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REVIEW 3 major objections 3 minor 86 references

The paper claims that trigonometric continuous-variable gates—unitaries generated by the cosine of an oscillator's position—can be implemented and benchmarked on a trapped-ion platform, with measured Fock-space transition probabilities matc

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2026-08-02 02:47 UTC pith:A2HXYWDT

load-bearing objection First trig-CV cosine gate demo has solid one-qumode results; two-qumode entangling claim is not supported by marginal-only data, but the paper merits review. the 3 major comments →

arxiv 2607.14085 v1 pith:A2HXYWDT submitted 2026-07-15 quant-ph physics.atom-ph

Benchmarking trigonometric continuous-variable gate primitives with trapped ions

Tommaso Rainaldi , Jake Montgomery , Christopher G. Yale , Brian K. McFarland , Melissa C. Revelle , Daniel Lobser , Edward C. Tortorici , Susan Clark
show 3 more authors
George Siopsis Matt Grau Felix Ringer
This is my paper
classification quant-ph physics.atom-ph MSC 81P6881P4581V80 PACS 03.67.Lx
keywords continuous-variable quantum computingtrigonometric gatescosine gatesqumodestrapped ionsFock-state tomographyTrotterizationWigner negativity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that cosine gates—quantum operations whose generator is the cosine of an oscillator's position—are not just theoretical constructs but reusable, characterizable primitives on trapped-ion hardware. It implements the single-mode gate e^{-iθ cos(c x̂)} and a two-mode version on collective motional modes of ion chains, using Trotterized circuits of conditional displacements and qubit rotations. The benchmark is gate-level: the authors reconstruct Fock-state transition probabilities from blue-sideband readout and show they agree with open-system simulations that include residual thermal phonons and motional dephasing, across gate parameters and Trotter depth. If right, bosonic simulations of periodic potentials, rotor models, compact gauge fields, and anharmonic dynamics could call these gates directly rather than approximating them with polynomials.

Core claim

The central discovery is that the ideal cosine gate has an exact decomposition as a Bessel-weighted superposition of displacements, which yields analytic Fock-basis matrix elements, Wigner functions, and characteristic functions; the same structure carries over to the two-mode gate e^{-iθ cos(c1 x̂1 + c2 x̂2)}. The experimental implementation approximates these unitaries with finite-step Trotter circuits, and postselecting on the ancilla qubit being unflipped removes the parity-violating error component. Measured, postselected Fock transition probabilities for one-qumode gates with c = 1, 2, 3 and Trotter steps 1, 2, 4, 8, and for two-qumode marginal distributions, match simulations based on

What carries the argument

The load-bearing object is the Jacobi-Anger expansion, e^{-iθ cos(c x̂)} = Σ_{k∈Z} (-i)^k J_k(θ) e^{i c k x̂}, which turns the cosine gate into a superposition of phase-space displacements with Bessel-function weights. This identity supplies the exact Fock matrix elements, Wigner and characteristic functions, and the negativity (mana) analysis. On the hardware side, the workhorse is a first-order Trotter circuit of conditional displacements and qubit rotations; its decomposition into a parity-preserving 'good' part and a parity-violating 'bad' part makes postselection meaningful. In the two-mode case the same circuit acts on both modes through the same ancilla, and total-parity conservation

Load-bearing premise

The two-qumode gate claim rests on mode-by-mode marginal Fock measurements, which cannot by themselves distinguish a genuinely entangling two-mode cosine gate from two single-mode cosine gates run in parallel with only classical correlations.

What would settle it

Measure the joint, rather than marginal, two-mode Fock distribution (or any intermode correlation witness) after the two-qumode circuit: if the joint distribution factorizes into the product of the measured marginals, or shows no signature of the predicted total-parity correlations, the two-qumode cosine-gate claim fails. A second, model-level check: pre-calibrate the dephasing rate and thermal occupation from independent measurements, then see whether the simulated transition probabilities match the data without fitting them to that same data.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Cosine gates become first-class building blocks for hybrid qubit-qumode simulation, so periodic-potential models (rotor, sine-Gordon, compact gauge, vibronic) can be compiled directly to hardware-native operations rather than high-order polynomial decompositions.
  • The postselection structure gives a built-in error-mitigation handle: discarding ancilla flips removes the leading Trotter error, and measured distributions converge toward the ideal gate as the step count grows.
  • The analytic matrix elements and phase-space formulas provide a transferable benchmark for other bosonic platforms to validate their own cosine-gate implementations against the same ideal expressions.
  • The derived mana growth bound—roughly logarithmic negativity scaling as ½ ln θ at large θ for single-mode cosine evolution—locates the non-Gaussian resource ceiling of these gates, useful for resource estimation in algorithms that need Wigner negativity.

Where Pith is reading between the lines

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

  • The two-qumode demonstration is not yet decisive on its own terms: because only marginal Fock distributions are measured, a product of two independent single-mode cosine gates with classical correlations could mimic the data; a joint or correlation-sensitive readout would settle it.
  • Because the Trotter circuits realize the cosine of a linear combination of quadratures as a primitive, composing several such gates with different c and θ could synthesize arbitrary Fourier-like periodic potentials—a natural extension testable on the same hardware.
  • A sharper test of the dephasing-plus-thermal error model would be to fit its parameters on one circuit and then predict the other circuits' transition probabilities without refitting; the paper instead fits the model to each dataset it explains.
  • The parity-conservation logic suggests a resource-saving variant: rather than discarding failed postselection runs, the unflipped and flipped components could in principle be treated as separate computational branches, though this would require taming the parity-violating 'bad' component.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The manuscript reports a combined theory-experiment study of trigonometric continuous-variable gates on a trapped-ion platform. The theoretical part derives Fock-space matrix elements, Wigner and characteristic functions, and mana bounds for the unitaries exp(-iθ cos(c x̂)) and exp(-iθ cos(c1 x̂1 + c2 x̂2)), together with a first-order Trotter circuit decomposition using conditional displacements and an ancilla qubit. The experimental part implements these circuits on QSCOUT with 171Yb+ ion chains, reconstructs Fock-state populations via blue-sideband readout and postselection, and compares the data with Lindblad simulations including thermal initial states and motional dephasing. The paper claims the first gate-level characterization of these non-polynomial trigonometric primitives, with a full one-qumode benchmark and a mode-resolved marginal benchmark for the two-qumode gate.

