Optimization of Two-Qubit Gates in Tunable-Coupler Architectures Using Single Flux Quantum Control

Bohdan Kulchytskyy; Boyan Torosov; Florian Hopfmueller; John Gunderson; Pooya Ronagh; Xiangzhou Kong

REVIEW 2 major objections 6 minor 28 references

Optimization of Two-Qubit Gates in Tunable-Coupler Architectures Using Single Flux Quantum Control

T0 review · 2 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A continuous-embedding optimizer turns discrete single-flux-quantum pulses into two-qubit gates with simulated fidelities near 99.99 percent.

desk verdict Gradient-based continuous embedding for SFQ two-qubit gates is a genuine step forward, but the missing post-discretization fidelity check leaves the headline numbers unverified against physically realizable pulses. read the letter →

arxiv 2412.15816 v1 pith:AYQ33YKO submitted 2024-12-20 quant-ph

Boyan Torosov , Bohdan Kulchytskyy , Florian Hopfmueller , John Gunderson , Xiangzhou Kong , Pooya Ronagh This is my paper · ORCID

classification quant-ph PACS 03.67.Lx85.25.-j

keywords single-flux-quantumcontroltunable-couplerarchitecturetransmonqubitstwo-qubitgatesgradient-basedoptimalcontinuousembeddingfSimgateCZ/CNOT

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes a way to program two-qubit gates on a chip with two transmon qubits (a common type of superconducting qubit) coupled through a tunable coupler, using single-flux-quantum (SFQ) pulses, short digital voltage spikes each carrying one flux quantum, instead of microwave control. The central claim is that the discrete, bit-like nature of these pulses can be handled by a continuous embedding: relax each pulse to a continuous amplitude, let gradient descent optimize the gate fidelity, and add penalties that pull the amplitudes back to physical 0-or-1 values. In simulation this yields fSim gates (an entangling $XX+YY$ rotation with a $ZZ$ phase) with average fidelity around 99.99% and CZ and CNOT gates above 99.9%, at durations under 80 ns. The paper also gives a semi-analytical construction of CZ and CNOT from two fSim layers plus single-qubit rotations, cutting the memory needed to store pulse schedules from thousands of bits per qubit to under two hundred. The reported fidelities are simulated, not measured, and the payoff would be a digital, cryogenic-friendly control route to scalable transmon processors.

What carries the argument

Two mechanisms carry the argument. The first is the continuous embedding of the discrete SFQ control: each pulse amplitude $\theta^i_{\rm sfq}\in[0,1]$ is a relaxed presence/absence bit, and the coupler on/off times are real-valued. The cost function (8) adds a binarizing penalty $P$ and a log-barrier smoothing term $\Phi$, with hyperparameters annealed on a schedule, so gradient descent can navigate the smooth landscape while the final solution is pushed toward physical 0/1 pulses and clock-aligned times. The second is the fSim-pair decomposition identity for CZ, hence CNOT: with $\Gamma(\theta,\phi)=e^{-i\theta(XX+YY)/2}e^{-i\phi ZZ/4}$, the circuit $R_x(\xi)\Gamma(\theta,\phi)R_x(2\alpha)\Gamma(-\theta,\phi)R_x(\xi)R_x(\eta)R_x(-\eta)$ realizes CZ up to equal single-qubit $Z$ rotations whenever Eq. (14) holds, giving a continuous family of decompositions parameterized by the fSim angles; the authors pick the member near a $\sqrt{i\mathrm{SWAP}}$ gate (hold time 17 ns, total duration 23.4 ns) as the shortest practical native gate. The simulation itself uses a five-level-per-transmon charge basis, symmetric orthogonalization of the degenerate logical states at the idling point, and fourth-order product-formula time evolution, all written with auto-differentiation so gradients of the roughly 6400 parameters cost about two forward passes.

