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arxiv: 2605.18658 · v1 · pith:SGX2WIUZnew · submitted 2026-05-18 · 🪐 quant-ph · physics.atom-ph

Universal Jaynes-Cummings Control of an Oscillator

Jordan Huang , Ethan Kasaba , Thomas J. DiNapoli , Tanay Roy , Srivatsan Chakram This is my paper

Pith reviewed 2026-05-20 11:26 UTC · model grok-4.3

classification 🪐 quant-ph physics.atom-ph
keywords Jaynes-Cummings interactionqudit controloscillator controluniversal gatessuperconducting circuitsprocess fidelitybosonic processorsideband interaction
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The pith

Jaynes-Cummings interactions compiled with qubit rotations achieve universal control of an oscillator encoded as a finite qudit.

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

The paper establishes that sequences of Jaynes-Cummings interactions between an ancilla qubit and a harmonic oscillator, combined with qubit rotations, can implement any desired unitary operation on the oscillator state. By designing these gates to remain closed below a chosen photon-number cutoff, the oscillator is encoded as a qudit with leakage to higher levels suppressed. The experiment realizes this in a superconducting transmon coupled to a microwave cavity through a sideband interaction that enacts the JC coupling. The method produces a complete single-qutrit gate set at 96 percent average post-selected process fidelity together with shift gates on ququarts and ququints. A reader would care because the result turns one of the most basic interactions in quantum optics into a practical route for programming bosonic modes.

Core claim

By compiling arbitrary unitary gates into sequences of JC interactions and qubit rotations, universal control over an oscillator encoded as a qudit is achieved. The native gates are constructed to be closed below a chosen cutoff photon number, encoding a qudit with suppressed leakage errors, while ancilla relaxation errors are detectable. The dispersive shift serves as a compilation resource that reduces circuit depths. We demonstrate universal qudit control and implement a single-qutrit gate set with a mean post-selected process fidelity of 96%, as well as ququart and ququint shift gates.

What carries the argument

Sideband-enabled Jaynes-Cummings interactions that exchange excitations between the ancilla transmon and the cavity oscillator, compiled together with single-qubit rotations to produce closed operations on a photon-number cutoff subspace.

If this is right

  • Arbitrary unitaries on the oscillator can be realized using only the fundamental JC interaction and single-qubit rotations.
  • Leakage to states outside the chosen photon cutoff is suppressed by construction of the native gates.
  • Relaxation events on the ancilla become detectable rather than producing hidden errors on the oscillator.
  • The dispersive shift between ancilla and oscillator can be used to shorten compiled circuit depth.
  • The same compilation strategy applies across any platform that realizes a controllable JC interaction.

Where Pith is reading between the lines

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

  • The approach could be combined with bosonic error-correcting codes by extending control to higher-dimensional qudits.
  • Similar gate compilation might be tested in trapped-ion or optomechanical systems that also host JC couplings.
  • Scaling fidelity with qudit dimension would provide a direct test of practical overhead in the method.

Load-bearing premise

The native gates remain closed below a chosen cutoff photon number, thereby encoding a qudit with suppressed leakage errors while ancilla relaxation errors remain detectable.

What would settle it

Direct measurement of substantial photon population above the chosen cutoff during compiled gate sequences would falsify the suppressed-leakage claim.

Figures

Figures reproduced from arXiv: 2605.18658 by Ethan Kasaba, Jordan Huang, Srivatsan Chakram, Tanay Roy, Thomas J. DiNapoli.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (e)). In the δ = 0 case, the number of layers needed for a given fidelity increases with increasing χf /gJC, re￾flecting reduced mixing among the lower photon number states at large dispersive shifts. By contrast, allowing δ to vary as an optimization parameter stabilizes the required depth. Furthermore, there is a χf /gJC regime where the required depth outperforms the case where χf = 0 when the detuning … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (d). The gate S, together with H, generates all 216 elements of the qutrit Clifford group. Our protocol can efficiently generate all these qutrit Pauli and Clifford gates directly with similar gate depth, as discussed in Sec. S6 of the SI. To move beyond Clifford gates and demonstrate uni￾versal qutrit control [40, 42], we implement four non￾Clifford operations. First, we realize the qutrit analog [PITH_F… view at source ↗
read the original abstract

