arxiv: 2605.11073 · v1 · submitted 2026-05-11 · 🪐 quant-ph

Recognition: no theorem link

Quantum Fanout Gates in Constant Depth via Resonance Engineering

Johannes Alexander Jaeger , Elias Zapusek , Florentin Reiter

Authors on Pith no claims yet

Pith reviewed 2026-05-13 03:30 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum fanout gateresonance engineeringJaynes-Cummings interactionconstant-depth circuitsharmonic oscillatorstabilizer measurementpermutation symmetry

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The pith

Resonance engineering with a shared oscillator implements n-qubit fanout gates in constant depth.

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

The paper establishes that Jaynes-Cummings interactions between multiple qubits and one common harmonic oscillator can produce an n-qubit fanout gate whose duration stays fixed even as the number of qubits grows. Theoretical bounds show the resulting infidelity scales only linearly with qubit number, a better trade-off than the quadratic growth expected from breaking the operation into pairwise CNOT gates. Numerical checks up to 100 qubits, made feasible by exploiting permutation symmetry, match these bounds and confirm the scheme works at large sizes. If the approach holds, it directly speeds up stabilizer measurements in quantum error correction and opens polynomial improvements in algorithms that use fanout steps repeatedly.

Core claim

By tuning the qubit-oscillator couplings to selected resonance conditions, the state of one control qubit is copied to all target qubits simultaneously through collective dynamics of the shared bosonic mode. The full operation completes in time independent of n, with an upper bound on total error that grows linearly rather than quadratically with system size.

What carries the argument

Jaynes-Cummings coupling of several qubits to a single harmonic oscillator, with resonance frequencies engineered so that the control qubit's excitation spreads to all targets in one collective step.

If this is right

Stabilizer readouts in surface codes or other error-correcting schemes can be completed in fixed time rather than scaling with code distance.
Quantum algorithms whose depth is dominated by fanout or parity-check layers receive a direct constant-factor speedup.
Large-scale simulations become tractable because permutation symmetry collapses the Hilbert space to a polynomial-sized effective model.
The linear error scaling remains favorable even when the oscillator is treated as a finite-dimensional mode rather than an ideal harmonic oscillator.

Where Pith is reading between the lines

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

The same resonance-engineering pattern could be adapted to implement other collective gates such as multi-controlled operations without increasing depth.
Because the method relies on a single ancillary mode, it may lower the hardware overhead compared with schemes that require many auxiliary qubits.
The polynomial simulation technique suggests that symmetric multi-qubit systems in general could be modeled efficiently even when full exponential simulation is intractable.

Load-bearing premise

The qubits and oscillator can be coupled and detuned precisely enough that the desired resonances dominate without significant unwanted interactions or decoherence.

What would settle it

A measurement showing the observed gate infidelity grows quadratically or faster with qubit number, or that the operation time must increase with n to keep error below a fixed threshold.

Figures

Figures reproduced from arXiv: 2605.11073 by Elias Zapusek, Florentin Reiter, Johannes Alexander Jaeger.

**Figure 2.** Figure 2: FIG. 2. An energy level diagram for the EIT system in [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. An energy level depiction of the steps of the gate [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Gate dynamics for excitation-dependent blocking of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Fidelity of computational basis states with different [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. An input-output mapping of computational basis [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. The gate infidelity as a function of the ratio between [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. The couplings present on a state with [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. The error probability for different computational basis states in the idle subspace, in the case of low and higher [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. The simulated fidelity for up to 100 qubits (a) and a zoomed range up to 30 qubits (b), assuming a ratio Ω [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. The fidelity for fanout gates with various qubit num [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. A comparison of the basis state approximation for [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. A double off-resonant drive to two levels with oppo [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16. (a) The couplings present on the [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗

read the original abstract

We present a novel implementation of an n-qubit fanout gate using resonance engineering. Our proposed mechanism uses Jaynes-Cummings interactions between multiple qubits and a common harmonic oscillator to realize a fanout gate at the system-level. Our theoretical analysis establishes upper bounds on the gate error, demonstrating linear infidelity scaling in constant time -- a favorable trade-off compared to a conventional CNOT decomposition. To validate the performance of our scheme at large system sizes, we exploit permutation symmetry to reduce the simulation complexity from exponential to polynomial in the number of qubits, enabling simulation up to 100 qubits. The results of this numerical analysis are consistent with our theoretical findings and allow us to characterize the performance well. Our gate will enable faster stabilizer readouts and could provide polynomial speedups in many quantum algorithms.