What would settle it

Take one optimized CZ sequence from Section V, round every relaxed pulse amplitude to the nearest binary value (0 or 1), keep the coupler times on the SFQ clock, and re-simulate the resulting pulse train under the same Hamiltonian; if the average fidelity drops below the reported 0.999 (or below 0.9999 for the fSim gate), the claim that these discrete pulse trains realize the reported fidelities is not yet established.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the binary combinatorial problem of choosing where to place SFQ kicks, and when to move the coupler, can be solved as a smooth optimization problem. The variational parameters are, for every clock tick and every qubit, a binary amplitude indicating the presence or absence of an SFQ pulse, together with the start and end times of the coupler excursions. Relaxing the amplitudes to the interval $[0,1]$ and the coupler times to real values turns the cost $C(\vec\theta)=1-F(\vec\theta)+P(\vec\theta)+\Phi(\vec\theta)$ into a differentiable function, with $P$ penalizing non-binary amplitudes and misaligned clock times and $\Phi$ a logarithmic barrier that keeps the search away from boundaries. Minimizing this cost by second-order gradient descent reproduces, in simulation, fSim gates with average fidelity on the order of 0.9999 and CZ and CNOT gates above 0.999, at SFQ clock frequencies of 20 and 40 GHz and durations of 70-80 ns. The semi-analytical alternative exploits the identity that a CZ gate can be decomposed into two fSim gates, with parameters satisfying Eq. (14), plus single-qubit rotations; choosing an fSim hold time near 17 ns that corresponds to an $XX+YY$ angle close to $\pi/4$ reaches fidelities close to 0.999 while storing each qubit's pulse sequence in under 200 bits.

Load-bearing premise

The paper does not state whether the fidelities in Section V are computed before or after the relaxed continuous pulse parameters of Section IV A are discretized to binary SFQ kicks; if the discrete pulse train is not re-simulated, the headline numbers may describe pulses a real controller cannot produce.

Editorial extensions

If this is right

SFQ control becomes a credible digital alternative to microwave control for two-qubit gates in tunable-coupler transmon processors, with simulated fidelities comparable to microwave-based gates.
Because the gate set is generated by streams of identical flux-quantum pulses rather than shaped microwave waveforms, the controller can be moved close to the cryogenic chip, easing cabling and heat-load constraints.
The analytical fSim-pair decomposition reduces the memory required to store a CZ or CNOT schedule from 3200 bits per qubit to under 200 bits, simplifying the classical-to-quantum interface.
Higher SFQ clock frequencies and longer gate durations both lower infidelity, so faster future SFQ controllers can trade speed against gate quality.
With both qubits idling at the same target frequency, single-qubit gates are obtained without qubit-specific optimization, which simplifies scaling to more qubits.

Reading between the lines

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

The paper reports simulation-only fidelities; a direct test is to round the optimized continuous amplitudes to binary kicks and re-simulate the resulting pulse train, since the paper does not state whether the discretized sequences were re-evaluated.
The continuous-embedding recipe is generic enough that the same penalty-and-barrier schedule could be applied to other discrete-control problems, such as flux-latching gates or DAC-step control, where combinatorial searches are currently the default.
The decomposition family in Eq. (14) leaves freedom in choosing the fSim angles; that freedom could be searched over to find implementations that are more robust to parameter drift or that minimize leakage, rather than only the shortest one selected here.
If the discretized schedules hold up, the next likely bottleneck is error accumulation across many gates and idling intervals, since the idling point still carries residual conditional phases not characterized in the paper.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The useful contribution here is the optimization method: relaxing discrete SFQ pulse presences to continuous variables and using JAX autodiff with L-BFGS-B to hit 99.99% fSim and >99.9% CZ/CNOT in simulation. That is a real improvement over the genetic-algorithm approach in Refs. [9,12], and the analytical fSim-pair decomposition with memory reduction is a nice practical add-on.

The Hamiltonian model and simulation basis are standard and carefully built: charge basis, diagonalization, five-level truncation, Löwdin orthogonalization for the degenerate logical states, Suzuki-Trotter. The calibration of idling fluxes is sensible. The paper is honest that this is simulation, and it does not oversell experimental readiness.

The main soft spot is the one the stress-test flags: Sec. IV A relaxes the binary pulse presence to continuous values and adds penalties, but there is no statement that the final optimized parameters are exactly 0/1, and no re-simulation after rounding. The penalty schedule is soft—gamma ends around 12, mu decays to roughly 1e-6—so nothing forces exact binary values. Fig. 4 shows binary-looking kicks, but that is a plot, not a check. The reported fidelities may be for continuous pulses, which an SFQ source cannot produce. This is not a fatal flaw; the fix is straightforward: round, re-simulate, report. But as written, the headline number for a physical pulse train is unverified. A second, smaller gap: no code or data, so the optimization details are not reproducible from the text alone. The 5-level truncation and delta-function kick model are standard in the subfield, so I would not call them flaws, though an error budget would strengthen the paper.

