Nondegenerate Josephson Mixers with Enhanced Bandwidth and Saturation Power for Quantum Signal Amplification and Transduction

Baleegh Abdo; Corrado Mancini; Dongbing Shao; Jae-woong Nah; Oblesh Jinka; Shayne Cairns; Srikanth Srinivasan; Thomas McConkey; Vincent Arena

REVIEW 3 major objections 4 minor 72 references

Nondegenerate Josephson Mixers with Enhanced Bandwidth and Saturation Power for Quantum Signal Amplification and Transduction

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read The paper shows that nondegenerate Josephson mixers, traditionally narrowband and low-power devices, can be engineered to amplify over roughly 400 MHz and convert over roughly 700 MHz while staying near the quantum limit, by coupling four l

desk verdict First impedance-matched nondegenerate JMs beat the bandwidth/saturation bottleneck, but the data are single-chip and the theory curves are fits, not predictions. read the letter →

arxiv 2508.06636 v1 pith:SL25DJCX submitted 2025-08-08 quant-ph

Baleegh Abdo , Dongbing Shao , Shayne Cairns , Jae-woong Nah , Oblesh Jinka , Srikanth Srinivasan , Thomas McConkey , Vincent Arena

show 1 more author

Corrado Mancini

This is my paper

classification quant-ph

keywords Josephsonringmodulatornondegeneratethree-wavemixingquantum-limitedamplifiernoiselessfrequencyconversionimpedancematchingnetworkbandwidthenhancementsaturationpowermultiplexedqubitreadout

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 tries to prove that the two classic limitations of resonator-based nondegenerate Josephson mixers—narrow bandwidth and low saturation power—can be overcome at the same time rather than traded off. The authors redesign the Josephson ring modulator's inductances to suppress higher-order mixing terms and insert lumped-element coupled-mode networks between the ring modulator and each differential port, giving four coupled modes per port. Measured devices amplify over about 400 MHz with saturation near -110 dBm and convert over about 700 MHz with saturation near -91 dBm, while adding only about 0.5-0.6 noise photons. A low-external-quality-factor resonant-mode design operated in conversion reaches about 670 MHz bandwidth and -86 dBm saturation. If these results hold, a single such mixer could serve frequency-multiplexed qubit readout, noiseless frequency transduction, and continuous-variable entanglement generation in large quantum processors.

What carries the argument

The load-bearing object is the lumped-element coupled-mode impedance-matching network: three capacitively coupled parallel LC resonators inserted between each differential port and the JRM, designed from a 4-pole Chebyshev prototype via admittance inverters J_{ij,k}. This network shapes the frequency response so that the amplifier no longer follows the amplitude-gain-bandwidth product sqrt(G)B = gamma, and it lowers the pump power needed for a given gain by raising the filter order. The JRM is modeled as a parametrically modulated mutual inductance M(t) = delta M cos(omega_p t) with no passive coupling, and its energy expansion shows the desired trilinear term proportional to varphi_a varphi

What would settle it

Fabricate a second batch of the coupled-mode JM design, extract the 22 LC values from the flux-dependent phase response, and compare them with the design tables. If devices whose extracted capacitances deviate by more than a few percent still show the 400/700 MHz bandwidths and -110/-91 dBm saturation points, the claimed sensitivity is wrong; conversely, if one or two mismatched LC resonators reliably produce the observed out-of-band dips and collapse the in-band bandwidth, the mechanism is confirmed.

Watch

Extended reading notes

Core claim

The central claim is that the narrow dynamic bandwidth and low saturation power of Josephson mixers built around a Josephson ring modulator are not intrinsic, but can be engineered away. The authors extend the coupled-mode impedance-matching technique, previously applied to grounded SQUID-based parametric devices, to the four-node JRM, which cannot be grounded without destroying its nondegenerate three-wave mixing. Each differential port is loaded by three capacitively coupled parallel LC resonators, so the whole device presents four coupled modes per port. On the nonlinear side, they choose an inductance ratio beta = L_J0/L_in around 3.6-4.4, dilute the JRM nonlinearity by lowering the part

Load-bearing premise

The central claim depends on the lumped-element capacitors and inductors (about 22 values in the coupled-mode devices) being fabricated accurately within a few percent of design, and the authors state the response is sensitive to systematic and random fabrication variations, especially in the capacitances.

Editorial extensions

If this is right

At a 70 MHz channel spacing, the coupled-mode amplifier can process about 6 frequency-multiplexed readout signals and the converter about 11, per the authors' estimate, up from the one or two tones conventional JMs handle.
The measured saturation powers, about -110 dBm in amplification and -91 to -86 dBm in conversion, reach the range previously associated with traveling-wave parametric amplifiers, but with only four Josephson junctions.
Added noise of 0.5-0.6 photons shows the bandwidth and saturation gains do not sacrifice quantum-limited operation.
A resonant-mode converter with low external quality factor reaches about 670 MHz bandwidth and -86 dBm saturation, indicating that noiseless frequency conversion can be made wide enough to cover a full qubit readout band.
The devices open routes to frequency-multiplexed readout, unidirectional routing of quantum signals, and continuous-variable entanglement generation in modular quantum networks.