Significance. The analytical formulas in Sec. IV are a useful and self-contained contribution, and the one-qumode experimental data across c ∈ {1,2,3} and Trotter depths i ∈ {1,2,4,8} are credible and thoughtfully analyzed. The paper is also transparent about several limitations, notably in Sec. VII where it concedes the absence of direct intermode-correlation readout. However, the central two-qumode claim is not established by the presented marginals, and the error-model validation is weakened by an in-sample two-stage fit. These are load-bearing issues for the paper's headline claims. With the two-qumode claims appropriately softened and the error model subjected to a genuine predictive test, the manuscript would be a valuable contribution.

major comments (3)
  1. [Sec. VI C, Eq. (64); Sec. VII] The evidence for the two-qumode gate is restricted to mode-resolved marginals, Eq. (64), which cannot distinguish exp(-iθ cos(c1 x1 + c2 x2)) from a classically correlated mixture of independent single-mode cosine gates: any separable state with the same marginals reproduces P_{n1}, P_{n2}. The 'odd-Fock enhancement' (Sec. VI C) is also present in product states with odd support per mode and is therefore not a two-mode witness. Since Sec. VII concedes that direct intermode correlation readout is unavailable, the conclusion that 'genuinely two-mode dynamics' was observed overstates the evidence. The two-qumode claim should be limited to a marginal benchmark, or a joint-correlation witness should be provided.
  2. [Sec. VI B, Eqs. (54),(65)] The central agreement plots validate the error model with parameters γ, n̄, Γ, ηΩ that were fit to the same data. Eq. (54) extracts Pdata from BSB traces; Eq. (65) then minimizes the difference between simulation and those same Pdata. This is a two-stage in-sample fit, so agreement does not test the model. The Hessian check in Sec. VI B is not a substitute for a falsifiable prediction. The claim that dephasing is the dominant error source and that the error model 'captures the dominant features' therefore goes beyond what the data establish. Add an out-of-sample test (e.g., fit one Trotter depth or c value and predict the others) or independently calibrate γ and n̄ and show the fitted values agree.
  3. [Sec. VI D, Fig. 13] The characteristic-function comparison that 'confirms' the error model uses a hand-chosen displacement miscalibration angle φ = -6°, together with γ and n̄ taken from the in-sample fits, and the agreement is described only as 'good qualitative'. No quantitative metric or uncertainty on φ is given. As it stands, this comparison is an illustration consistent with the error model, not an independent confirmation. A quantitative distance between simulated and reconstructed χ(β), with φ included in a constrained fit or scan over the expected detuning range, would be appropriate.
minor comments (3)
  1. [Abstract/Conclusions] The abstract carefully says 'mode-resolved marginal benchmark' for the two-qumode gate, but the Conclusions state that the odd-Fock enhancement 'provides a qualitative signature of genuinely two-mode dynamics'. Please align the wording with the admitted lack of intermode-correlation readout.
  2. [Sec. VI C, Fig. 10] The text says the parameters are obtained via a 'global fit to the four circuits', while Fig. 10 appears to display per-plot optimized parameters. Clarify whether the fit is truly global or performed per circuit, and state the total number of free parameters in each case.
  3. [Sec. VI A, Eq. (54)] For reproducibility, please state whether the statistical uncertainties in Eq. (55) account for the postselection denominator N↑, and consider depositing the raw BSB traces and fitting/simulation code, which would materially strengthen a benchmark paper.

Circularity Check

0 steps flagged

No significant circularity: gate matrix elements, Trotter circuits, and parity rules are derived from standard identities and explicit expansions; fitted noise parameters are disclosed as such, and the two-mode marginal limitation is acknowledged rather than disguised as a prediction.

full rationale

The paper's derivation chain is self-contained. The ideal one- and two-qumode cosine-gate matrix elements (Eqs. (10)-(18)) follow from Jacobi-Anger expansions and known displacement matrix elements; they do not assume the experimental data. The Trotter circuits in Eqs. (35)-(49) are explicitly expanded into 'good' and 'bad' components, and the convergence to exp(-iθ cos(c·x̂)) in Eqs. (39) and (B5) is derived from a recurrence, not taken as an input. The parity-based postselection rules are direct consequences of these expansions, so the odd-Fock two-mode population enhancement is a genuine theoretical prediction about the circuit. The experiment uses the circuit implementations to measure Fock transition probabilities; the only fitted quantities (initial thermal occupation n̄, dephasing rate γ, readout dephasing Γ, and sideband coupling ηΩ) are used to make a noisy simulation match the same data (Eqs. (54), (65)). The paper explicitly labels this as an 'optimized simulation' rather than an independent prediction, so this is a limited model-validation procedure, not a circular derivation. The characteristic-function comparison (Fig. 13) uses parameters obtained from a different observable and provides a partly independent check. The two-qumode validation is based on mode-resolved marginals (Eq. (64)), and the paper itself concedes that direct intermode correlation readout is 'beyond current trapped-ion hardware' (Sec. VII). This is an evidentiary limitation for certifying an entangling two-mode operation, but it does not make the theoretical derivation circular: the gate unitary and its matrix elements are defined independently of the marginal data, and the abstract carefully says 'mode-resolved marginal benchmark.' No load-bearing step reduces to a self-citation; Ref. [63] (same authors) is used for provenance of the gate framework, while the circuit convention is from Ref. [64] with an explicit equivalence proof in Appendix C. Hence there is no circular reduction of the claimed benchmark to its inputs.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central claim rests on standard Bessel/Laguerre mathematics, the trapped-ion SDF-to-CD mapping, and a dephasing-plus-thermal error model whose rates are fit to the data. No new physical entities are introduced. The fitted parameters (γ, n̄, Γ, ηΩ, φ) are the most honest measure of the gap between derivation and independent validation.