The citation pattern is fine; the self-citation to Ref. [21] is to the single-qubit sequences they actually use.

This paper is for people working on SFQ control and cryogenic digital control architectures. It deserves a serious referee: the method is novel and the results are plausible, but the authors need to close the discretization gap and, ideally, release code. Send it to review, with a request for a post-rounding fidelity report and code.

Referee Report

2 major / 6 minor

Summary. This paper presents two approaches for realizing two-qubit gates (fSim, CZ, CNOT) in a tunable-coupler transmon architecture controlled by single-flux-quantum (SFQ) pulses. The first approach relaxes the discrete SFQ pulse amplitudes to continuous variables and uses gradient-based optimization with penalties to drive them toward binary values. The second approach uses an exact decomposition of CZ/CNOT into two fSim gates and single-qubit rotations, using a previously reported SFQ-based single-qubit control method. The authors report simulated average gate fidelities of about 99.99% for fSim and above 99.9% for CZ and CNOT, and show that the decomposition method requires significantly less memory to store the pulse sequences.

Significance. If the reported fidelities are achieved for physically realizable binary pulse sequences, the paper demonstrates a scalable, microwave-free route to high-fidelity two-qubit gates, which would be an important step for SFQ-based quantum control. The use of auto-differentiation for continuous embedding of discrete pulses is a practical technique, and the analytical decomposition provides a compact, memory-efficient representation. However, the manuscript does not presently demonstrate that the optimized continuous pulse parameters are converted to binary SFQ sequences without significant fidelity loss, which is essential for the physical relevance of the headline numbers. The paper is therefore interesting but requires a key verification before the claims can be accepted.

major comments (2)

[Sec. IV A, Eqs. (8)-(10); Sec. V, Figs. 4-5] The optimization relaxes discrete SFQ amplitudes to continuous values in [0,1] and adds the penalty P and the logarithmic barrier Φ. Because the barrier in Eq. (10) keeps the amplitudes strictly in the interior of the interval during the run, and the penalty weight γ is finite at the end of the schedule, the optimized parameters are not guaranteed to be exactly binary. The manuscript never states that the final parameters are thresholded to 0 or 1, nor that the resulting binary pulse train is re-simulated. Since each SFQ pulse has a quantized area, the fidelities reported for gradient-optimized CZ and CNOT gates in Fig. 5 and in the abstract likely describe continuous drive amplitudes that an SFQ source cannot produce. Please provide the fidelity of the thresholded/rounded binary sequence, or explicitly demonstrate that the optimizer converges to exact binary values within a specified tolerance.
[Sec. V, final paragraph] The memory comparison between the optimized and decomposition-based sequences (3200 vs. less than 200 bits per qubit) is presented without the encoding details. The optimized sequence is a raw per-slot binary pulse train, while the decomposition exploits the encoding of Ref. [21] and the repeated structure of the sequence. Please specify the encoding rules and the exact bit-count calculation so that the claimed memory reduction can be reproduced.

minor comments (6)

[Abstract] The phrase 'average a gate fidelity' should be 'average gate fidelity'.
[Sec. I] Ref. [21] is a preprint by overlapping authors; the text should note that it is not yet peer-reviewed, if that is the case.
[Sec. IV A] The schedule 'after every sequence of 20 parameter updates' is ambiguous; please specify whether this is 20 gradient steps or 20 L-BFGS-B iterations.
[Sec. V, Fig. 5] The y-axis of Fig. 5 is logarithmic with a range that makes exact infidelities for the best points hard to read; consider adding numerical values in the text.
[Sec. V, Fig. 4 caption] The sentence 'The four kick plots in the top and middle panels correspond to the four possible SFQ-clock slots during a qubit period' could be clarified with a concrete example of how the slots are indexed.
[Sec. III A] The truncation to n = ±50 and five levels is stated, but there is no convergence check with respect to the truncation; a brief statement that the results are converged would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the optimization target is independent of the control parameters, the fSim decomposition comes from an external reference, and the only overlapping-author citation is used as an input rather than as a load-bearing definition.