Reading between the lines

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

If the same Chebyshev coupled-mode synthesis can be applied to other floating multi-node nonlinear elements, the bandwidth enhancement may generalize beyond JRM-based devices, for example to SNAIL-based or rf-SQUID converters that cannot be grounded.
The multiplexing count of 6 and 11 signals assumes a fixed 70 MHz channel spacing; sharper filter prototypes could push the channel count higher, since the authors note the saturation power alone would allow tens of tones in amplification and hundreds in conversion.
Because conversion bandwidth is not governed by the amplitude-gain-bandwidth product, an impedance-matched transducer can be optimized for bandwidth nearly independently of gain, suggesting a modular quantum-link architecture where one converter serves many qubit frequencies.
The reported device performance depends on about 22 lumped-element values staying within a few percent of design; if fabrication variability can be tightened, coupled-mode JMs could become a standard multiplexed readout front-end, whereas on-chip tuning would otherwise be needed.

Share X Bluesky LinkedIn Reddit HN

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

Here's my take. This paper delivers a real first: impedance-matched nondegenerate Josephson mixers built around a four-node JRM, with coupled-mode networks on both ports. The headline numbers hold up as measurements: about 400 MHz of gain bandwidth at 10 dB for the amplifier, about 700 MHz conversion bandwidth for the converter, and saturation powers around -110 and -91 dBm, respectively. That is an order-of-magnitude improvement over the resonator-based JM baselines, and the direct reflection, transmission, saturation, and noise-rise data support it. The paper is also unusually honest: it spells out the cable-ripple problem, the few-percent sensitivity of the 22-parameter matching networks, and the convergence limits of the harmonic-balance simulations.

The soft spots are real but not fatal. The leftover author note in the Fig. 11 gutter about the noise-rise fit being off by 0.7 dB is sloppy and means the nadd values of 0.5-0.6 have a small, acknowledged correction. That is a minor flaw, not a dealbreaker. More substantive: the calculated and simulated responses are not independent confirmations. The circuit parameters come from fits to the same devices' flux-dependent resonances, the Chebyshev coefficients and |Ra|,|Rb| were tweaked in simulation, and the flux/pump settings were treated as degrees of freedom. So the theory curves show consistency, not prediction. Still, standard for this kind of device paper. The single-device-per-design issue is the one I'd push on. Only one JM3 and one JM4 were measured, and the paper admits the fabricated values need to be within a few percent. The observed Ca variation between JM1 and JM2 (~4%) shows that tolerance is not always met. The out-of-band dips are likely the consequence. That undercuts the "blueprint" claim in Sec. VII, but not the demonstration that a working chip can achieve those numbers.

I'd send this to peer review. It's a strong experimental result with acknowledged limitations. The referee should ask for a corrected noise-fit analysis, error bars on the P1dB points, and a softer claim in the conclusion about reproducibility. I'd cite it and bring it to reading group.

Referee Report

3 major / 4 minor

Summary. The paper reports a redesign of nondegenerate Josephson mixers (JMs) based on Josephson ring modulators, combining inductance-ratio optimization with lumped-element coupled-mode impedance-matching networks. Four devices are presented: two resonant-mode JMs (JM1, JM2) and two coupled-mode JMs (JM3, JM4), operated in amplification and frequency conversion. The headline claims are bandwidths of about 400 MHz (amplification) and 700 MHz (conversion) for the coupled-mode devices, with saturation powers of about -110 dBm at 15 dB and -91 dBm at -26 dB, respectively, plus a resonant-mode conversion bandwidth of about 670 MHz and saturation power of about -86 dBm. The authors also claim near-quantum-limited operation with added noise nadd = 0.5-0.6 for the coupled-mode amplifier. The paper includes a transmission-matrix model, Keysight ADS harmonic-balance simulations, detailed fabrication information, and extensive appendices describing the model, setup, and ripple analysis.

Significance. If the results are taken at face value, this is a significant advance: it demonstrates that resonator-based Josephson mixers can be impedance-matched to achieve bandwidths and saturation powers approaching those of traveling-wave parametric amplifiers while retaining the simplicity and low noise of a four-junction nonlinear element. The direct reflection, transmission, and saturation-power measurements are valuable and appear to support the main bandwidth/saturation claims. The paper also provides unusually complete device parameter tables and appendices, which strengthen reproducibility. However, the near-quantum-limited noise claim is undermined by an explicit leftover note in Fig. 11 indicating that the G/G_N data were rescaled to match theory, and the calculated-vs-measured comparisons are weakened by the use of parameters extracted from the same devices and working points chosen to match the data.

major comments (3)

[Fig. 11 (gutter note); Sec. V] The figure contains an unattributed author note: 'G/G_N is shrinked by a factor 0.7 dB (x0.85). In other words, the gain is correct, the noise rise fit G_N is underestimated by a factor 1.17 (17%).' If this note describes how the plotted data or fitted curves were produced, then the SNR-improvement data and the quoted nadd = 0.5-0.6 are not raw measurements; they have been rescaled to match theory. This is load-bearing because the paper claims operation 'near the quantum limit.' The authors must reanalyze the unadjusted data, report the actual G/G_N values, and state explicitly whether any normalization was applied. As published, the noise characterization is not credible.
[Appendix D, Tables VI-VII] The calculated and simulated responses in Figs. 6(i,j), 10(c,d), and 12(c,d) are compared with experiment, but Appendix D states that the flux and pump parameters used in calculation/simulation were 'generally treated as degrees of freedom, whose values are chosen based on the resultant agreement between the measured and generated response.' In addition, the circuit parameters in Tables II, IV, and V are extracted from fits to the same devices' flux-dependent resonances. Consequently, these comparisons do not validate the design or the model; they are postdictions. Please separate predictive from postdictive comparisons and provide at least one out-of-sample prediction, e.g., a working point not used during fitting.
[Sec. VI (first disadvantage paragraph); Sec. VII] The authors correctly state that JM3/JM4 have about 22 capacitance/inductance parameters that must be accurate within a few percent, and they attribute out-of-band dips to unmatched fabricated values of one or two LC resonators. Only one JM3 and one JM4 are measured, and the extracted Ca values for nominally identical JM1/JM2 differ by about 4%. Thus the 'blueprint' claim in Sec. VII is not established as reproducible; the headline bandwidths and saturation powers may be properties of a favorable chip. Please quantify yield sensitivity, e.g., via a Monte Carlo tolerance analysis, or tone down the blueprint claim to a single-device demonstration.

