References and support boundaries
Use this ledger to ask what supports a statement, and how far does that support extend? The linked concepts own the explanations and derivations. This page records source context, not another physics course or a list of design targets. Citation classes are explained in Overview; contributor instructions live in the Authoring Guide.
The identified-source entries below are reorganized source explanations, not direct quotations. Their citations support the stated source role, not every extension in a linked concept. A concept’s own derivation must identify its starting model and assumptions. A source’s device number is not a universal range, process default, acceptance condition, or independently validated target.
Identified source families
Engineering vocabulary
Krantz and colleagues’ 2019 review supplies a broad vocabulary for Hamiltonians, tunability, coupling, noise, control, readout, filtering, and amplification (Krantz et al. 2019). Its role here is taxonomy, not a process-specific specification.
| Family | Vocabulary retained from the source summary |
|---|---|
| General | Frequency and detuning conventions, phase, intervals, impedance, matrix elements, linewidth, quality factor, coherence, noise PSD. |
| Qubit | Josephson and charging energies, their ratio, qubit frequency, anharmonicity, capacitance, critical current, participation. |
| Tunability | External flux, effective Josephson energy, sweet spots, asymmetry, tuning range, flux sensitivity. |
| Coupling and filtering | Capacitive/inductive elements distinguished from transverse/longitudinal Hamiltonian interactions; qubit–resonator and qubit–qubit coupling; Purcell rate and filter Q. |
| Noise and material loss | Relaxation, dephasing, charge/flux noise, photon fluctuations, quasiparticles, participation and mitigation assumptions. |
| Control | Drive voltage/frequency, IQ, Rabi rotations, DRAG, flux pulses, iSWAP, controlled phase and cross-resonance vocabulary. |
| Readout | Detuning, coupling, linewidth, dispersive shift, critical/readout photon number, SNR and measurement time. |
| Amplification | System/stage noise temperature, gain, pump/signal/idler frequencies and quantum-limited context. |
The previous parameter-table organization used this vocabulary to distinguish circuit elements from interaction axes, noise spectra from susceptibilities, and readout physics from measurement-chain noise. Those are organizational choices, not requirements imposed by the review. Symbols are normalized local notation, not exact PDF transcription. Narrower device/process sources remain necessary for numerical targets and tolerance claims. Start with Josephson energy, anharmonicity, flux tunability, or quantization.
Two qualitative relationships in the inherited source summary are retained explicitly: increasing the transmon \(E_J/E_C\) ratio trades charge-noise suppression against anharmonicity, and Purcell-filter design balances readout speed with qubit protection (Krantz et al. 2019). These are model-dependent design relationships, not universal numerical targets or evidence that a particular device meets them.
Circuit quantum electrodynamics
The cQED review is a model/definition source for dispersive readout, qubit–resonator coupling, critical photon number, Purcell decay and measurement efficiency (Blais et al. 2021). The retained parameter roles are dispersive shift chi (readout contrast), linewidth kappa (speed/bandwidth), coupling g, detuning Delta (approximation validity), ncrit (dispersive photon scale), Gamma_P (environment-mediated decay), and efficiency (chain noise and state discrimination). It does not supply a numeric target for every device. See linewidth versus trace width and quantum dynamics conventions.
Energy-participation quantization
The EPR source connects EM mode frequencies and junction participations to Hamiltonian-facing anharmonicity, self-/cross-Kerr and dispersive parameters (Minev et al. 2021). The retained families are omega_m, p_mj, chi_mn, and EM-to-Hamiltonian provenance. Junction-field accuracy and sign conventions matter; global frequency convergence alone does not establish this handoff’s accuracy. The quantization and Josephson cosine concepts own the general construction.
Supplementary loss and port context
Keep the supplementary material paired with the main source when using dissipative participation, port loss, port impedance, participation signs or inverse-Q budgeting (Minev et al. 2021, supplementary material). A citation to the main article alone should not imply that these details were checked independently. The former supplement page supplied no separate bibliographic identity or locators; that limitation remains visible here.