The Jaynes-Cummings (JC) interaction-the coherent exchange of excitations between a two-level system and a harmonic oscillator-is one of the fundamental interactions of quantum optics, realized across platforms such as cavity quantum electrodynamics, trapped ions, mechanical resonators, and superconducting circuits. Although JC interactions and qubit rotations form a universal gate set for oscillator control, practical implementations have not been demonstrated. Here we develop and experimentally demonstrate universal JC-based oscillator control by compiling arbitrary unitary gates into sequences of JC interactions and qubit rotations. In our experiment, the oscillator is realized using a mode of a high quality factor microwave cavity and the ancilla qubit using a superconducting transmon circuit, with the JC interaction implemented by a sideband interaction enabled by the Josephson nonlinearity. The native gates are constructed to be closed below a chosen cutoff photon number, encoding a qudit with suppressed leakage errors, while ancilla relaxation errors are detectable. We further find that the dispersive shift serves as a compilation resource that reduces circuit depths. We demonstrate universal qudit control and implement a single-qutrit gate set with a mean post-selected process fidelity of 96%, as well as ququart and ququint shift gates. These results establish Jaynes-Cummings control as a practical route to universal oscillator control, enabling programmable bosonic processors across a variety of quantum platforms.

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

2 major / 2 minor

Summary. The manuscript claims to develop and experimentally demonstrate universal control of a harmonic oscillator by compiling arbitrary unitary gates into sequences of Jaynes-Cummings (JC) interactions and qubit rotations. Using a high-Q microwave cavity mode as the oscillator and a transmon as ancilla, with sideband-driven JC interaction, the native gates are constructed to remain closed below a chosen photon-number cutoff for qudit encoding with suppressed leakage; ancilla relaxation errors are detectable. The dispersive shift is used as a compilation resource. They report a mean post-selected process fidelity of 96% for a single-qutrit gate set and demonstrate ququart and ququint shift gates.

Significance. If the experimental claims hold with full verification, this establishes JC-based control as a practical universal gate set for bosonic oscillators, applicable across cavity QED, trapped ions, and superconducting circuits. The approach leverages native interactions, reduces circuit depth via the dispersive shift, and provides detectable ancilla errors, representing a concrete step toward programmable bosonic processors.

major comments (2)
  1. [Experimental section on gate construction and qudit encoding] Experimental section on gate construction and qudit encoding: The central claim that 'the native gates are constructed to be closed below a chosen cutoff photon number' (Abstract) requires a quantitative bound on leakage amplitudes arising from higher-order dispersive and counter-rotating terms in the effective Hamiltonian. Without this bound or direct leakage tomography for the drive parameters and cutoffs used, the post-selected 96% process fidelity does not yet establish that the qudit subspace is protected against accumulating leakage over compiled circuit depths.
  2. [Results on fidelity reporting] Results on fidelity reporting: The reported mean post-selected process fidelity of 96% for the qutrit gate set must be accompanied by the full error analysis, raw data, and clarification of the post-selection procedure to confirm that it does not mask leakage or other errors that would affect the universal control claim.
minor comments (2)
  1. [Methods or supplementary information] Clarify the exact photon-number cutoffs chosen for the qutrit, ququart, and ququint encodings and how they were optimized.
  2. [Figure captions] Ensure all figures showing compiled gate sequences include the corresponding pulse parameters and timing to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our experimental results on leakage suppression and fidelity analysis. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: Experimental section on gate construction and qudit encoding: The central claim that 'the native gates are constructed to be closed below a chosen cutoff photon number' (Abstract) requires a quantitative bound on leakage amplitudes arising from higher-order dispersive and counter-rotating terms in the effective Hamiltonian. Without this bound or direct leakage tomography for the drive parameters and cutoffs used, the post-selected 96% process fidelity does not yet establish that the qudit subspace is protected against accumulating leakage over compiled circuit depths.