minor comments (4)

[Sec. IV, pQ product discussion] The expression 'γ = 2 γaγb/(γaγb)' is dimensionally inconsistent and appears to be a typo; I assume the denominator should be γa + γb. Please correct.
[Sec. V, paragraph after Fig. 12] The text states 'a comparable wide bandwidth of about 765 GHz at −10 dB'; this should be 765 MHz.
[Abstract vs. Introduction] The Introduction quotes a coupled-mode conversion saturation power of about −95 dBm, while the Abstract and Fig. 12 report about −91 dBm. Please harmonize these numbers.
[Appendix G, Fig. 19] The ripple model is helpful, but the parameters t, r22, lc, and ε are chosen constants with no uncertainty or sensitivity study. A brief statement of their relation to measured cable/circulator specifications would strengthen the comparison.

Circularity Check

1 steps flagged · score 2.0 of 10

Ancillary model-validation curves are fit to the same devices with free working-point parameters, but the headline bandwidth/saturation claims are direct measurements, so there is no load-bearing circularity.

fitted input called prediction [Appendix D; Sec. V (Figs. 10(c,d), 12(c,d); Tables IV,V)]
"The flux and pump parameters employed in the calculation and simulation were generally treated as degrees of freedom, whose values are chosen based on the resultant agreement between the measured and generated response with respect to their frequency range, shape, and magnitude."

The 'calculated' scattering responses used to validate the coupled-mode designs are produced with circuit parameters extracted from fits to the same devices' flux-dependent resonance frequencies (Tables IV, V), with filter coefficients and effective resistances additionally tweaked in ADS (Table III, Appendix C.1), and with flux/pump values explicitly chosen to match the measured data. Agreement between these calculated curves and the measured curves is therefore partly guaranteed by construction rather than being an independent prediction. However, this circularity affects only the model-validation panels, not the paper's headline experimental bandwidths and saturation powers, which are direct measurements.

full rationale

The paper's central claims are direct measurements of fabricated devices (Figs. 4, 6, 10, 12, 13), so the headline bandwidth and saturation-power numbers are not derived from the model and cannot be circular. The only exhibitable reduction is in the model-validation portion: 'calculated' and 'simulated' scattering curves are generated with device parameters extracted from fits to the same devices' resonance-vs-flux data, with Chebyshev coefficients and effective resistances tuned in ADS, and with flux/pump parameters explicitly treated as free degrees of freedom chosen to match the measured response. These curves therefore demonstrate model consistency, not independent prediction. This is a real but ancillary fitted-input issue. No load-bearing self-citation chain is present: the cited JRM model [28], coupled-mode synthesis [41], and Kerr-nulling calculations [49,50,52] are prior results with independent content, and the measured performance is benchmarked against other groups' devices (e.g., TWPAs and microstrip JMs). Accordingly, a modest score of 2 is appropriate rather than a higher circularity score.

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

The central demonstration is a measurement, so the model is not the claim. However, every 'calculated' or 'simulated' result rests on fitted or tuned inputs: circuit elements extracted from flux-dependent fits, Chebyshev coefficients tuned in ADS, active resistances chosen by simulation, and per-working-point flux/pump settings selected for agreement. The physical axioms are standard JRM three-wave-mixing theory and the applicability of coupled-mode matching to a half-circuit representation of the JRM. No new physical entities are introduced.

free parameters (6)

JRM/resonator circuit parameters (I0, LJ0, Ls, Lin, Lout, Ca, Cb) = Tables II, IV, V
Extracted from fits to measured resonance frequency vs flux (Figs. 14, 16, 17); used to compute all 'calculated' scattering responses.
Chebyshev prototype coefficients g0...g5 = Table III
Tweaked from textbook values to optimize the ADS harmonic-balance response; not a fixed first-principles design value.
Effective active resistances |Ra|, |Rb| = |Ra| = 15 Ohm, |Rb| = 30 Ohm
Set/optimized based on microwave simulations to fix the fractional bandwidths wk in Eq. (C12).
Flux and pump parameters for each working point = Tables VI, VII
Authors state these were treated as degrees of freedom chosen to match the measurements (Appendix D).
Dimensionless pump amplitude rho and pump phase phi_p
Used in the resonant-mode model (Eqs. F1-F5) to match measured gain levels; calibrated per working point.
Interference model parameters (t, r22, lc, epsilon) = t = 0.95, r22 = 0.17, lc = 1.1 m, epsilon = 2.1
Assumed values in Appendix G chosen to reproduce the measured ripple spacing of about 80-90 MHz.