Finite-circuit quantization
Vool and Devoret support branch/node flux and charge, reference-node and spanning-tree coordinates, static loop-flux offsets, capacitive kinetic energy, inductive/Josephson potential energy, conjugate charge and the Legendre transform (Vool and Devoret 2017). The ideal LC Hamiltonian, natural frequency and impedance scale are explained in the LC concept; the quantization concept owns the finite conservative construction.
This introductory source does not resolve every constrained, singular, nonreciprocal or time-dependent-flux circuit. The current concept’s unresolved rank-deficiency boundary is a local implementation boundary, not a universal scientific prohibition inferred from this paper. Dissipation requires an environment description, not treating a resistor as a finite conservative degree of freedom. Specialized singular-circuit sources remain separately cited by the concept.
Harmonic balance
El-Rabaie, Fusco and Stewart support truncating a periodic response into Fourier components, balancing retained components to obtain nonlinear algebraic equations, and iterative fixed-point/modified Newton–Raphson solution approaches (El-Rabaie et al. 1988). See harmonic balance.
This is classical nonlinear-microwave context, not support for quantum noise, efficiency or commutators. It does not establish uniqueness or dynamical stability of every algebraic solution. Mode ordering, strong-tone versus linearized meanings, arrays, cache identity and convergence controls belong to the JosephsonCircuits documentation, not the tutorial. Recording solver/termination evidence and examining basis refinement are separate engineering choices in the inherited workflow; they are not source-created pass/fail rules or newly activated requirements.
Multiconductor transmission lines
Williams, Holloway and Rogers support distinguishing conductor and modal representations, per-unit-length impedance/admittance matrices, voltage/current transformations and declared modal normalization (Williams et al. 1999). Their lossy, asymmetric printed-line characterization context also warns against assuming elementary symmetric even/odd-mode formulas apply unchanged. Calibration, transitions and approximation choices affect extracted meanings and accuracy. See RLGC matrices.
The paper is not an AEDT/Q2D artifact schema: it does not define conductor names, current directions, Maxwell-to-branch lowering, pi-section consumer behavior or Human acceptance rules. Those boundaries belong to the relevant model and package contracts.
Power-wave definitions
Kurokawa supports incident/outgoing wave coordinates defined from port voltage, current and reference impedance, and the scattering matrix between those waves (Kurokawa 1965). Complex-reference power waves use a conjugate in the outgoing definition and cannot be interchanged indiscriminately with traveling or pseudo waves. The real-positive subset reduces to familiar network conversions. See port reference impedance.
This source does not specify package port lowering or JosephsonCircuits output semantics. Missing complex-reference wave conventions remain a declared local failure boundary; HB photon-flux/cross-frequency normalization needs separate solver mode metadata.
Complex resonator fitting under noise
Probst and colleagues support complex-plane resonator fitting under noise, separating internal/coupling/loaded Q, and correcting gain, phase and cable delay before interpreting resonator parameters (Probst et al. 2015). The inherited summary also records mismatch/asymmetry through a complex coupling-Q phase. See decay, linewidth and Q. Reflection-only or multimode data still require the appropriate local scattering model: this fitting source does not establish Purcell-filter topology, and a generic circle fit is not interchangeable with every measurement geometry.
Heinsoo source-device context
Reported multiplexed-readout device
Heinsoo and colleagues provide the multiplexed-readout example with per-resonator Purcell filtering and off-target readout/spectator-dephasing context (Heinsoo et al. 2018). The inherited summary described two supplied PDFs as byte-identical copies of one source. Their bytes were not independently checked in this restructure; the duplication note is not independent corroboration.
The following table preserves the inherited source-device summary; its rounded values are not new targets or a new extraction. Read frequency/rate units with the original table’s conventions, not as an implicit conversion between angular rate and ordinary frequency (Heinsoo et al. 2018).