free parameters (5)
  • γ (motional dephasing rate, per mode) = γ = 0.1884 in Fig. 13 (units of reciprocal CDx gate time); per-circuit fits in Figs. 10-12
    Fit to the experimental transition probabilities in a second fitting stage (Eq. 65); also used in the characteristic-function comparison.
  • n̄ (initial thermal mean phonon number, per mode) = n̄ = 0.136 in Fig. 13; per-mode fits in Figs. 10-12
    Fit to the experimental transition probabilities (Eq. 65); represents imperfect ground-state initialization and enters the open-system simulation.
  • Γ (readout dephasing rate) = 2π×(0.0014–0.095) µs⁻¹ (Sec. VIA)
    Fit in the BSB readout reconstruction (Eq. 54) to extract Fock-state probabilities from probe-qubit Rabi oscillations.
  • ηΩ (effective sideband Rabi coupling) = 2π×(0.0167–0.0175) µs⁻¹ (Sec. VIA)
    Fit in the BSB readout reconstruction (Eq. 54); the nominal value is 2π×16.66 kHz (Sec. III).
  • φ (displacement miscalibration angle) = φ = −6° (chosen middle value, Fig. 13)
    Selected to match the characteristic-function comparison; not obtained from a rigorous fit and not included in the transition-probability fits because probabilities are argued to be φ-insensitive.
axioms (6)
  • standard math Jacobi-Anger expansion and Fock-space matrix elements of displacement operators (Ref. [80])
    Used in Eqs. (10)-(17) to express cosine gates as infinite sums of displacements and to derive transition-probability formulas.
  • domain assumption The spin-dependent-force Hamiltonian (Eq. 9) realizes ideal conditional displacements in the Lamb-Dicke regime
    The trapped-ion implementation of CD gates relies on this mapping (Sec. III); deviations are modeled only through dephasing and calibration errors.
  • domain assumption Motional dephasing with Lindblad operator L = n-hat captures all relevant circuit errors; heating and qubit errors are neglected
    Sec. VIB states the error model; the rates are fit to data, so the assumption that this is the complete error channel is not independently tested.
  • domain assumption Fock-space truncation at Λ=40 (one-mode) or Λ=15 (two-mode) is sufficient for faithful simulation and readout reconstruction
    Used throughout the simulations and BSB reconstruction (Sec. VIA); the paper states it 'provides a good description of the data' without a convergence study.
  • standard math Postselecting on the gate qubit in |↑> removes the O(θ²) bad component and leaves the ideal cosine gate up to the stated Trotter order
    Proven in Eqs. (35)-(49) and Appendix B for the first-order circuit; relies on the operator structure of the hybrid unitary.
  • standard math Stationary-phase approximation used for the large-θ mana bound (Appendix A)
    The bound M ~ (1/2)Δlnθ assumes a single dominant stationary point and subdominant caustics; the derivation is standard asymptotic analysis.

pith-pipeline@v1.3.0-alltime-deepseek · 29095 in / 12168 out tokens · 130126 ms · 2026-08-02T02:47:46.474485+00:00 · methodology

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read the original abstract

Hybrid continuous-discrete-variable quantum processors can represent bosonic degrees of freedom directly in oscillator modes, or qumodes, while using qubits for control, readout, and nonlinear operations. Recently proposed trigonometric continuous-variable (CV) gate sets promote periodic functions of oscillator quadratures to elementary operations, making them natural primitives for compact variables, rotor models, lattice gauge theories, and anharmonic dynamics. Here we experimentally demonstrate and benchmark one-qumode cosine gates, and perform a mode-resolved marginal benchmark of two-qumode cosine-gate implementations, on the QSCOUT trapped-ion quantum platform. Our implementation uses collective motional modes of three- and four-ion $^{171}{\rm Yb}^{+}$ chains and realizes finite-step trigonometric-gate circuits through hybrid qubit-qumode operations and conditional phase-space displacements. In contrast to previous theoretical and compilation work, we focus on the gate-level characterization of the trigonometric primitives. We measure Fock-space transition probabilities, study their dependence on gate parameters and Trotter step number, and compare with simulations incorporating thermal initialization and motional dephasing. We also derive ideal gate matrix elements and phase-space diagnostics, connecting the measurements to the non-Gaussian structure generated by these gates. These results establish trigonometric CV gates as reusable building blocks for bosonic Hamiltonian simulations and hybrid quantum algorithms requiring intrinsically non-polynomial operations.

Figures

Figures reproduced from arXiv: 2607.14085 by Brian K. McFarland, Christopher G. Yale, Daniel Lobser, Edward C. Tortorici, Felix Ringer, George Siopsis, Jake Montgomery, Matt Grau, Melissa C. Revelle, Susan Clark, Tommaso Rainaldi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
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Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
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Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
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Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
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Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗

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Reference graph

Works this paper leans on

86 extracted references · 11 canonical work pages

  1. [1]

    col- lide

    Thus, we obtain Pm←0(θ, c)(15) =    0, c2m 2mm! P k∈Z(−1)kik+mJk(θ)e− c2 k2 4 km 2 , where the only non-vanishing probabilities are ob- tained for evenm. Next, we consider the two-qumode extension of the cosine gate. Mirroring the results of the single- mode case, we can once again regard the ideal gate as an infinite sum of displacements e−iθcos(c· ˆx...

  2. [2]

    For the two-qumode simulation, the initial mean phonon occupations¯n1,¯n2 and dephasing ratesγ 1, γ2 are treated as independent parameters

    The state after the noisy circuit is therefore ˆρ(i) G ≡ G(γ) ˆCi 1 [ˆρin],(60) and the normalized Fock-state transition probabili- ties are P (i) n (θ, c;γ,¯n| ↑) = ⟨n,↑|ˆρ(i) G |n,↑⟩ ΛX n′=0 ⟨n′,↑|ˆρ(i) G |n′,↑⟩ .(61) The projection onto|↑⟩mirrors the experimental postselection procedure, and the denominator nor- malizes the postselected distribution to...