assumptions (6)

domain assumption JRM potential (Eq. 1) expanded to third order around a stable ground state; the three-wave-mixing term dominates and higher-order Kerr terms are suppressed by design
Sec. II, Eq. (2). The design relies on operating near the Kerr-nulling point; the observed 'shark-fin' saturation features show residual fourth-order effects at some working points.
domain assumption JRM has zero passive (pump-off) mutual inductance between modes a and b, providing same-frequency isolation
Sec. III, Fig. 3: 'with the former the coupling is purely parametric since it nulls the passive part of the coupling, i.e., M0 = 0.' Requires ideal junction symmetry.
domain assumption The four-node JRM can be split along its virtual ground so that each half behaves as a grounded parametric element, making the coupled-mode synthesis of Ref. [41] applicable
Sec. V, Fig. 8(b): matching networks mirrored across the symmetry axes of modes a and b; validity hinges on symmetric device arms, which the authors list as a known disadvantage.
domain assumption The pump line, with an on-chip lambda_p/2 section and a lambda_p/4 shorted stub, excites only the common mode of the JRM
Sec. III pump-delivery description: the geometry is designed to drive opposite nodes with the same polarity and to place rf-voltage antinodes near the coupling capacitors.
ad hoc to paper The ripple/standing-wave model of Appendix G with chosen constant coefficients explains the measured ripples
Appendix G, Eq. (G1): parameters t, r22, lc, epsilon are assumed, not independently measured, to reproduce the characteristic 80-90 MHz ripple spacing.
domain assumption Dissipation in the JRM itself is negligible; dielectric loss in plate capacitors is treated as insertion loss and is the only significant internal loss
Sec. IV and Appendix H: the noise model attributes all added noise to nadd and all insertion loss to capacitor dielectric loss.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Nondegenerate Josephson Mixers with Enhanced Bandwidth and Saturation Power for Quantum Signal Amplification and Transduction." pith.science (2026). https://pith.science/paper/SL25DJCX

@misc{pith2026250806636,
  author       = {Pith},
  title        = {Pith review of: Nondegenerate Josephson Mixers with Enhanced Bandwidth and Saturation Power for Quantum Signal Amplification and Transduction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SL25DJCX}},
  note         = {Machine review of arXiv:2508.06636}
}

abstract

Nondegenerate Josephson mixers (JMs), formed by coupling two different transmission-line resonators to Josephson ring modulators (JRMs), are vital and versatile devices capable of processing microwave signals at the quantum limit. Owing to the lossless nondegenerate three-wave mixing process enabled by the JRM, JMs can perform phase preserving amplification of quantum signals, generate two-mode squeezed states, and perform noiseless frequency conversion. However, due to their limited bandwidth and saturation power, such resonator-based JMs are generally unable to simultaneously process frequency-multiplexed signals required in large quantum processors. To overcome this longstanding dual challenge, we redesign the JRM parameters by optimizing its inductances to suppress higher order mixing products and engineer its electromagnetic environment by incorporating lumped-element coupled-mode networks between the JRM and the two distinct ports of the JM. By implementing these strategies, we measure for JMs realized with four coupled modes per port, operated in amplification (conversion), bandwidths of about 400 MHz (700 MHz) with power reflections above 10 dB (below -10 dB) and saturation powers of about -110 dBm at 15 dB (-91 dBm at -26 dB). Similarly, we demonstrate for a low external quality factor resonant-mode JM operated in conversion, a maximum bandwidth of about $670$ MHz with power reflections below -10 dB and a maximum saturation power of about -86 dBm at -17 dB. Such nondegenerate JMs with enhanced bandwidths and saturation powers could serve in a variety of frequency-multiplexed settings ranging from high fidelity qubit readout and unidirectional routing of quantum signals to generation of remote entanglement with continuous variables.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

72 extracted references · 68 canonical work pages

[1]

1(a), the inductance of the JRM reads [51] LJRM = (LJ + Ls) || (2Lin) = 2Lin (LJ + Ls) LJ + Ls + 2Lin

Flux tunability Based on Fig. 1(a), the inductance of the JRM reads [51] LJRM = (LJ + Ls) || (2Lin) = 2Lin (LJ + Ls) LJ + Ls + 2Lin . (B1) The total inductance of the resonant-mode JM is given by La = Lb = 2 Lout + LJRM, where Lout is the series inductance connecting the JRM to the shunt capacitors. Lout is usually designed to yield a certain participatio...

work page
[2]

1 (a), (b)), we measure the phase response of mode a and b as a function of applied flux Φ e as shown in Fig

Device parameters To extract the lumped-element circuit parameters of JM1 and JM 2 devices (introduced in Fig. 1 (a), (b)), we measure the phase response of mode a and b as a function of applied flux Φ e as shown in Fig. 14, and apply theory fits to the data based on Eq. (B3), which are plotted on top of the data using dashed black curves. The circuit par...

work page
[3]

JM model To obtain the scattering parameters of resonant-mode JM devices such as, JM 1,2, we calculate first their trans- mission ( ABCD ) matrix, which can be expressed as Pump off Open end Loss BW=347 MHz fmax=7.83506 GHz Pump off Open end Loss BW=912 MHz fmax=10.832 GHz Signal Idler BW=347 MHz BW=912 MHz fmax=7.83506 GHz fmax=10.832 GHz Open Pump off P...

work page
[4]

decrement relation

JM model Extending the instantaneous (dynamical) bandwidth of Josephson-based amplifiers beyond the amplitude- gain-bandwidth product by incorporating impedance matching elements between the active Josephson-circuit and the external feedlines has been generally successful [42, 43]. However, applying similar techniques to extend the dy- namical bandwidth o...

work page
[5]

appreciable

Flux tunability and device parameters Figure 16 (a) and (b) exhibit the reflection parameter phase measured for port a and b of JM 3 as a function of frequency and applied external flux. We fit the resonance frequencies of the coupled modes of the device using the theoretical model outlined in Appendix C.1. The cal- culated fits are plotted on top of the ...

work page 2023
[6]

