repeated accumulation of photonnumber–dependent phases arisi… view at source ↗

**Figure 2.** Multi-pulse JC–displacement protocol for large-N photon-number state generation. (a) Target-Fock fidelity F as a function of photon-number N for p = 1, p = 2, and the optimized multi-pulse protocol (p ≤ 10). Colored markers indicate the optimal pulse number p(N) for each N. The grey staircase in the background shows the corresponding optimal interaction index ℓ. (b) Post-selection success probability Psucc for the o… view at source ↗

**Figure 3.** Robustness of the multi-pulse protocol against detuning, control noise. (a) Detuning tolerance quantified by the full width at half maximum (FWHM) of F¯(∆/Ω) as a function of the protocol time scale ΩT (ℓ) R for different ℓ-families. Marker shapes denote the circuit depth p and colors indicate the target photon-number N. Inset: representative linecuts of F(∆/Ω) at p = 10. (b) Average post-selected fidelity F¯ under … view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: At discrete revival times (labeled by ℓ), the bosonic state refocuses in phase space and becomes Fock-like under the resonant Jaynes–Cummings Hamiltonian. cavity state transforms into: |Ψ(β, t)⟩ = Dˆ(β)e −iHt ˆ |Ψ0⟩ = X∞ n=0 |Kn(t)⟩ ⊗ |n⟩,(A1) where |Km(t)⟩ represents …

**Figure 6.** Figure 6: Distribution of optimal qubit projection angles. Opti [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

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