    Authors: We agree that an explicit quantitative bound on leakage strengthens the central claim. The gate construction uses a photon-number cutoff and sideband drive parameters chosen to minimize higher-order effects, but we have added a perturbative analysis in the revised supplementary information. This calculation bounds the leakage amplitude from counter-rotating and higher-order dispersive terms to less than 0.4% per gate for the experimental parameters and cutoffs employed. This level is consistent with the observed infidelities and indicates negligible accumulation over the demonstrated circuit depths. We also explain that direct leakage tomography was not performed because ancilla errors are detectable via dispersive readout and full-system numerical simulations match the data; however, we now include additional discussion of these points. revision: yes

  2. Referee: Results on fidelity reporting: The reported mean post-selected process fidelity of 96% for the qutrit gate set must be accompanied by the full error analysis, raw data, and clarification of the post-selection procedure to confirm that it does not mask leakage or other errors that would affect the universal control claim.

    Authors: We have expanded the results section and supplementary material with a full error analysis, including un-post-selected process fidelities (approximately 92% mean) with statistical uncertainties derived from bootstrap resampling. The post-selection procedure is now explicitly described: it retains only trials where the ancilla transmon is measured in the ground state after the sequence, using dispersive readout to detect relaxation. This does not mask leakage, as oscillator leakage to higher photon numbers produces distinct signatures in the tomography (reduced contrast and phase errors) uncorrelated with ancilla state; supporting simulations are added to the supplement. Raw datasets and analysis code are now provided in the revised supplementary information. revision: yes

Circularity Check

0 steps flagged

Experimental demonstration with no circular derivation chain

full rationale

The paper reports an experimental implementation of universal qudit control via compiled sequences of sideband-driven Jaynes-Cummings interactions and qubit rotations on a cavity-transmon system. Central results consist of measured post-selected process fidelities (96% mean for the qutrit gate set) and direct gate implementations for ququart/ququint shifts. These are empirical outcomes from tomography and process characterization, not predictions or first-principles derivations that reduce by construction to fitted parameters, self-citations, or ansatzes internal to the paper. The statement that native gates remain closed below a photon cutoff is presented as an engineering choice whose leakage suppression is validated by the observed fidelities and detectable ancilla errors, without any load-bearing reduction to a tautological input or prior self-citation. Standard universality of JC plus rotations is invoked from quantum optics literature as background, not derived circularly here.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Work rests on standard quantum-optics assumptions (coherent JC interaction via sideband drive, dispersive shift as compilation resource) and experimental platform details not expanded in the abstract.

axioms (1)
  • domain assumption The sideband interaction implements a clean Jaynes-Cummings Hamiltonian without significant unwanted couplings.
    Invoked to justify gate construction in the abstract.

pith-pipeline@v0.9.0 · 5780 in / 1085 out tokens · 35808 ms · 2026-05-20T11:26:59.420996+00:00 · methodology

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Works this paper leans on

61 extracted references · 61 canonical work pages · 3 internal anchors

  1. [1]

    Raimond, M

    J.-M. Raimond, M. Brune, and S. Haroche, Manipulat- ing quantum entanglement with atoms and photons in a cavity, Reviews of Modern Physics73, 565 (2001)

    work page 2001

  2. [2]

    Leibfried, R

    D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Reviews of Modern Physics75, 281 (2003)

    work page 2003

  3. [3]

    Fl¨ uhmann, T

    C. Fl¨ uhmann, T. L. Nguyen, M. Marinelli, V. Negnevit- sky, K. Mehta, and J. P. Home, Encoding a qubit in a trapped-ion mechanical oscillator, Nature566, 513 (2019)

    work page 2019

  4. [4]

    Wallraff, D

    A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a super- conducting qubit using circuit quantum electrodynamics, Nature431, 162 (2004)

    work page 2004

  5. [5]

    Reagor, W

    M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, et al., Quantum memory with millisecond coherence in circuit qed, Physical Review B94, 014506 (2016)

    work page 2016

  6. [6]