Yurke, L

B. Yurke, L. R. Corruccini, P. G. Kaminsky, and L. W. Rupp, A. D. Smith, A. H. Silver, R. W. Simon, and E. A. Whittaker, Observation of parametric amplification and deamplification in a Josephson parametric amplifier , Phys. Rev. A 39, 2519 (1989)

work page 1989
[7]

C. M. Caves, Quantum limits on noise in linear ampli- fiers, Phys. Rev. D 26, 1817 (1982)

work page 1982
[8]

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification , Rev. Mod. Phys. 82, 1155 (2010)

work page 2010

Show all 72 references

[9]

M. H. Devoret and R. J. Schoelkopf, Superconducting cir- cuits for quantum information: An Outlook , Science 339, 1169 (2013)

2013
[10]

Gambetta, Jerry M

Jay M. Gambetta, Jerry M. Chow, and Matthias Stef- fen, Building logical qubits in a superconducting quantum computing system, npj Quantum Inf. 3, 2 (2017)

2017
[11]

Boissonneault, A

Jay Gambetta, Alexandre Blais, M. Boissonneault, A. A. Houck, D. I. Schuster, and S. M. Girvin, Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect , Phys. Rev. A 77, 012112 (2008)

2008
[12]

Vijay, D

R. Vijay, D. H. Slichter, and I. Siddiqi, Observation of quantum jumps in a superconducting artificial atom , Phys. Rev. Lett. 106, 110502 (2011)

2011
[13]

Vijay, C

R. Vijay, C. Macklin, D. H. Slichter1, S. J. Weber, K. W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabi- lizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature 490, 77 (2012)

2012
[14]

Hatridge, S

M. Hatridge, S. Shankar, M. Mirrahimi, F. Schackert, K. Geerlings, T. Brecht, K. M. Sliwa, B. Abdo, L. Frun- zio, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Quantum back-action of an individual variable-strength measurement, Science 339, 178 (2013)

2013
[15]

Nissim Ofek, Andrei Petrenko, Reinier Heeres, Philip Reinhold, Zaki Leghtas, Brian Vlastakis, Yehan Liu,, Luigi Frunzio, S. M. Girvin, L. Jiang, Mazyar Mirrahimi, M. H. Devoret, and R. J. Schoelkopf Extending the life- time of a quantum bit with error correction in super- cond...

2016
[16]

Dou- glas Stone, and Michel Devoret Full Coherent Frequency Conversion between Two Propagating Microwave Modes , Phys

Baleegh Abdo, Katrina Sliwa, Flavius Schackert, Nico- las Bergeal, Michael Hatridge, Luigi Frunzio, A. Dou- glas Stone, and Michel Devoret Full Coherent Frequency Conversion between Two Propagating Microwave Modes , Phys. Rev. Lett. 110, 173902 (2013)

2013
[17]

Chapman, Stijn J

Benjamin J. Chapman, Stijn J. de Graaf, Sophia H. Xue, Yaxing Zhang, James Teoh, Jacob C. Curtis, Takahiro Tsunoda, Alec Eickbusch, Alexander P. Read, Akshay Koottandavida, Shantanu O. Mundhada, Luigi Frun- zio, M.H. Devoret, S.M. Girvin, and R.J. Schoelkopf, High-On-Off-Ratio...

2023
[18]

Flurin, N

E. Flurin, N. Roch, J. D. Pillet, F. Mallet, and B. Huard, Superconducting quantum node for entanglement and storage of microwave radiation , Phys. Rev. Lett. 114, 090503 (2015)

2015
[19]

A. J. Sirois, M. A. Castellanos-Beltran, M. P. DeFeo, L. Ranzani, F. Lecocq, R. W. Simmonds, J. D. Teufel, and J. Aumentado, Coherent-state storage and retrieval bet- ween superconducting cavities using parametric frequency conversion, Appl. Phys. Lett. 106, 172603 (2015)

2015
[20]

Yao Lu, Aniket Maiti, John W. O. Garmon, Suhas Gan- jam, Yaxing Zhang, Jahan Claes, Luigi Frunzio, Steven M. Girvin, andRobert J. Schoelkopf, High-fidelity para- metric beamsplitting with a parity-protected converter , Nat. Commun. 14, 5767 (2023)

2023
[21]

Ranzani, and J

L. Ranzani, and J. Aumentado, Circulators at the quan- tum limit: Recent realizations of quantum-limited super- conducting circulators and related approaches, IEEE Mi- cro. Mag. 20, 112-122 (2019)

2019
[22]

Sirois, Michael P

Leonardo Ranzani, Shlomi Kotler, Adam J. Sirois, Michael P. DeFeo, Manuel Castellanos-Beltran, Kata- rina Cicak, Leila R. Vale, and Jos´ e Aumentado, Wide- band Isolation by Frequency Conversion in a Josephson- Junction Transmission Line , Phys. Rev. Applied 8, 054035 (2017)

2017
[23]

E. I. Rosenthal, B. J. Chapman, A. P. Higginbotham, J. Kerckhoff, and K. W. Lehnert, Breaking Lorentz reci- procity with frequency conversion and delay , Phys. Rev. Lett. 119, 147703 (2017)

2017
[24]

K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frun- zio, R. J. Schoelkopf, and M. H. Devoret, Reconfigurable Josephson circulator/directional amplifier, Phys. Rev. X 5, 041020 (2015)

2015
[25]

Randy Kwende, Theodore White, Ofer Naaman, Joseph- son parametric circulator with same-frequency signal ports, 200 MHz bandwidth, and high dynamic range , Appl. Phys. Lett. 122, 224001 (2023)

2023
[26]

Bronn, Oblesh Jinka, Sal- vatore Olivadese, Antonio D

Baleegh Abdo, Nicholas T. Bronn, Oblesh Jinka, Sal- vatore Olivadese, Antonio D. C´ orcoles, Vivekananda P. Adiga, Markus Brink, Russell E. Lake, Xian Wu, David P. Pappas, and Jerry M. Chow, Active protection of a superconducting qubit with an interferometric Josephson isolato...