| Parameter area | Retained source-device notes |
|---|---|
| Readout frequency | Reported band around 6.409–7.214 GHz. |
| Readout linewidth | Paper kappa_R: target about 10 MHz; measured about 3.1–14.3 MHz; readout-like hybrid-pole linewidth. |
| Dispersive shift | Reported about −1.11 to −4.80 MHz. |
| Qubit–readout coupling | Reported about 108–134 MHz. |
| Photon budget | ncrit=8.2–30.2; nRO=2.9–22.2. |
| Readout time | 80 ns pulse and less than 250 ns resonator occupation. |
| Assignment | Average about 97%; per-qubit about 92.9–98.8%. |
| Filter frequency | About 6.392–7.196 GHz. |
| Filter linewidth | Paper kappa_P=tilde(kappa_a): designed around 40 MHz; measured about 32.2–57.8 MHz; boundary-conditioned total filter external linewidth. |
| Readout–filter coupling | Designed around 10 MHz; measured about 6.9–9.2 MHz. |
| Frequency spacing | Readout spacing around 160 MHz. |
| Measurement-induced dephasing | Spectator dephasing from off-target tones. |
The device uses C_in=40 fF; Sections II–III place couplings near voltage antinodes approximately half-wavelength multiples from the input capacitor. In that source boundary model about 98% of emitted readout photons go toward the output. This is reciprocal interference/directionality, not a nonreciprocity claim (Heinsoo et al. 2018, secs. II–III). Appendix C neglects dispersion between the T-junction and capacitor; it does not establish a general finite-distance substitution rule. The placement and approximation discussion owns that boundary, while the linewidth discussion owns the detailed equations and phasor translation.
This source is not a modern coherence benchmark for another device. Its stack, band and coherence limits cannot be transferred without device-specific review. Its Gamma, input-capacitor boundary and reference kappa_a cannot silently become another design’s port decomposition. A design-selected sum of identity-continued open-pole linewidths needs its own qualified symbol; it is not renamed kappa_P by analogy. Ring-down pole linewidth, channel-collected power and an interfering trace’s −3 dB width remain distinct observations.
Other identified models already used by Knowledge
The linked concepts carry claim-level accounting for these sources; this list is an identity/role lookup, not blanket support for their whole contents.
| Source role | Identity | Concept |
|---|---|---|
| Input–output damping and bath boundary | (Gardiner and Collett 1985; Clerk et al. 2010) | Node/line-flux bridge |
| Passive multimode direct-path constraints | (Suh et al. 2004) | Multimode scattering |
| Rational approximation and S-model passivity assessment | (Gustavsen and Semlyen 1999, 2008) | Vector fitting |
| Circuit reduction | (D"orfler and Bullo 2013) | Schur/Kron reduction |
| Differential/common-mode coordinates | (Bockelman and Eisenstadt 1995) | Admittance transforms |
| Passive realization and tridiagonalization | (Gough and Zhang 2013; Paige 1976) | Finite-order response |
| Coupling capacitor and extended open-circuit quantization | (Malekakhlagh and T"ureci 2016; Parra-Rodriguez and Egusquiza 2025) | Node/line-flux bridge |
| Specialized finite/singular circuit construction | (Rasmussen et al. 2021; Rymarz and DiVincenzo 2023) | Circuit quantization |
| Intrinsic MTL filtering device context | DOI 10.1103/PRXQuantum.6.020345 | Poles and zeros |
Inherited notes with unresolved support
The previous Core/Supporting/Watchlist lists labeled all entries “Source-backed,” including pages containing only a title and a relevance note. That label does not establish a bibliographic identity or verify an extraction. The entries below preserve their inherited-note / support-gap status until an exact source and claim locator are supplied. They are not newly established physics, verified numeric evidence, or active design requirements. The former tiers describe intended relevance, not source quality or promotion authority.
Floating tunable coupler
The inherited Core title is now resolved to Sete and colleagues’ source (Sete et al. 2021). Its effective coupling and residual-ZZ discussions (§IV–V) support distinguishing direct, qubit–coupler, mediated and net exchange from conditional shifts. This supplies a source for the qualitative coupler concept, not every local coefficient definition. The inherited note’s residual-ZZ number still needs exact figure/table verification before numerical use; source identity alone does not close that gap.
Material-loss measurements
Inherited Core title: “Material loss measurements using superconducting microwave resonators.” Intended families: Q_i, Q_c, loss tangent, TLS loss, filling factor, power/temperature dependence, conductor participation, vortex threshold and junction-barrier loss. Retained caution: a material-loss number is not portable without filling factors, photon number, temperature, coupling Q, fit model, fabrication stack, cooldown and shielding. No exact identity or numeric extraction was provided.