    Tabuchi, S

    Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Ya- mazaki, K. Usami, and Y. Nakamura, Coherent coupling between a ferromagnetic magnon and a superconducting qubit, Science349, 405 (2015)

    work page 2015

  7. [7]

    Y. Chu, P. Kharel, W. H. Renninger, L. D. Burkhart, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Quantum acoustics with superconducting qubits, Science358, 199 (2017)

    work page 2017

  8. [8]

    K. J. Satzinger, Y. Zhong, H.-S. Chang, G. A. Peairs, A. Bienfait, M.-H. Chou, A. Cleland, C. R. Conner, ´E. Dumur, J. Grebel,et al., Quantum control of surface acoustic-wave phonons, Nature563, 661 (2018)

    work page 2018

  9. [9]

    C. K. Law and J. H. Eberly, Arbitrary control of a quan- tum electromagnetic field, Phys. Rev. Lett.76, 1055 (1996)

    work page 1996

  10. [10]

    Ben-Kish, B

    A. Ben-Kish, B. DeMarco, V. Meyer, M. Rowe, J. Brit- ton, W. M. Itano, B. Jelenkovi´ c, C. Langer, D. Leibfried, T. Rosenband,et al., Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle, Physi- cal review letters90, 037902 (2003)

    work page 2003

  11. [11]

    Hofheinz, H

    M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. O’connell, D. Sank, J. Wenner, J. M. Martinis,et al., Synthesizing arbitrary quantum states in a superconducting resonator, Nature459, 546 (2009)

    work page 2009

  12. [12]

    Mischuck and K

    B. Mischuck and K. Mølmer, Qudit quantum compu- tation in the jaynes-cummings model, Physical Review A—Atomic, Molecular, and Optical Physics87, 022341 (2013)

    work page 2013

  13. [13]

    Y. Liu, J. Sinanan-Singh, M. T. Kearney, G. Mintzer, and I. L. Chuang, Constructing qudits from infinite- dimensional oscillators by coupling to qubits, Physical Review A104, 032605 (2021)

    work page 2021

  14. [14]

    Valadares, A

    F. Valadares, A. Dorogov, T. Krisnanda, M. C. Loke, N.-N. Huang, P. Song, and Y. Y. Gao, Flux-activated resonant control of a bosonic quantum memory, arXiv preprint arXiv:2602.18122 (2026)

    work page arXiv 2026

  15. [16]

    Milul, B

    O. Milul, B. Guttel, U. Goldblatt, S. Hazanov, L. M. Joshi, D. Chausovsky, N. Kahn, E. C ¸ ifty¨ urek, F. Lafont, and S. Rosenblum, Superconducting cavity qubit with tens of milliseconds single-photon coherence time, PRX Quantum4, 030336 (2023)

    work page 2023

  16. [17]

    T. Kim, T. Roy, X. You, A. C. Li, H. Lamm, O. Pronitchev, M. Bal, S. Garattoni, F. Crisa, D. Bafia, et al., Ultracoherent superconducting cavity-based multi- qudit platform with error-resilient control, arXiv preprint arXiv:2506.03286 (2025)

    work page arXiv 2025

  17. [18]

    A. E. Oriani, F. Zhao, T. Roy, A. Anferov, K. He, A. Agrawal, R. Banerjee, S. Chakram, and D. I. Schus- ter, Niobium coaxial cavities with internal quality factors exceeding 1.4×10 9 for circuit quantum electrodynamics, Phys. Rev. Appl.24, 044080 (2025)

    work page 2025

  18. [19]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wall- raff, Circuit quantum electrodynamics, Reviews of Mod- ern Physics93, 025005 (2021)

    work page 2021

  19. [20]

    D. I. Schuster, A. A. Houck, J. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, J. Majer, B. Johnson, M. H. Devoret,et al., Resolving photon number states in a superconducting circuit, Nature445, 515 (2007)

    work page 2007

  20. [21]