2019
[27]

Bronn, Salva- tore Olivadese, and Markus Brink, High-Fidelity Qubit 25 Readout Using Interferometric Directional Josephson Devices, PRX Quantum 2, 040360 (2021)

Baleegh Abdo, Oblesh Jinka, Nicholas T. Bronn, Salva- tore Olivadese, and Markus Brink, High-Fidelity Qubit 25 Readout Using Interferometric Directional Josephson Devices, PRX Quantum 2, 040360 (2021)

2021
[28]

Hatridge, R

M. Hatridge, R. Vijay, D. H. Slichter, John Clarke, and I. Siddiqi, Dispersive magnetometry with a quantum limited SQUID parametric amplifier , Phys. Rev. B 83, 134501, (2011)

2011
[29]

N. E. Frattini, V. V. Sivak, A. Lingenfelter, S. Shankar, and M. H. Devoret, Optimizing the Nonlinearity and Dis- sipation of a SNAIL Parametric Amplifier for Dynamic Range, Phys. Rev. Applied 10, 054020 (2018)

2018
[30]

Bergeal, F

N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, Phase-preserving am- plification near the quantum limit with a Josephson ring modulator, Nature 465, 64 (2010)

2010
[31]

Baleegh Abdo, Flavius Schackert, Michael Hatridge, Chad Rigetti, and Michel Devoret, Josephson amplifier for qubit readout , Appl. Phys. Lett. 99, 162506 (2011)

2011
[32]

Bergeal, R

N. Bergeal, R. Vijay, V. E. Manucharyan, I. Siddiqi, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, Ana- log information processing at the quantum limit with a Josephson ring modulator , Nature Phys. 6, 296 (2010)

2010
[33]

Baleegh Abdo, Archana Kamal, and Michel Devoret, Nondegenerate three-wave mixing with the Josephson ring modulator, Phys. Rev. B 87, 014508 (2013)

2013
[34]

Chavez-Garcia, Markus Brink, George Keefe, and Jerry M

Baleegh Abdo, Jose M. Chavez-Garcia, Markus Brink, George Keefe, and Jerry M. Chow, Time-multiplexed am- plification in a hybrid-less and coil-less Josephson para- metric converter, Appl. Phys. Lett. 110, 082601 (2017)

2017
[35]

Macklin, K

C. Macklin, K. O’Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, A near–quantum-limited Josephson traveling-wave para- metric amplifier , Science 350, 307-310 (2015)

2015
[36]

Knecht, Gre- gory D

Jennifer Wang, Kaidong Peng, Jeffrey M. Knecht, Gre- gory D. Cunningham, Andres E. Lombo, Alec Yen, Daniela A. Zaidenberg, Michael Gingras, Bethany M. Niedzielski, Hannah Stickler, Katrina Sliwa, Kyle Ser- niak, Mollie E. Schwartz, William D. Oliver, Kevin P. O’Brien, High-Eff...

2025 arXiv
[37]

C. W. Sandbo Chang, Arjan F. Van Loo, Chih-Chiao Hung, Yu Zhou, Christian Gnandt, Shuhei Tamate, Ya- sunobu Nakamura, Josephson traveling-wave paramet- ric amplifier based on low-intrinsic-loss coplanar lumped- element waveguide, arXiv:2503.07559 (2025)

2025
[38]

T. C. White, J. Y. Mutus, I.-C. Hoi, R. Barends, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wen- ner, S. Chaudhuri, J. Gao, John M. Martinis Traveling wave param...

2015
[39]

Martina Esposito, Arpit Ranadive, Luca Planat, S´ ebastien Leger, Dorian Fraudet, Vincent Jouanny, Olivier Buisson, Wiebke Guichard, C´ ecile Naud, Jos´ e Aumentado, Florent Lecocq, and Nicolas Roch, Observa- tion of two-mode squeezing in a traveling wave parametric amplifier,...

2022
[40]

Perelshtein, K.V

M.R. Perelshtein, K.V. Petrovnin, V. Vesterinen, S. Hamedani Raja, I. Lilja, M. Will, A. Savin, S. Sim- bierowicz, R.N. Jabdaraghi, J.S. Lehtinen, L. Gr¨ onberg, J. Hassel, M.P. Prunnila, J. Govenius, G.S. Paraoanu, and P.J. Hakonen, Broadband continuous variable entan- glemen...

2022
[41]

Zorin, Josephson Traveling-Wave Parametric Amplif- ier with Three-Wave Mixing , Phys

A. Zorin, Josephson Traveling-Wave Parametric Amplif- ier with Three-Wave Mixing , Phys. Rev. Appl. 6, 034006 (2016)

2016
[42]

Victor Gaydamachenko, Christoph Kissling, Lukas Gr¨ unhaupt,An rf-SQUID-based traveling-wave paramet- ric amplifier with -84 dBm input saturation power across more than one octave bandwidth , arXiv:2503.02489v1 (2025)

2025
[43]

Kevin O’Brien, Chris Macklin, Irfan Siddiqi, and Xiang Zhang, Resonant Phase Matching of Josephson Junction Traveling Wave Parametric Amplifiers , Phys. Rev. Lett. 113, 157001 (2014)