  3. [3]

    Quantum computation over continuous variables,

    S. Lloyd and S. L. Braunstein, “Quantum computation over continuous variables,”Phys. Rev. Lett.82(1999) 1784–1787, arXiv:quant-ph/9810082

    Pith/arXiv arXiv 1999

  4. [4]

    Quantum information with continuous variables,

    S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,”Rev. Mod. Phys.77(Jun, 2005) 513–577.https://link.aps. org/doi/10.1103/RevModPhys.77.513

    doi:10.1103/revmodphys.77.513 2005

  5. [5]

    Hybrid discrete- and continuous-variable quantum information,

    U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, “Hybrid discrete- and continuous-variable quantum information,”Nature Physics11no. 9, (2015) 713–719. https://doi.org/10.1038/nphys3410

    doi:10.1038/nphys3410 2015

  6. [6]

    Quantum dynamics of single trapped ions,

    D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, “Quantum dynamics of single trapped ions,”Rev. Mod. Phys.75(Mar, 2003) 281–324.https://link.aps.org/doi/10.1103/ RevModPhys.75.281

    2003

  7. [7]

    Circuit quantum electrodynamics,

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, “Circuit quantum electrodynamics,” Rev. Mod. Phys.93no. 2, (2021) 025005, arXiv:2005.12667 [quant-ph]

    Pith/arXiv arXiv 2021

  8. [8]

    C2QA - Bosonic Qiskit,

    T. J. Stavenger, E. Crane, K. C. Smith, C. T. Kang, S. M. Girvin, and N. Wiebe, “C2QA - Bosonic Qiskit,” in26th IEEE High Performance Extreme Computing. 9, 2022.arXiv:2209.11153 [quant-ph]

    Pith/arXiv arXiv 2022

  9. [9]

    Hybrid oscillator-qubit quantum processors: Instruction set architectures, abstract machine models, and applications,

    Y. Liu, S. Singh, K. C. Smith, E. Crane, J. M. Martyn, A. Eickbusch, A. Schuckert, R. D. Li, J. Sinanan-Singh, M. B. Soley, T. Tsunoda, I. L. Chuang, N. Wiebe, and S. M. Girvin, “Hybrid oscillator-qubit quantum processors: Instruction set architectures, abstract machine models, and applications,”PRX Quantum7(Jan, 2026) 010201. https://link.aps.org/doi/10....

    work page doi:10.1103/4rf7-9tfx 2026

  10. [10]

    Hybrid quantum simulations with 22 qubits and qumodes on trapped-ion platforms,

    J. Y. Araz, M. Grau, J. Montgomery, and F. Ringer, “Hybrid quantum simulations with 22 qubits and qumodes on trapped-ion platforms,” Phys. Rev. A112no. 1, (2025) 012620, arXiv:2410.07346 [quant-ph]

    Pith/arXiv arXiv 2025

  11. [11]

    Encoding a qubit in a trapped-ion mechanical oscillator,

    C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. Home, “Encoding a qubit in a trapped-ion mechanical oscillator,”Nature566no. 7745, (2019) 513–517, arXiv:1807.01033 [quant-ph]

    Pith/arXiv arXiv 2019

  12. [12]

    Error correction of a logical grid state qubit by dissipative pumping,

    B. de Neeve, T.-L. Nguyen, T. Behrle, and J. P. Home, “Error correction of a logical grid state qubit by dissipative pumping,”Nature Physics18 no. 3, (2022) 296–300. https://doi.org/10.1038/s41567-021-01487-7

    doi:10.1038/s41567-021-01487-7 2022

  13. [13]

    Cavity State Manipulation Using Photon-Number Selective Phase Gates,

    R. W. Heeres, B. Vlastakis, E. Holland, S. Krastanov, V. V. Albert, L. Frunzio, L. Jiang, and R. J. Schoelkopf, “Cavity State Manipulation Using Photon-Number Selective Phase Gates,” Phys. Rev. Lett.115no. 13, (2015) 137002, arXiv:1503.01496 [quant-ph]

    Pith/arXiv arXiv 2015

  14. [14]

    Fast universal control of an oscillator with weak dispersive coupling to a qubit,

    A. Eickbusch, V. Sivak, A. Z. Ding, S. S. Elder, S. R. Jha, J. Venkatraman, B. Royer, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, “Fast universal control of an oscillator with weak dispersive coupling to a qubit,”Nature Phys.18 (2022) 1464–1469,arXiv:2111.06414 [quant-ph]

    Pith/arXiv arXiv 2022

  15. [15]

    Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor,

    C. S. Wang, J. C. Curtis, B. J. Lester, Y. Zhang, Y. Y. Gao, J. Freeze, V. S. Batista, P. H. Vaccaro, I. L. Chuang, L. Frunzio, L. Jiang, S. M. Girvin, and R. J. Schoelkopf, “Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor,”Phys. Rev. X 10no. 2, (2020) 021060,arXiv:1908.03598 [quant-ph]

    Pith/arXiv arXiv 2020

  16. [16]

    Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion,

    P. C. Haljan, K.-A. Brickman, L. Deslauriers, P. J. Lee, and C. Monroe, “Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion,”Phys. Rev. Lett.94(Apr, 2005) 153602.https://link.aps. org/doi/10.1103/PhysRevLett.94.153602

    work page doi:10.1103/physrevlett.94.153602 2005

  17. [17]

    Scalable and programmable phononic network with trapped ions,

    W. Chen, Y. Lu, S. Zhang, K. Zhang, G. Huang, M. Qiao, X. Su, J. Zhang, J.-N. Zhang, L. Banchi, M. S. Kim, and K. Kim, “Scalable and programmable phononic network with trapped ions,”Nature Physics19no. 6, (2023) 877–883. https://doi.org/10.1038/s41567-023-01952-5

    work page doi:10.1038/s41567-023-01952-5 2023

  18. [19]

    Phonon arithmetic in a trapped ion system,

    M. Um, J. Zhang, D. Lv, Y. Lu, S. An, J.-N. Zhang, H. Nha, M. S. Kim, and K. Kim, “Phonon arithmetic in a trapped ion system,”Nature Communications7no. 1, (2016) 11410. https://doi.org/10.1038/ncomms11410

    work page doi:10.1038/ncomms11410 2016

  19. [20]

    HyQBench: A Benchmark Suite for Hybrid CV-DV Quantum Computing,

    S. Mohapatra, Y. Liu, E. Z. Zhang, and H. Zhou, “HyQBench: A Benchmark Suite for Hybrid CV-DV Quantum Computing,”arXiv:2603.04398 [quant-ph]

    arXiv

  20. [21]