full rationale

The derivation is self-contained in the circularity sense. The reported gate fidelities in Sec. V are the optimization objective C = 1 - F (Eq. 8), but the map from SFQ pulse parameters and coupler excursions to the unitary evolution is an independently specified circuit-QED Hamiltonian (Eqs. 1-5) with fixed circuit parameters; high fidelity is therefore not imposed by construction. The fSim-based CZ/CNOT decomposition is taken from Ref. [16] (an external source, Arute et al.), and Eqs. (13)-(14) are exact identities for ideal fSim gates, while the physical fSim fidelity is evaluated separately in Fig. 2. The only overlapping-author citation, Ref. [21], supplies single-qubit SFQ rotation sequences that serve as inputs to the decomposition; the paper re-evaluates those sequences in its own architecture in Fig. 3 rather than defining the two-qubit result through them. The continuous-embedding penalty in Eqs. (9)-(10) is a soft regularizer, and the absence of an explicit post-binarization re-evaluation is a physical-realism or correctness concern, not a circularity: it does not make any reported quantity equal to its own input. No step was found where a predicted result reduces by construction to a fitted parameter or to the authors' own uniqueness claim.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim does not introduce new physical entities. It relies on a calibrated circuit model, a standard decomposition, and several modeling approximations (delta kicks, 5-level truncation, no decoherence). The main unverified step is the mapping from relaxed continuous parameters back to exactly binary SFQ pulses.

free parameters (4)

Phi_off = [0.130, 0.352, 0.130] Phi_0
Idling flux values calibrated numerically to equalize qubit frequencies and null the effective coupling (Sec. III A).
Phi_on = [0.130, 0.376, 0.130] Phi_0
Coupler on-point flux chosen for two-qubit interaction (Sec. III A).
fSim hold time = 17 ns
Chosen to set the iSWAP angle near pi/4 and satisfy the decomposition conditions (Sec. IV B, Fig. 2).
gamma and mu schedule = gamma_0=1e-5, mu_0=1, factor 1.1 per 20 updates
Hand-picked optimization hyperparameters controlling binarization and smoothing; they tune the search, not the physics (Sec. IV A).

assumptions (5)

domain assumption SFQ pulses can be modeled as delta-function voltage kicks (Ref. [6]).
Used to write the drive term H_d in Eq. (5); if pulse duration or shape matters, the optimized sequences may not transfer to hardware.
domain assumption Each transmon can be truncated to five energy levels in simulation.
Used in Sec. III A; leakage to higher levels is assumed negligible for the fidelity computation.
domain assumption Decoherence (T1, T2) is neglected during gate execution.
Fidelities are gate fidelities in a closed system; no relaxation or dephasing is included in the model (Sec. II-III).
domain assumption The logical subspace is defined by joint eigenstates of the idle Hamiltonian; idling does not produce leakage.
Sec. III B; the construction assumes the logical states are exact eigenstates so no transitions occur during idling.
standard math The CZ-to-two-fSim decomposition from Ref. [16] is exact and holds for the native gate parameters.
Used in Sec. IV B, Eqs. (12)-(14); conditions (14a,b) must be satisfied, which guides the hold-time choice.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Optimization of Two-Qubit Gates in Tunable-Coupler Architectures Using Single Flux Quantum Control." pith.science (2026). https://pith.science/paper/AYQ33YKO

@misc{pith2026241215816,
  author       = {Pith},
  title        = {Pith review of: Optimization of Two-Qubit Gates in Tunable-Coupler Architectures Using Single Flux Quantum Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AYQ33YKO}},
  note         = {Machine review of arXiv:2412.15816}
}

read the original abstract

We present a gradient-based method to construct high-fidelity, two-qubit quantum gates in a system consisting of two transmon qubits coupled via a tunable coupler. In particular, we focus on single flux quantum (SFQ) pulses as a promising and scalable alternative to traditional control schemes that use microwave electronics. We develop a continuous embedding scheme to optimize these discrete pulses, taking advantage of auto-differentiation of our model. This approach allows us to achieve fSim-type gates with average gate fidelities on the order of 99.99% and CZ and CNOT gates with fidelities above 99.9%. Furthermore, we provide an alternative semi-analytical construction of these gates via an exact decomposition using a pair of fSim gates which leads to the reduction in memory required to store the associated pulse sequences.

Figures

Figures reproduced from arXiv: 2412.15816 by the authors.