2014
[44]

, Readout of a quantum proces- sor with high dynamic range Josephson parametric am- plifiers, Appl

Theodore White et al. , Readout of a quantum proces- sor with high dynamic range Josephson parametric am- plifiers, Appl. Phys. Lett. 122, 014001 (2023)

2023
[45]

Kevin O’Brien, Nonlinear Light-Matter Interactions in Metamaterials, PhD Thesis (2016)

2016
[46]

Naaman and J

O. Naaman and J. Aumentado, Synthesis of parametri- cally coupled networks, PRX Quantum 3, 020201 (2022)

2022
[47]

Tanay Roy, Suman Kundu, Madhavi Chand, A. M. Vadi- raj, A. Ranadive, N. Nehra, Meghan P. Patankar, J. Au- mentado, A. A. Clerk, and R. Vijay, Broadband paramet- ric amplification with impedance engineering: Beyond the gain-bandwidth product, Appl. Phys. Lett. 107, 262601 (2015)

2015
[48]

J. Y. Mutus, T. C. White, R. Barends, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, K. M. Sundqvist, A. N. Cleland, and John M. Martinis, Strong environmen- tal coupling...

2014
[49]

Grebel, A

J. Grebel, A. Bienfait, ´E. Dumur, H.-S. Chang, M.-H. Chou, C. R. Conner, G. A. Peairs, R. G. Povey, Y. P. Zhong, and A. N. Cleland, Flux-pumped impedance- engineered broadband Josephson parametric amplifier , Appl. Phys. Lett. 118, 142601 (2021)

2021
[50]

P. Duan, Z. Jia, C. Zhang, L. Du, H. Tao, X. Yang, L. Guo, Y. Chen, H. Zhang, Z. Peng, W. Kong, H.-O. Li, G. Cao, and G.-P. Guo, Broadband flux-pumped Josephson parametric amplifier with an on-chip coplanar waveguide impedance transformer, Appl. Phys. Express 14, 042011 (2021)

2021
[51]

Nguyen, Xinyu Liu, Hengjiang Ren, William P

Bingcheng Qing, Long B. Nguyen, Xinyu Liu, Hengjiang Ren, William P. Livingston, Noah Goss, Ahmed Hajr, Trevor Chistolini, Zahra Pedramrazi, David I. Santi- ago, Jie Luo, and Irfan Siddiqi, Broadband coplanar- waveguide-based impedance-transformed Josephson para- metric amplif...

2024
[52]

Dykman, An- drea Iorio, George Sterling, Sabrina Hong, Alex Oprem- cak, Andreas Bengtsson, Lara Faoro, Joseph C

Ryan Kaufman, Theodore White, Mark I. Dykman, An- drea Iorio, George Sterling, Sabrina Hong, Alex Oprem- cak, Andreas Bengtsson, Lara Faoro, Joseph C. Bardin, Tim Burger, Robert Gasca, and Ofer Naaman, Joseph- son parametric amplifier with Chebyshev gain profile and high satur...

2023
[53]

V. R. Joshi, S. Hazra, A. Z. Ding, A. Miano, W. Dai, G. Umasankar, A. Kottandavida, G. Liu, L. Frunzio, and M. H. Devoret, Lumped-element broadband SNAIL para- metric amplifier with on-chip pump filter for multiplexed readout, arXiv:2505.02740v1 (2025). 26

2025 arXiv
[54]

Liu, T.-C

G. Liu, T.-C. Chien, X. Cao, O. Lanes, E. Alpern, D. Pekker, M. Hatridge, Josephson parametric converter saturation and higher order effects , Appl. Phys. Lett. 111, 202603 (2017)

2017
[55]

Chien, O

T.-C. Chien, O. Lanes, C. Liu, X. Cao, P. Lu, S. Motz, G. Liu, D. Pekker, and M. Hatridge, Multiparametric ampli- fication and qubit measurement with a Kerr-free Joseph- son ring modulator , Phys. Rev. A 101, 042336 (2020)

2020
[56]

N. Roch, E. Flurin, F. Nguyen, P. Morfin, P. Campagne- Ibarcq, M. H. Devoret, and B. Huard, Widely tunable, nondegenerate three-wave mixing microwave device op- erating near the quantum limit , Phys. Rev. Lett. 108, 147701 (2012)

2012
[57]

Chenxu Liu, Tzu-Chiao Chien, Michael Hatridge, and David Pekker, Optimizing Josephson-ring- modulator-based Josephson parametric amplifiers via full Hamiltonian control , Phys. Rev. A 101, 042323 (2020)

2020
[58]

Kirtley, Yihua Wang, Philip A

Zheng Cui, John R. Kirtley, Yihua Wang, Philip A. Kratz, Aaron J. Rosenberg, Christopher A. Watson, Ger- ald W. Gibson Jr., Mark B. Ketchen, and Kathryn. A. Moler, Scanning SQUID sampler with 40-ps time resolu- tion, Rev. Sci. Instrum. 88, 083703 (2017)

2017
[59]

Kim, Squeezing Limit of the Josephson Ring Modulator as a Nondegenerate Parametric Ampl- ifier, Phys

Dong Hwan Kim, Su-Yong Lee, Zaeill Kim, Taek Jeong, and Duk Y. Kim, Squeezing Limit of the Josephson Ring Modulator as a Nondegenerate Parametric Ampl- ifier, Phys. Rev. Applied 19, 034015 (2023)

2023
[60]

J. M. Manely and H. E. Rowe, Some general properties of nonlinear elements-part I , Proc. IRE 44, 904 (1956)

1956
[61]