    HyPulse: A Pulse Synthesis Framework for Hybrid Qubit-Oscillator Gates on Trapped-Ion Platform,

    M. H. Heris, Y. Liu, and F. Mueller, “HyPulse: A Pulse Synthesis Framework for Hybrid Qubit-Oscillator Gates on Trapped-Ion Platform,” arXiv:2604.26804 [quant-ph]

    Pith/arXiv arXiv

  21. [22]

    Universal hybrid quantum computing in trapped ions,

    R. T. Sutherland and R. Srinivas, “Universal hybrid quantum computing in trapped ions,”Phys. Rev. A104no. 3, (2021) 032609, arXiv:2105.05768 [quant-ph]

    Pith/arXiv arXiv 2021

  22. [23]

    Quantum computation and simulation with vibrational modes of trapped ions,

    W. Chen, J. Gan, J.-N. Zhang, D. Matuskevich, and K. Kim, “Quantum computation and simulation with vibrational modes of trapped ions,”Chinese Physics B30no. 6, (Jun, 2021) 060311.https: //doi.org/10.1088%2F1674-1056%2Fac01e3

    2021

  23. [24]

    Hybrid continuous-discrete-variable quantum computing: a guide to utility,

    A. F. Kemper, A. Alvertis, M. Asaduzzaman, B. N. Bakalov, D. Baron, J. Bierman, B. Burgstahler, S. Chundury, E. R. Das, J. Furches, F. Guo, R. G. Jha, K. Klymko, A. Kushwaha, A. Li, A. Majumdar, C. O. Marrero, S. Mohapatra, C. Mori, F. Mueller, D. T. Popovici, T. Stavenger, M. Tirfe, N. M. Tubman, M. Zheng, H. Zhou, and Y. Liu, “Hybrid continuous-discrete...

    arXiv 2025

  24. [25]

    Encoding a qubit in an oscillator,

    D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,”Phys. Rev. A 64(2001) 012310,arXiv:quant-ph/0008040

    Pith/arXiv arXiv 2001

  25. [26]

    Quantum error correction and universal gate set operation on a binomial bosonic logical qubit,

    L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. P. Song, C. L. Zou, S. M. Girvin, L.-M. Duan, and L. Sun, “Quantum error correction and universal gate set operation on a binomial bosonic logical qubit,”Nature Physics15 no. 5, (2019) 503–508. https://doi.org/10.1038/s41567-018-0414-3

    work page doi:10.1038/s41567-018-0414-3 2019

  26. [27]

    Quantum error correction of a qubit encoded in grid states of an oscillator,

    P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys-Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf, L. Frunzio, M. Mirrahimi, and M. H. Devoret, “Quantum error correction of a qubit encoded in grid states of an oscillator,”Nature584no. 7821, (2020) 368–372. https://doi.org/10.1038/s41586-020-2603-3. 23

    doi:10.1038/s41586-020-2603-3 2020

  27. [28]

    Quantum error correction of qudits beyond break-even,

    B. L. Brock, S. Singh, A. Eickbusch, V. V. Sivak, A. Z. Ding, L. Frunzio, S. M. Girvin, and M. H. Devoret, “Quantum error correction of qudits beyond break-even,”Nature641no. 8063, (2025) 612–618,arXiv:2409.15065 [quant-ph]

    Pith/arXiv arXiv 2025

  28. [29]

    Robust and deterministic preparation of bosonic logical states in a trapped ion,

    V. G. Matsos, C. H. Valahu, T. Navickas, A. D. Rao, M. J. Millican, X. C. Kolesnikow, M. J. Biercuk, and T. R. Tan, “Robust and deterministic preparation of bosonic logical states in a trapped ion,”Phys. Rev. Lett.133(Jul, 2024) 050602. https://link.aps.org/doi/10.1103/ PhysRevLett.133.050602

    2024

  29. [30]

    Universal quantum gate set for Gottesman–Kitaev–Preskill logical qubits,

    V. G. Matsos, C. H. Valahu, M. J. Millican, T. Navickas, X. C. Kolesnikow, M. J. Biercuk, and T. R. Tan, “Universal quantum gate set for Gottesman–Kitaev–Preskill logical qubits,”Nature Phys.21no. 10, (2025) 1664–1669, arXiv:2409.05455 [quant-ph]

    Pith/arXiv arXiv 2025

  30. [31]

    About the Pauli exclusion principle,

    P. Jordan and E. P. Wigner, “About the Pauli exclusion principle,”Z. Phys.47(1928) 631–651

    1928

  31. [32]

    Ab initio polaritonic chemistry on diverse quantum computing platforms: Ansatz circuit design for qubit, qudit, and hybrid qubit-qumode architectures,

    E. Chiari, W. Makhlouf, L. Pepe, E. Koridon, J. Klein, B. Senjean, B. Lasorne, and S. Yalouz, “Ab initio polaritonic chemistry on diverse quantum computing platforms: Ansatz circuit design for qubit, qudit, and hybrid qubit-qumode architectures,”Phys. Rev. A112no. 5, (2025) 052433,arXiv:2506.12504 [quant-ph]

    arXiv 2025

  32. [33]

    Observation of hopping and blockade of bosons in a trapped ion spin chain,

    S. Debnath, N. M. Linke, S.-T. Wang, C. Figgatt, K. A. Landsman, L.-M. Duan, and C. Monroe, “Observation of hopping and blockade of bosons in a trapped ion spin chain,”Phys. Rev. Lett.120 (Feb, 2018) 073001.https://link.aps.org/doi/ 10.1103/PhysRevLett.120.073001

    work page doi:10.1103/physrevlett.120.073001 2018

  33. [34]

    Hamiltonian Formulation of Wilson’s Lattice Gauge Theories,

    J. B. Kogut and L. Susskind, “Hamiltonian Formulation of Wilson’s Lattice Gauge Theories,” Phys. Rev. D11(1975) 395–408

    1975

  34. [35]

    Quantum Computation of Scattering in Scalar Quantum Field Theories,

    S. P. Jordan, K. S. M. Lee, and J. Preskill, “Quantum Computation of Scattering in Scalar Quantum Field Theories,”Quant. Inf. Comput.14 (2014) 1014–1080,arXiv:1112.4833 [hep-th]