**Figure 2.** FIG. 2. Infidelity of the fSim gate as a function of the hold [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Infidelities of single-qubit rotations for different clock [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Control sequences used to produce a CZ gate us [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 6.** Figure 6: FIG. 6. Control sequences used to produce a CZ gate us [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 25 canonical work pages

[21]

Compact Pulse Schedules for High-Fidelity Single-Flux Quantum Qubit Control

R. Shillito, F. Hopfmueller, B. Kulchytskyy, and P. Ron- agh, Compact pulse schedules for high-fidelity single-flux quantum qubit control, arXiv:2309.04606 (2023)

work page Pith review arXiv 2023
[1]

Krinner, S

S. Krinner, S. Storz, P. Kurpiers, P. Magnard, J. Hein- soo, R. Keller, J. Luetolf, C. Eichler, and A. Wallraff, Engineering cryogenic setups for 100-qubit scale super- conducting circuit systems, EPJ Quantum Technology 6, 2 (2019)

2019
[2]

Lin and V

J.-C. Lin and V. Semenov, Timing circuits for rsfq digital systems, IEEE transactions on applied superconductivity 5, 3472 (1995)

work page 1995
[3]

C. A. Mancini and M. F. Bocko, Phase-locked operation of rsfq ring oscillators, Superconductor Science and Tech- nology 12, 789 (1999)

work page 1999
[4]

Leonard Jr, M

E. Leonard Jr, M. A. Beck, J. Nelson, B. G. Christensen, T. Thorbeck, C. Howington, A. Opremcak, I. V. Pech- enezhskiy, K. Dodge, N. P. Dupuis, et al., Digital coher- ent control of a superconducting qubit, Physical Review Applied 11, 014009 (2019)

work page 2019
[5]

K. Li, R. McDermott, and M. G. Vavilov, Hardware- efficient qubit control with single-flux-quantum pulse se- quences, Physical Review Applied 12, 014044 (2019)

work page 2019
[6]

McDermott and M

R. McDermott and M. G. Vavilov, Accurate qubit control with single flux quantum pulses, Physical Review Applied 2, 014007 (2014)

work page 2014
[7]

L. Howe, M. Castellanos-Beltran, A. Sirois, D. Olaya, J. Biesecker, P. Dresselhaus, S. P. Benz, and P. Hop- kins, Digital control of a superconducting qubit using a Josephson pulse generator at 3K, PRX Quantum 3, 010350 (2022)

work page 2022

Show all 28 references

[8]

C.-H. Liu, A. Ballard, D. Olaya, D. R. Schmidt, J. Biesecker, T. Lucas, J. Ullom, S. Patel, O. Rafferty, A. Opremcak, et al., Single flux quantum-based digital con- trol of superconducting qubits in a multichip module, PRX Quantum 4, 030310 (2023)

2023
[9]

P. J. Liebermann and F. K. Wilhelm, Optimal qubit con- trol using single-flux quantum pulses, Physical Review Applied 6, 024022 (2016)

2016
[10]

McDermott, M

R. McDermott, M. Vavilov, B. Plourde, F. Wilhelm, P. Liebermann, O. Mukhanov, and T. Ohki, Quantum– classical interface based on single flux quantum digi- tal logic, Quantum Science and Technology 3, 024004 (2018)

2018
[11]

Dalgaard, F

M. Dalgaard, F. Motzoi, J. J. Sørensen, and J. Sher- son, Global optimization of quantum dynamics with Al- phaZero deep exploration, NPJ Quantum Information 6, 6 (2020)

2020
[12]

M. R. Jokar, R. Rines, and F. T. Chong, Practical impli- cations of SFQ-based two-qubit gates, Proceedings of the 2021 IEEE International Conference on Quantum Com- puting and Engineering (QCE), pp. 402–412 (2021)

2021
[13]

M. R. Jokar, R. Rines, G. Pasandi, H. Cong, A. Holmes, Y. Shi, M. Pedram, and F. T. Chong, DigiQ: A scalable digital controller for quantum computers using SFQ logic, Proceedings of the 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA), pp. 400...

2022
[14]

Y. Wang, W. Gao, K. Liu, B. Ji, Z. Wang, and Z. Lin, Single-flux-quantum-activated controlled-Z gate for transmon qubits, Physical Review Applied 19, 044031 (2023)

2023
[15]

F. Yan, P. Krantz, Y. Sung, M. Kjaergaard, D. L. Camp- bell, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Tunable coupling scheme for implementing high-fidelity two-qubit gates, Phys. Rev. Appl. 10, 054062 (2018)

2018
[16]

Arute, K

F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. 8 Buell, et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019)

2019
[17]

Acharya, I

R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, M. Ans- mann, F. Arute, K. Arya, A. Asfaw, R. B. J. Atalaya, et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature 614, 676 (2023)

2023
[18]