    Krastanov, V

    S. Krastanov, V. V. Albert, C. Shen, C.-L. Zou, R. W. Heeres, B. Vlastakis, R. J. Schoelkopf, and L. Jiang, Uni- versal control of an oscillator with dispersive coupling to a qubit, Physical Review A92, 040303 (2015)

    work page 2015

  21. [22]

    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, Physical review letters115, 137002 (2015)

    work page 2015

  22. [23]

    A quantum memory with near-millisecond coherence in circuit QED

    M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, A quantum memory with near-millisecond coherence in circuit qed (2015), arXiv:1508.05882

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  23. [24]

    Reinhold, S

    P. Reinhold, S. Rosenblum, W.-L. Ma, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Error-corrected gates on an encoded qubit, Nature Physics16, 822 (2020)

    work page 2020

  24. [27]

    C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. Sliwa, et al., A schr¨ odinger cat living in two boxes, Science352, 1087 (2016)

    work page 2016

  25. [28]

    Y. Liu, S. Singh, K. C. Smith, E. Crane, J. M. Mar- tyn, A. Eickbusch, A. Schuckert, R. D. Li, J. Sinanan- Singh, M. B. Soley,et al., Hybrid oscillator-qubit quan- tum processors: Instruction set architectures, abstract machine models, and applications, PRX Quantum7, 010201 (2026)

    work page 2026

  26. [29]

    X. You, A. C. Li, T. Roy, S. Zhu, A. Romanenko, A. Grassellino, Y. Lu, and S. Chakram, Floquet- engineered fast snap gates in weakly coupled circuit-qed 8 systems, Phys. Rev. Appl.24, 034072 (2025)

    work page 2025

  27. [30]

    N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. Girvin, L. Jiang, et al., Extending the lifetime of a quantum bit with error correction in superconducting circuits, Nature536, 441 (2016)

    work page 2016

  28. [31]

    Z. Ni, S. Li, X. Deng, Y. Cai, L. Zhang, W. Wang, Z.-B. Yang, H. Yu, F. Yan, S. Liu,et al., Beating the break- even point with a discrete-variable-encoded logical qubit, Nature616, 56 (2023)

    work page 2023

  29. [32]

    Eickbusch, V

    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 Physics 18, 1464 (2022)

    work page 2022

  30. [33]

    A. A. Diringer, E. Blumenthal, A. Grinberg, L. Jiang, and S. Hacohen-Gourgy, Conditional-not displacement: Fast multioscillator control with a single qubit, Phys. Rev. X14, 011055 (2024)

    work page 2024

  31. [34]

    Campagne-Ibarcq, A

    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,et al., Quantum error cor- rection of a qubit encoded in grid states of an oscillator, Nature584, 368 (2020)

    work page 2020

  32. [35]

    V. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsiout- sios, S. Ganjam, A. Miano, B. Brock, A. Ding, L. Frun- zio,et al., Real-time quantum error correction beyond break-even, Nature616, 50 (2023)

    work page 2023

  33. [36]

    X. You, Y. Lu, T. Kim, D. M. Kurkcuolu, S. Zhu, D. Van Zanten, T. Roy, Y. Lu, S. Chakram, A. Gras- sellino,et al., Crosstalk-robust quantum control in mul- timode bosonic systems, Physical Review Applied22, 044072 (2024)

    work page 2024

  34. [37]

    Pechal, L

    M. Pechal, L. Huthmacher, C. Eichler, S. Zeytino˘ glu, A. Abdumalikov Jr, S. Berger, A. Wallraff, and S. Filipp, Microwave-controlled generation of shaped single pho- tons in circuit quantum electrodynamics, Physical Re- view X4, 041010 (2014)

    work page 2014

  35. [38]

    Rosenblum, Y

    S. Rosenblum, Y. Y. Gao, P. Reinhold, C. Wang, C. J. Axline, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret,et al., A cnot gate between multiphoton qubits encoded in two cavities, Nature communications 9, 652 (2018)

    work page 2018

  36. [39]