    Pith/arXiv arXiv 2014

  35. [36]

    Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices,

    E. Zohar, J. I. Cirac, and B. Reznik, “Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices,”Rept. Prog. Phys.79no. 1, (2016) 014401,arXiv:1503.02312 [quant-ph]

    Pith/arXiv arXiv 2016

  36. [37]

    Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench,

    D. Banerjee, M. Dalmonte, M. Muller, E. Rico, P. Stebler, U. J. Wiese, and P. Zoller, “Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench,”Phys. Rev. Lett.109(2012) 175302,arXiv:1205.6366 [cond-mat.quant-gas]

    Pith/arXiv arXiv 2012

  37. [38]

    Simulating lattice gauge theories within quantum technologies,

    M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, “Simulating lattice gauge theories within quantum technologies,”The European Physical Journal D ...

    doi:10.1140/epjd/e2020-100571-8 2020

  38. [39]

    Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization,

    M. Kreshchuk, S. Jia, W. M. Kirby, G. Goldstein, J. P. Vary, and P. J. Love, “Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization,”Phys. Rev. A103no. 6, (2021) 062601,arXiv:2011.13443 [quant-ph]

    Pith/arXiv arXiv 2021

  39. [40]

    A resource efficient approach for quantum and classical simulations of gauge theories in particle physics,

    J. F. Haase, L. Dellantonio, A. Celi, D. Paulson, A. Kan, K. Jansen, and C. A. Muschik, “A resource efficient approach for quantum and classical simulations of gauge theories in particle physics,”Quantum5(2021) 393, arXiv:2006.14160 [quant-ph]

    Pith/arXiv arXiv 2021

  40. [41]

    Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods,

    E. Zohar, “Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods,”Phil. Trans. A. Math. Phys. Eng. Sci. 380no. 2216, (2022) 20210069,arXiv:2106.04609 [quant-ph]

    Pith/arXiv arXiv 2022

  41. [42]

    Digitization of scalar fields for quantum computing,

    N. Klco and M. J. Savage, “Digitization of scalar fields for quantum computing,”Phys. Rev. A99 no. 5, (2019) 052335,arXiv:1808.10378 [quant-ph]

    Pith/arXiv arXiv 2019

  42. [43]

    Quantum simulation for high-energy physics,

    C. W. Bauer, Z. Davoudi, A. B. Balantekin, T. Bhattacharya, M. Carena, W. A. de Jong, P. Draper, A. El-Khadra, N. Gemelke, M. Hanada, D. Kharzeev, H. Lamm, Y.-Y. Li, J. Liu, M. Lukin, Y. Meurice, C. Monroe, B. Nachman, G. Pagano, J. Preskill, E. Rinaldi, A. Roggero, D. I. Santiago, M. J. Savage, I. Siddiqi, G. Siopsis, D. Van Zanten, N. Wiebe, Y. Yamauchi...

    2023

  43. [44]

    Toward coherent quantum computation of scattering amplitudes with a measurement-based photonic quantum processor,

    R. A. Briceño, R. G. Edwards, M. Eaton, C. González-Arciniegas, O. Pfister, and G. Siopsis, “Toward coherent quantum computation of scattering amplitudes with a measurement-based photonic quantum processor,”Phys. Rev. Res.6 no. 4, (2024) 043065,arXiv:2312.12613 [quant-ph]

    Pith/arXiv arXiv 2024

  44. [45]

    Toward simulating quantum field theories with controlled 24 phonon-ion dynamics: A hybrid analog-digital approach,

    Z. Davoudi, N. M. Linke, and G. Pagano, “Toward simulating quantum field theories with controlled 24 phonon-ion dynamics: A hybrid analog-digital approach,”Phys. Rev. Res.3no. 4, (2021) 043072, arXiv:2104.09346 [quant-ph]

    Pith/arXiv arXiv 2021

  45. [46]

    Programmable Quantum Simulations of Bosonic Systems with Trapped Ions,

    O. Katz and C. Monroe, “Programmable Quantum Simulations of Bosonic Systems with Trapped Ions,”Phys. Rev. Lett.131no. 3, (2023) 033604, arXiv:2207.13653 [quant-ph]

    Pith/arXiv arXiv 2023

  46. [47]

    Primitive quantum gates for an SU(3) discrete subgroup:Σ(36×3),

    E. J. Gustafson, Y. Ji, H. Lamm, E. M. Murairi, S. O. Perez, and S. Zhu, “Primitive quantum gates for an SU(3) discrete subgroup:Σ(36×3),”Phys. Rev. D110no. 3, (2024) 034515, arXiv:2405.05973 [hep-lat]

    Pith/arXiv arXiv 2024

  47. [48]

    Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits,

    R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, “Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits,”PRX Quantum5no. 2, (2024) 020315, arXiv:2308.04481 [quant-ph]

    Pith/arXiv arXiv 2024

  48. [49]

    Quantum computation of SU(2) lattice gauge theory with continuous variables,

    V. Ale, N. M. Bauer, R. G. Jha, F. Ringer, and G. Siopsis, “Quantum computation of SU(2) lattice gauge theory with continuous variables,”JHEP06 (2025) 084,arXiv:2410.14580 [hep-lat]

    Pith/arXiv arXiv 2025

  49. [50]

    Real-time scattering processes with continuous-variable quantum computers,

    S. Abel, M. Spannowsky, and S. Williams, “Real-time scattering processes with continuous-variable quantum computers,”Phys. Rev. A112no. 1, (2025) 012614, arXiv:2502.01767 [quant-ph]

    Pith/arXiv arXiv 2025

  50. [51]

    Hybrid oscillator-qubit quantum processors: Simulating fermions, bosons, and gauge fields,

    E. Crane, K. C. Smith, T. Tomesh, A. Eickbusch, J. M. Martyn, S. Kühn, L. Funcke, M. A. DeMarco, I. L. Chuang, N. Wiebe, A. Schuckert, and S. M. Girvin, “Hybrid oscillator-qubit quantum processors: Simulating fermions, bosons, and gauge fields,” 9, 2024

    2024

  51. [52]