D. M. Pozar, Microwave Engineering . 3rd edn (Wiley, Hoboken, 2005)

2005
[62]

G. L. Matthaei, A study of the optimum design of wideband parametric amplifiers and up-converters , IRE Trans. MTT 9, 23 (1961)

1961
[63]

W. J. Getsinger, Prototypes for use in broadbanding reflection amplifiers, IEEE Trans. MTT 11, 486 (1963)

1963
[64]

B. T. Henoch, A new method for designing wide-band parametric amplifiers , IEEE Trans. Microw. Theory Tech. 11, 62 (1963)

1963
[65]

Mellor and J

D. Mellor and J. Linvill, Synthesis of interstage networks of prescribed gain versus frequency slopes , IEEE Trans. Microw. Theory Tech. 23, 1013 (1975)

1975
[66]

G. Liu,, X. Cao, T.-C. Chien, C. Zhou, P. Lu, and M. Hatridge, Noise Reduction in Qubit Readout with a Two- Mode Squeezed Interferometer , Phys. Rev. Applied 18, 064092, (2022)

2022
[67]

B. Abdo, W. Shanks, O. Jinka, J. R. Rozen, J. Or- cutt, Teleportation and Entanglement Swapping of Con- tinuous Quantum Variables of Microwave Radiation , arXiv:2501.05537 (2025)

2025
[68]

W. K. Yam, M. Renger, S. Gandorfer, F. Fesquet, M. Handschuh, K. E. Honasoge, F. Kronowetter, Y. No- jiri, M. Partanen, M. Pfeiffer, H. van der Vliet, A. J. Matthews, J. Govenius, R. N. Jabdaraghi, M. Prunnila, A. Marx, F. Deppe, R. Gross, and K. G. Fedorov, Cryo- genic microw...

2023 arXiv
[69]

Flurin, N

E. Flurin, N. Roch, F. Mallet, M. H. Devoret, and B. Huard, Generating entangled micorwave radiation over two transmission lines , Phys. Rev. Lett. 109, 183901 (2012)

2012
[70]

Braunstein and Peter van Loock, Quantum information with continuous variables , Rev

Samuel L. Braunstein and Peter van Loock, Quantum information with continuous variables , Rev. Mod. Phys. 77, 513-577 (2005)

2005
[71]

Barzanjeh, S

S. Barzanjeh, S. Pirandola, D. Vitali, and J. M. Fink, Microwave quantum illumination using a digital receiver , Sci. Adv. 6, eabb0451 (2020)

2020
[72]

Lloyd, Enhanced sensitivity of photodetection via quan- tum illumination , Science 321, 1463 (2008)

S. Lloyd, Enhanced sensitivity of photodetection via quan- tum illumination , Science 321, 1463 (2008)

2008

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

1(a), the inductance of the JRM reads [51] LJRM = (LJ + Ls) || (2Lin) = 2Lin (LJ + Ls) LJ + Ls + 2Lin

Flux tunability Based on Fig. 1(a), the inductance of the JRM reads [51] LJRM = (LJ + Ls) || (2Lin) = 2Lin (LJ + Ls) LJ + Ls + 2Lin . (B1) The total inductance of the resonant-mode JM is given by La = Lb = 2 Lout + LJRM, where Lout is the series inductance connecting the JRM to the shunt capacitors. Lout is usually designed to yield a certain participatio...

work page

[2] [2]

1 (a), (b)), we measure the phase response of mode a and b as a function of applied flux Φ e as shown in Fig

Device parameters To extract the lumped-element circuit parameters of JM1 and JM 2 devices (introduced in Fig. 1 (a), (b)), we measure the phase response of mode a and b as a function of applied flux Φ e as shown in Fig. 14, and apply theory fits to the data based on Eq. (B3), which are plotted on top of the data using dashed black curves. The circuit par...

work page

[3] [3]

JM model To obtain the scattering parameters of resonant-mode JM devices such as, JM 1,2, we calculate first their trans- mission ( ABCD ) matrix, which can be expressed as Pump off Open end Loss BW=347 MHz fmax=7.83506 GHz Pump off Open end Loss BW=912 MHz fmax=10.832 GHz Signal Idler BW=347 MHz BW=912 MHz fmax=7.83506 GHz fmax=10.832 GHz Open Pump off P...

work page

[4] [4]

decrement relation

JM model Extending the instantaneous (dynamical) bandwidth of Josephson-based amplifiers beyond the amplitude- gain-bandwidth product by incorporating impedance matching elements between the active Josephson-circuit and the external feedlines has been generally successful [42, 43]. However, applying similar techniques to extend the dy- namical bandwidth o...

work page

[5] [5]

appreciable

Flux tunability and device parameters Figure 16 (a) and (b) exhibit the reflection parameter phase measured for port a and b of JM 3 as a function of frequency and applied external flux. We fit the resonance frequencies of the coupled modes of the device using the theoretical model outlined in Appendix C.1. The cal- culated fits are plotted on top of the ...

work page 2023

[6] [6]

Yurke, L

B. Yurke, L. R. Corruccini, P. G. Kaminsky, and L. W. Rupp, A. D. Smith, A. H. Silver, R. W. Simon, and E. A. Whittaker, Observation of parametric amplification and deamplification in a Josephson parametric amplifier , Phys. Rev. A 39, 2519 (1989)

work page 1989

[7] [7]

C. M. Caves, Quantum limits on noise in linear ampli- fiers, Phys. Rev. D 26, 1817 (1982)

work page 1982

[8] [8]

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification , Rev. Mod. Phys. 82, 1155 (2010)

work page 2010