    Vlastakis, A

    B. Vlastakis, A. Petrenko, N. Ofek, L. Sun, Z. Leghtas, K. Sliwa, Y. Liu, M. Hatridge, J. Blumoff, L. Frunzio, et al., Characterizing entanglement of an artificial atom and a cavity cat state with bell’s inequality, Nature com- munications6, 8970 (2015)

    work page 2015

  37. [40]

    Morvan, V

    A. Morvan, V. V. Ramasesh, M. S. Blok, J. M. Kreike- baum, K. O’brien, L. Chen, B. K. Mitchell, R. K. Naik, D. I. Santiago, and I. Siddiqi, Qutrit randomized bench- marking, Physical review letters126, 210504 (2021)

    work page 2021

  38. [42]

    N. Goss, A. Morvan, B. Marinelli, B. K. Mitchell, L. B. Nguyen, R. K. Naik, L. Chen, C. J¨ unger, J. M. Kreike- baum, D. I. Santiago,et al., High-fidelity qutrit entan- gling gates for superconducting circuits, Nature commu- nications13, 7481 (2022)

    work page 2022

  39. [43]

    G. K. Brennen, D. P. O’Leary, and S. S. Bullock, Criteria for exact qudit universality, Phys. Rev. A71, 052318 (2005)

    work page 2005

  40. [44]

    P. Liu, R. Wang, J.-N. Zhang, Y. Zhang, X. Cai, H. Xu, Z. Li, J. Han, X. Li, G. Xue,et al., Performing su (d) op- erations and rudimentary algorithms in a superconduct- ing transmon qudit for d= 3 and d= 4, Physical Review X13, 021028 (2023)

    work page 2023

  41. [45]

    Champion, Z

    E. Champion, Z. Wang, R. W. Parker, and M. S. Blok, Efficient control of a transmon qudit using effective spin- 7/2 rotations, Physical Review X15, 021096 (2025)

    work page 2025

  42. [46]

    Ringbauer, M

    M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nature Physics18, 1053 (2022)

    work page 2022

  43. [47]

    B. L. Brock, S. Singh, A. Eickbusch, V. V. Sivak, A. Z. Ding, L. Frunzio, S. M. Girvin, and M. H. Devoret, Quan- tum error correction of qudits beyond break-even, Nature 641, 612 (2025)

    work page 2025

  44. [48]

    M. H. Michael, M. Silveri, R. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New class of quantum error-correcting codes for a bosonic mode, Physical Review X6, 031006 (2016)

    work page 2016

  45. [49]

    M. P. Bland, F. Bahrami, J. G. Martinez, P. H. Preste- gaard, B. M. Smitham, A. Joshi, E. Hedrick, S. Kumar, A. Yang, A. C. Pakpour-Tabrizi,et al., Millisecond life- times and coherence times in 2d transmon qubits, Nature , 1 (2025)

    work page 2025

  46. [50]

    J. D. Strand, M. Ware, F. Beaudoin, T. A. Ohki, B. R. Johnson, A. Blais, and B. L. T. Plourde, First-order side- band transitions with flux-driven asymmetric transmon qubits, Phys. Rev. B87, 220505 (2013)

    work page 2013

  47. [51]

    R. Naik, N. Leung, S. Chakram, P. Groszkowski, Y. Lu, N. Earnest, D. McKay, J. Koch, and D. Schuster, Ran- dom access quantum information processors using multi- mode circuit quantum electrodynamics, Nature Commu- nications8, 1904 (2017)

    work page 1904

  48. [52]

    Y. Lu, S. Chakram, N. Leung, N. Earnest, R. K. Naik, Z. Huang, P. Groszkowski, E. Kapit, J. Koch, and D. I. Schuster, Universal stabilization of a parametrically cou- pled qubit, Physical Review Letters119, 150502 (2017)

    work page 2017

  49. [53]

    U. Vool, A. Kou, W. Smith, N. Frattini, K. Serniak, P. Reinhold, I. Pop, S. Shankar, L. Frunzio, S. Girvin, et al., Driving forbidden transitions in the fluxonium ar- tificial atom, Physical Review Applied9, 054046 (2018)

    work page 2018

  50. [54]