    Simulating quantum electrodynamics in 2+1 dimensions with qubits and qumodes,

    V. Ale, T. Rainaldi, E. Rico, F. Ringer, and G. Siopsis, “Simulating quantum electrodynamics in 2+1 dimensions with qubits and qumodes,” JHEP04(2026) 122,arXiv:2511.14506 [quant-ph]

    arXiv 2026

  52. [53]

    Real-Time Observation of Aharonov-Bohm Interference in aZ2 Lattice Gauge Theory on a Hybrid Qubit-Oscillator Quantum Computer,

    S. Saner, O. Băzăvan, D. J. Webb, G. Araneda, C. J. Ballance, R. Srinivas, D. M. Lucas, and A. Bermúdez, “Real-Time Observation of Aharonov-Bohm Interference in aZ2 Lattice Gauge Theory on a Hybrid Qubit-Oscillator Quantum Computer,”arXiv:2507.19588 [quant-ph]

    Pith/arXiv arXiv

  53. [54]

    Observation of quantum-field-theory dynamics on a spin-phonon quantum computer,

    A. T. Than, S. V. Kadam, V. Vikramaditya, N. H. Nguyen, X. Liu, Z. Davoudi, A. M. Green, and N. M. Linke, “Observation of quantum-field-theory dynamics on a spin-phonon quantum computer,” 2025.https://arxiv.org/abs/2509.11477

    arXiv 2025

  54. [55]

    Hadronic tensor in lattice gauge theories by quantum computing,

    D. Zou, T. Li, J. Liang, E. Wang, and H. Xing, “Hadronic tensor in lattice gauge theories by quantum computing,”arXiv:2606.17003 [hep-ph]

    arXiv

  55. [56]

    Continuous-variable ADAPT-VQE for bosonic lattice models,

    D. Athanasakos, G. Tejedor-García, J. Y. Araz, M. Ramôa, B. Sambasivam, S. E. Economou, and F. Ringer, “Continuous-variable ADAPT-VQE for bosonic lattice models,”arXiv:2606.05297 [quant-ph]

    Pith/arXiv arXiv

  56. [57]

    Quantum Simulation of Nucleon-Antinucleon Interaction in Large-NQCD 2 on an IBM Quantum Nighthawk Processor,

    C. V. Cogburn, S. Grieninger, and D. E. Kharzeev, “Quantum Simulation of Nucleon-Antinucleon Interaction in Large-NQCD 2 on an IBM Quantum Nighthawk Processor,” arXiv:2606.02574 [quant-ph]

    Pith/arXiv arXiv

  57. [58]

    Quantum simulation of the quantum rabi model in a trapped ion,

    D. Lv, S. An, Z. Liu, J.-N. Zhang, J. S. Pedernales, L. Lamata, E. Solano, and K. Kim, “Quantum simulation of the quantum rabi model in a trapped ion,”Phys. Rev. X8(Apr, 2018) 021027.https:// link.aps.org/doi/10.1103/PhysRevX.8.021027

    doi:10.1103/physrevx.8.021027 2018

  58. [59]

    Quantum-mechanical modeling of the femtosecond isomerization in rhodopsin,

    S. Hahn and G. Stock, “Quantum-mechanical modeling of the femtosecond isomerization in rhodopsin,”The Journal of Physical Chemistry B 104no. 6, (2000) 1146–1149, https://doi.org/10.1021/jp992939g. https://doi.org/10.1021/jp992939g

    doi:10.1021/jp992939g 2000

  59. [60]

    Quantum optical emulation of molecular vibronic spectroscopy using a trapped-ion device,

    Y. Shen, Y. Lu, K. Zhang, J. Zhang, S. Zhang, J. Huh, and K. Kim, “Quantum optical emulation of molecular vibronic spectroscopy using a trapped-ion device,”Chem. Sci.9(2018) 836–840. http://dx.doi.org/10.1039/C7SC04602B

    work page doi:10.1039/c7sc04602b 2018

  60. [61]

    Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor,

    C. S. Wang, J. C. Curtis, B. J. Lester, Y. Zhang, Y. Y. Gao, J. Freeze, V. S. Batista, P. H. Vaccaro, I. L. Chuang, L. Frunzio, L. Jiang, S. M. Girvin, and R. J. Schoelkopf, “Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor,”Phys. Rev. X 10(Jun, 2020) 021060.https://link.aps.org/ doi/10.1103/PhysRevX.10.021060

    doi:10.1103/physrevx.10.021060 2020

  61. [62]

    Direct observation of geometric-phase interference in dynamics around a conical intersection,

    C. H. Valahu, V. C. Olaya-Agudelo, R. J. MacDonell, T. Navickas, A. D. Rao, M. J. Millican, J. B. Pérez-Sánchez, J. Yuen-Zhou, M. J. Biercuk, C. Hempel, T. R. Tan, and I. Kassal, “Direct observation of geometric-phase interference in dynamics around a conical intersection,”Nature Chemistry15no. 11, (2023) 1503–1508. https://doi.org/10.1038/s41557-023-01300-3

    doi:10.1038/s41557-023-01300-3 2023

  62. [63]

    Simulating chemistry on bosonic quantum 25 devices,

    R. Dutta, D. G. A. Cabral, N. Lyu, N. P. Vu, Y. Wang, B. Allen, X. Dan, R. G. Cortiñas, P. Khazaei, M. Schäfer, A. C. C. d. Albornoz, S. E. Smart, S. Nie, M. H. Devoret, D. A. Mazziotti, P. Narang, C. Wang, J. D. Whitfield, A. K. Wilson, H. P. Hendrickson, D. A. Lidar, F. Pérez-Bernal, L. F. Santos, S. Kais, E. Geva, and V. S. Batista, “Simulating chemist...

    work page doi:10.1021/acs.jctc.4c 2024

  63. [64]

    The Quantum Sine-Gordon Equation as the Massive Thirring Model,

    S. R. Coleman, “The Quantum Sine-Gordon Equation as the Massive Thirring Model,”Phys. Rev. D11(1975) 2088

    1975

  64. [65]

    Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model,

    T. Rainaldi, V. Ale, M. Grau, D. Kharzeev, E. Rico, F. Ringer, P. Shome, and G. Siopsis, “Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model,”JHEP03(2026) 125,arXiv:2512.19582 [quant-ph]

    arXiv 2026

  65. [66]