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.

Desk Editor's Note private letter to a colleague

The paper gives a concrete mechanism for constant-time n-qubit fanout by resonance-tuning a shared oscillator to multiple qubits, with analytic linear-error bounds and symmetry-reduced simulations to 100 qubits that match the scaling.

read the letter

The core claim is that Jaynes-Cummings coupling to one common mode, with careful resonance engineering, produces an effective fanout unitary whose infidelity grows only linearly in n while the interaction time stays fixed. That is the main takeaway, and it is distinct from the usual decomposition into sequential CNOTs that costs depth linear in n. If the bounds are tight, it would cut the cost of stabilizer readouts and some multi-qubit primitives without adding extra layers of gates.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes realizing an n-qubit fanout gate in constant depth by engineering resonances in Jaynes-Cummings interactions between the qubits and a shared harmonic oscillator. Theoretical upper bounds are derived showing linear scaling of infidelity with n at fixed interaction time, and these are validated by permutation-symmetric numerical simulations whose complexity is reduced from exponential to polynomial, allowing runs up to 100 qubits whose results are stated to be consistent with the bounds.

Significance. If the bounds and scaling hold under realistic noise, the scheme would replace the O(log n) depth of CNOT decompositions with constant-depth fanout, directly benefiting stabilizer readout circuits and algorithms that rely on collective operations. The explicit use of permutation symmetry to enable large-scale numerics is a concrete methodological strength that supports the large-n claims.

major comments (2)

[Theoretical analysis] Theoretical analysis (section containing the upper-bound derivation): the claim of linear infidelity scaling independent of n rests on the effective unitary obtained after resonance engineering, yet the manuscript does not exhibit the explicit Trotter or Magnus expansion steps that convert the multi-qubit Jaynes-Cummings Hamiltonian into the target fanout operator while bounding the error term; without these steps the linear scaling cannot be verified as load-bearing.
[Numerical simulations] Numerical simulations (section reporting the 100-qubit runs): although permutation symmetry reduces the Hilbert-space dimension, the reported consistency with theory is stated only qualitatively; the manuscript must include the explicit infidelity values versus n, the precise error model (e.g., oscillator damping, qubit dephasing rates), and the fitting procedure used to confirm linear scaling, as these data are required to assess whether the numerics actually corroborate the analytic bound.

minor comments (2)

[Abstract] The abstract states 'linear infidelity scaling in constant time' but does not define the precise figure of merit (e.g., diamond-norm distance or average gate fidelity) nor the reference time unit; this notation should be fixed for clarity.
[Discussion] The manuscript should add a short discussion of how the required resonance tuning avoids unwanted cross-talk or higher-order dispersive shifts that are generic in multi-qubit cavity QED systems.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major point below and will incorporate the requested clarifications in a revised version.

read point-by-point responses

Referee: [Theoretical analysis] Theoretical analysis (section containing the upper-bound derivation): the claim of linear infidelity scaling independent of n rests on the effective unitary obtained after resonance engineering, yet the manuscript does not exhibit the explicit Trotter or Magnus expansion steps that convert the multi-qubit Jaynes-Cummings Hamiltonian into the target fanout operator while bounding the error term; without these steps the linear scaling cannot be verified as load-bearing.

Authors: We agree that the explicit intermediate steps were not presented in sufficient detail. In the revised manuscript we will add the Trotter or Magnus expansion that derives the effective fanout unitary from the multi-qubit Jaynes-Cummings Hamiltonian and show the explicit error-term bound that establishes the linear infidelity scaling with n at fixed interaction time. revision: yes
Referee: [Numerical simulations] Numerical simulations (section reporting the 100-qubit runs): although permutation symmetry reduces the Hilbert-space dimension, the reported consistency with theory is stated only qualitatively; the manuscript must include the explicit infidelity values versus n, the precise error model (e.g., oscillator damping, qubit dephasing rates), and the fitting procedure used to confirm linear scaling, as these data are required to assess whether the numerics actually corroborate the analytic bound.