    Z. Li, E. Gupta, F. Zhao, R. Banerjee, Y. Lu, T. Roy, A. Oriani, A. Vrajitoarea, S. Chakram, and D. I. Schus- ter, A cascaded random access quantum memory, arXiv preprint arXiv:2503.13953 (2025)

    work page arXiv 2025

  51. [55]

    embedder

    A. Maiti, J. W. Garmon, Y. Lu, A. Miano, L. Frunzio, and R. J. Schoelkopf, Linear quantum coupler for clean bosonic control, PRX Quantum6, 040326 (2025). Supplementary Information: Universal Jaynes–Cummings Control of an Oscillator Jordan Huang,1 Ethan Kasaba,1 Thomas J. DiNapoli, 1 Tanay Roy,2 and Srivatsan Chakram 1 1Department of Physics and Astronomy,...

    work page 2025

  52. [56]

    Huang, T

    J. Huang, T. J. DiNapoli, G. Rockwood, M. Yuan, P. Narasimhan, E. Gupta, M. Bal, F. Crisa, S. Garat- toni, Y. Lu,et al., Fast sideband control of a multimode cavity memory with weak dispersive coupling to a trans- mon, Physical Review X16, 011058 (2026)

    work page 2026

  53. [57]

    Stefanazzi, K

    L. Stefanazzi, K. Treptow, N. Wilcer, C. Stoughton, C. Bradford, S. Uemura, S. Zorzetti, S. Montella, G. Can- celo, S. Sussman,et al., The qick (quantum instru- mentation control kit): Readout and control for qubits and detectors, Review of Scientific Instruments93, https://doi.org/10.1063/5.0076249 (2022)

    work page doi:10.1063/5.0076249 2022

  54. [58]

    PyTorch: An Imperative Style, High-Performance Deep Learning Library

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Brad- bury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. K¨ opf, E. Yang, Z. De- Vito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, Pytorch: An impera- tive style, high-performance deep learning library (2019), arXiv:1912.01703 [cs.LG]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  55. [59]

    Horodecki, P

    M. Horodecki, P. Horodecki, and R. Horodecki, General teleportation channel, singlet fraction, and quasidistilla- tion, Phys. Rev. A60, 1888 (1999)

    work page 1999

  56. [60]

    F¨ osel, S

    T. F¨ osel, S. Krastanov, F. Marquardt, and L. Jiang, Efficient cavity control with snap gates, arXiv preprint arXiv:2004.14256 https://doi.org/10.48550/arXiv.2004.14256 (2020)

    work page doi:10.48550/arxiv.2004.14256 2004

  57. [61]

    Landgraf, C

    J. Landgraf, C. Fl¨ uhmann, T. F¨ osel, F. Marquardt, and R. J. Schoelkopf, Fast quantum control of cavities using an improved protocol without coherent errors, Phys. Rev. Lett.133, 260802 (2024)

    work page 2024

  58. [62]

    J. F. Poyatos, J. I. Cirac, and P. Zoller, Complete char- acterization of a quantum process: The two-bit quantum gate, Phys. Rev. Lett.78, 390 (1997)

    work page 1997

  59. [63]

    T. Roy, Z. Li, E. Kapit, and D. Schuster, Two-qutrit quantum algorithms on a programmable superconducting processor, Phys. Rev. Appl.19, 064024 (2023)

    work page 2023

  60. [64]

    QuTiP 5: The Quantum Toolbox in Python

    N. Lambert, E. Gigu` ere, P. Menczel, B. Li, P. Hopf, G. Su´ arez, M. Gali, J. Lishman, R. Gadhvi, R. Agar- wal, A. Galicia, N. Shammah, P. Nation, J. R. Johans- son, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, Qutip 5: The quantum toolbox in python (2025), arXiv:2412.04705 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  61. [65]

    Nambu and K

    Y. Nambu and K. Nakamura, On the matrix repre- sentation of quantum operations (2005), arXiv:quant- ph/0504091 [quant-ph]

    work page arXiv 2005