Cross-cutting design concerns
Inherited Core title: “A review of design concerns in superconducting quantum circuits.” Intended checklist role: qubit parameters, interface/material loss, radiation/packaging, EM simulation, measurement constraints and tolerance. The note explicitly does not override narrower topology/device sources. Bibliographic identity and claim support remain unresolved.
Flip-chip crosstalk
Inherited Core title: “Signal crosstalk in a flip-chip quantum processor.” Intended families: interchip gap, qubit pitch, bump count/width/density, shielding-tunnel geometry, control-line spacing, XY and DC/AC flux crosstalk. The note reports fabrication-offset frequency shifts without supplying values or locators. Preserve its distinction between measured qubit/coupler bands and intended target bands; the measurement claim remains unverified here.
Fixed-frequency tunable-bus gates
Inherited Core title: “Tunable coupling architecture for fixed-frequency transmon qubits.” Intended families: g12, qubit–coupler coupling, effective exchange, ZZ, flux bias, conditional-phase duration and gate benchmarking. The note distinguishes gate-error evidence from geometry parameters. No source identity or measured values were supplied.
Bandpass Purcell filtering
Inherited Supporting title: “Quantum theory of a bandpass Purcell filter.” The unverified source-example table is preserved below, not promoted into numeric evidence. Its topology was explicitly distinguished from intrinsic MTL-notch filtering; it is not an MTL geometry recipe.
| Inherited example | Value recorded in the old note |
|---|---|
| Filter frequency | Around 6.75 GHz. |
| Filter Q and bandwidth | Q_f ~ 30, bandwidth around 0.22 GHz. |
| Readout–filter coupling | Around 18.9 MHz. |
| Purcell suppression | Roughly 50–100× in example bandpass designs. |
Exact identity and figure/table support for these values remain a support gap.
Coplanar-waveguide resonators
Inherited Supporting title: “Coplanar waveguide resonators for circuit QED.” Retained, unverified examples: frequency around 2–9 GHz, coupling capacitance around 0.24–56.4 fF, loaded Q around 3.7e2–2.3e5, with internal loss kept separate from coupling loss. These values lack an exact identity/locator here. The intended role was resonator/external-coupler background, not a replacement for an intrinsic-MTL model or a package extraction contract.
Environmental radiation
Inherited Supporting title: “Environmental radiation impact on lifetimes and quasiparticle tunneling.” Intended relevance: T1, T2, quasiparticle tunneling/parity switching, shielding stack and radiation-sensitive lifetime changes. Device/environment context is not a universal layout target. Exact source identity and measurement support are missing.
Open electromagnetic simulations
Inherited Supporting title: “Open-source highly parallel electromagnetic simulations.” Intended families: eigenfrequency, EPR participation, material stack, PEC box, 50-ohm ports and convergence evidence. The old note distinguishes benchmark reproducibility settings from local solver/process defaults. Its title does not by itself establish a source; the field-extraction concept also cites authoritative Palace documentation separately.
Radiation-suppressed planar device
Inherited Supporting title: “Radiation-suppressed superconducting qubit in a planar geometry.” Intended relevance: radiation loss, backside grounding, packaging, frequency, Josephson/charging-energy ratio and coherence. Its TiN/microstrip process assumptions were explicitly not transferable to flip-chip targets without review. Exact identity and device evidence remain unresolved.
Multimode gauge watchlist
Inherited Watchlist title: “Optimal gauge for the multimode Rabi model in circuit QED.” Intended future question: gauge choice in truncated multimode Hamiltonians near strong/multimode coupling. No active design input or verified gauge-parameter extraction is claimed. The prior “Source-backed” label was not accompanied by an identity; this remains an inactive relevance note, not model-validity evidence.
Bibliographic identities
The bibliography contains identified sources already used by the current concepts. Presence here establishes identity only; follow the adjacent citation and concept’s model/assumptions to determine actual support. Entries with incomplete author lists retain the recorded lead author plus “others”; missing fields are not guessed.