Authors: We will include in the revision the explicit infidelity values versus n (tabulated or plotted up to 100 qubits), a precise statement of the error model employed (including oscillator damping and qubit dephasing rates), and a description of the fitting procedure used to verify linear scaling. These quantitative details will allow direct comparison with the analytic bound. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper presents a theoretical derivation of upper bounds on gate infidelity from Jaynes-Cummings resonance engineering on a shared oscillator, followed by independent numerical validation via permutation symmetry reduction. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work; the linear scaling claim is stated as an output of the interaction Hamiltonian analysis rather than an input. The scheme is benchmarked against conventional CNOT decompositions without circular redefinition of the target unitary.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides insufficient detail to enumerate free parameters or invented entities; the approach rests on standard Jaynes-Cummings physics.

axioms (1)

domain assumption Jaynes-Cummings interactions accurately model the qubit-oscillator coupling in the relevant regime
The scheme is built directly on this standard quantum-optics model.

pith-pipeline@v0.9.0 · 5426 in / 1228 out tokens · 97310 ms · 2026-05-13T03:30:20.269988+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

48 extracted references · 48 canonical work pages

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Excite the harmonic oscillator conditioned on the control qubit using a Jaynes-Cummings π-pulse: H1 = Ωca†|e⟩⟨0|1 + H.c. (11)

work page
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Apply conditional phase to target qubits using a 2π pulse carrier drive Ωt, while applying a strong anti- Jaynes-Cummings drive Ω c to block the transition 4 on the one phonon manifold: H2 = nX i=2 Ωca|f ⟩⟨e|i + Ωt|e⟩⟨1| + H.c. (12)

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(13) The steps of the control sequence are shown on an en- ergy level diagram in Fig

Restore the control qubit state and de-excite the harmonic oscillator using a Jaynes-Cummings π- pulse: H3 = Ωca†|e⟩⟨0|1 + H.c. (13) The steps of the control sequence are shown on an en- ergy level diagram in Fig. 3. Here it is easier to see how the drives operate on the different subspaces. In the first step (depicted in panel (a)), the harmonic oscillat...

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3, and therefore the harmonic os- cillator remains in the ground state

Transition Subspace |1⟩c The transition subspace is not excited by the π pulse in the first step of Fig. 3, and therefore the harmonic os- cillator remains in the ground state. In the second step, we apply a carrier drive |1⟩ to |e⟩ and an anti-Jaynes- Cummings drive |e⟩ to |f ⟩ to the target qubits. Since the anti-Jaynes-Cummings drive needs to annihilat...

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On the excited manifold, a state with m target qubits in the |1⟩ state couples to m excited states, the states with one target qubit in the |e⟩ state

Idle Subspace |0⟩c If the control qubit is in the |0⟩c state, the first step will excite the harmonic oscillator to the first fock state. On the excited manifold, a state with m target qubits in the |1⟩ state couples to m excited states, the states with one target qubit in the |e⟩ state. Each of these states is coupled further via the red sideband to a st...

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Fidelity Using the evolutions on the two subspaces, we can eval- uate the fidelity using the approximate formula given in Eq. (15). We then find a infidelity of 1 − F = 1 2n X b 1 − | ⟨b| U †e−iHt |b⟩ |2 (20) ≤ 1 2n X m n − 1 m 4mΩ2 t Ω2c + mΩ2 t (21) ≤ 1 2n Ω2 t Ω2c X m 4m n − 1 m . (22) This sum can be evaluated to 1 2n nX m=0 n m m = n 2 , (23) for all...

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Timing Condition The infidelity of the different computational basis states in the idle subspace is shown in Fig. 5. We notice that in the limit Ω 2 c ≫ mΩ2 t , the off-resonant excitations all have approximately the same frequency. It is there- fore possible to time the gate in such a way, that the off-resonant excitation disappears. 0 1 2 3 4 5 Time (a....

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