    Programmable generation of arbitrary continuous-variable anharmonicities and nonlinear couplings,

    T. Chalermpusitarak, K. Schwennicke, I. Kassal, and T. R. Tan, “Programmable generation of arbitrary continuous-variable anharmonicities and nonlinear couplings,”arXiv:2511.22286 [quant-ph]

    arXiv

  66. [67]

    Engineering the quantum scientific computing open user testbed,

    S. M. Clark, D. Lobser, M. C. Revelle, C. G. Yale, D. Bossert, A. D. Burch, M. N. Chow, C. W. Hogle, M. Ivory, J. Pehr, B. Salzbrenner, D. Stick, W. Sweatt, J. M. Wilson, E. Winrow, and P. Maunz, “Engineering the quantum scientific computing open user testbed,”IEEE Transactions on Quantum Engineering2(2021) 1–32

    2021

  67. [68]

    Determination of multimode motional quantum states in a trapped ion system,

    Z. Jia, Y. Wang, B. Zhang, J. Whitlow, C. Fang, J. Kim, and K. R. Brown, “Determination of multimode motional quantum states in a trapped ion system,”Phys. Rev. Lett.129(Aug, 2022) 103602.https://link.aps.org/doi/10.1103/ PhysRevLett.129.103602

    2022

  68. [69]

    Programmable quantum simulation of anharmonic dynamics,

    C. McGarry, T. Chalermpusitarak, K. Schwennicke, F. Scuccimarra, M. J. Millican, V. G. Matsos, C. H. Valahu, P. Nagpal, H.-K. Chan, H. L. Nourse, I. Kassal, and T. R. Tan, “Programmable quantum simulation of anharmonic dynamics,” 2026. https://arxiv.org/abs/2603.04744

    arXiv 2026

  69. [70]

    Squeezing, trisqueezing and quadsqueezing in a hybrid oscillator–spin system,

    O. Băzăvan, S. Saner, D. J. Webb, E. M. Ainley, P. Drmota, D. P. Nadlinger, G. Araneda, D. M. Lucas, C. J. Ballance, and R. Srinivas, “Squeezing, trisqueezing and quadsqueezing in a hybrid oscillator–spin system,”Nature Physics22no. 5, (2026) 757–762. https://doi.org/10.1038/s41567-026-03222-6

    work page doi:10.1038/s41567-026-03222-6 2026

  70. [71]

    Single-shot Quantum Signal Processing Interferometry,

    J. Sinanan-Singh, G. L. Mintzer, I. L. Chuang, and Y. Liu, “Single-shot Quantum Signal Processing Interferometry,”Quantum8(2024) 1427, arXiv:2311.13703 [quant-ph]

    Pith/arXiv arXiv 2024

  71. [72]

    Toward mixed analog-digital quantum signal processing: Quantum ad/da conversion and the fourier transform,

    Y. Liu, J. M. Martyn, J. Sinanan-Singh, K. C. Smith, S. M. Girvin, and I. L. Chuang, “Toward mixed analog-digital quantum signal processing: Quantum ad/da conversion and the fourier transform,”IEEE Transactions on Signal Processing73(2025) 3641–3655

    2025

  72. [73]

    Oscillator-qubit generalized quantum signal processing for vibronic models: a case study of uracil cation,

    J. Hong, S. H. Kim, S. K. Min, and J. Huh, “Oscillator-qubit generalized quantum signal processing for vibronic models: a case study of uracil cation,” 2025. https://arxiv.org/abs/2510.10495

    Pith/arXiv arXiv 2025

  73. [74]

    QSCOUT’s Qubit-Boson Gate Set,

    E. C. Tortorici, E. C. McGarrigle, B. K. McFarland, W. L. Johnson, D. S. Lobser, M. C. Revelle, B. P. Ruzic, S. M. Clark, and C. G. Yale, “QSCOUT’s Qubit-Boson Gate Set,” arXiv:2607.08560 [quant-ph]

    Pith/arXiv arXiv

  74. [75]

    Phoenix and peregrine ion traps,

    M. C. Revelle, “Phoenix and peregrine ion traps,” 2020.https://arxiv.org/abs/2009.02398

    Pith/arXiv arXiv 2020

  75. [76]

    Experimental issues in coherent quantum-state manipulation of trapped atomic ions,

    D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” 1998. https://arxiv.org/abs/quant-ph/9710025

    Pith/arXiv arXiv 1998

  76. [77]

    Flühmann,Encoding a qubit in the motion of a trapped ion using superpositions of displaced squeezed states

    C. Flühmann,Encoding a qubit in the motion of a trapped ion using superpositions of displaced squeezed states. PhD thesis, ETH Zürich, 2019. https://doi.org/10.3929/ethz-b-000355836

    work page doi:10.3929/ethz-b-000355836 2019

  77. [78]

    Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator,

    C. Flühmann and J. P. Home, “Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator,”Phys. Rev. Lett.125(Jul, 2020) 043602.https://link. aps.org/doi/10.1103/PhysRevLett.125.043602

    doi:10.1103/physrevlett.125.043602 2020

  78. [79]

    Experimental determination of the motional quantum state of a trapped atom,

    D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, “Experimental determination of the motional quantum state of a trapped atom,”Phys. Rev. Lett.77(Nov, 1996) 4281–4285.https://link. aps.org/doi/10.1103/PhysRevLett.77.4281

    doi:10.1103/physrevlett.77.4281 1996

  79. [80]

    Generation of nonclassical motional states of a trapped atom,

    D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, “Generation of nonclassical motional states of a trapped atom,” Phys. Rev. Lett.76(Mar, 1996) 1796–1799. https://link.aps.org/doi/10.1103/ PhysRevLett.76.1796

    1996

  80. [81]

    Reconstruction of the jaynes-cummings field state of ionic motion in a harmonic trap,

    D. Lv, S. An, M. Um, J. Zhang, J.-N. Zhang, M. S. Kim, and K. Kim, “Reconstruction of the jaynes-cummings field state of ionic motion in a harmonic trap,”Phys. Rev. A95(Apr, 2017) 043813.https://link.aps.org/doi/10.1103/ PhysRevA.95.043813

    2017

Showing first 80 references.