Stehlik, D

J. Stehlik, D. M. Zajac, D. L. Underwood, T. Phung, J. Blair, S. Carnevale, D. Klaus, G. Keefe, A. Carniol, M. Kumph, et al., Tunable coupling architecture for fixed-frequency transmon superconducting qubits, Phys- ical Review Letters 127, 080505 (2021)

2021
[19]

E. A. Sete, V. Tripathi, J. A. Valery, D. Lidar, and J. Y. Mutus, Error budget of a parametric resonance en- tangling gate with a tunable coupler, Physical Review Applied 22, 014059 (2024)

2024
[20]

Y. Sung, L. Ding, J. Braum¨ uller, A. Veps¨ al¨ ainen, B. Kannan, M. Kjaergaard, A. Greene, G. O. Samach, C. McNally, D. Kim, et al., Physical Review X 11, 021058 (2021)

2021
[22]

A. F. Kirichenko, A. Jafari-Salim, P. Truitt, N. K. Katam, C. Jordan, and O. A. Mukhanov, System and method of flux bias for superconducting quantum cir- cuits, U.S. Patent Application 17/838,207 (2022)

2022
[23]

Vool and M

U. Vool and M. Devoret, Introduction to quantum elec- tromagnetic circuits, Int. J. Circuit Theory Appl.45, 897 (2017)

2017
[24]

Mayer, On L¨ owdin’s method of symmetric orthogonal- ization, Int

I. Mayer, On L¨ owdin’s method of symmetric orthogonal- ization, Int. J. Quantum Chem. 90, 63 (2002)

2002
[25]

Murray and K.-M

W. Murray and K.-M. Ng, An algorithm for nonlinear optimization problems with binary variables, Comput. Optim. Appl. 47, 257 (2010)

2010
[26]

Bradbury, R

J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. Vander- Plas, S. Wanderman-Milne, and Q. Zhang, JAX: com- posable transformations of Python+NumPy programs (2018)

2018
[27]

Virtanen, R

P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, ˙I. Polat, Y. Feng...

2020
[28]

O. A. Mukhanov, Rapid single flux quantum (rsfq) shift register family, IEEE Trans. Appl. Supercond. 3, 2578 (1993)

1993

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [21]

Compact Pulse Schedules for High-Fidelity Single-Flux Quantum Qubit Control

R. Shillito, F. Hopfmueller, B. Kulchytskyy, and P. Ron- agh, Compact pulse schedules for high-fidelity single-flux quantum qubit control, arXiv:2309.04606 (2023)

work page Pith review arXiv 2023

[2] [1]

Krinner, S

S. Krinner, S. Storz, P. Kurpiers, P. Magnard, J. Hein- soo, R. Keller, J. Luetolf, C. Eichler, and A. Wallraff, Engineering cryogenic setups for 100-qubit scale super- conducting circuit systems, EPJ Quantum Technology 6, 2 (2019)

2019

[3] [2]

Lin and V

J.-C. Lin and V. Semenov, Timing circuits for rsfq digital systems, IEEE transactions on applied superconductivity 5, 3472 (1995)

work page 1995

[4] [3]

C. A. Mancini and M. F. Bocko, Phase-locked operation of rsfq ring oscillators, Superconductor Science and Tech- nology 12, 789 (1999)

work page 1999

[5] [4]

Leonard Jr, M

E. Leonard Jr, M. A. Beck, J. Nelson, B. G. Christensen, T. Thorbeck, C. Howington, A. Opremcak, I. V. Pech- enezhskiy, K. Dodge, N. P. Dupuis, et al., Digital coher- ent control of a superconducting qubit, Physical Review Applied 11, 014009 (2019)

work page 2019

[6] [5]

K. Li, R. McDermott, and M. G. Vavilov, Hardware- efficient qubit control with single-flux-quantum pulse se- quences, Physical Review Applied 12, 014044 (2019)

work page 2019

[7] [6]

McDermott and M

R. McDermott and M. G. Vavilov, Accurate qubit control with single flux quantum pulses, Physical Review Applied 2, 014007 (2014)

work page 2014

[8] [7]

L. Howe, M. Castellanos-Beltran, A. Sirois, D. Olaya, J. Biesecker, P. Dresselhaus, S. P. Benz, and P. Hop- kins, Digital control of a superconducting qubit using a Josephson pulse generator at 3K, PRX Quantum 3, 010350 (2022)

work page 2022