Superconducting MOC

Curated map of Zoo entries in the Superconducting family.

Entries

Entry	Type	Status
tunable-coupler	coupling	demonstrated
binomial-code	encoding	demonstrated
binomial-codes	encoding	demonstrated
circuit-qed	infrastructure	demonstrated
0-pi-qubit	qubit	demonstrated
blochnium	qubit	demonstrated
bosonic-qubit	qubit	demonstrated
cat-codes	qubit	demonstrated
cooper-pair-box-charge-qubit	qubit	demonstrated
cos2phi-qubit	qubit	proposed
dual-rail-superconducting-qubit	qubit	demonstrated
flux-qubit	qubit	demonstrated
fluxonium	qubit	demonstrated
gkp-codes	qubit	demonstrated
gmon	qubit	demonstrated
heavy-fluxonium-qubit	qubit	demonstrated
kerr-cat-qubit	qubit	demonstrated
mergemon	qubit	demonstrated
phase-qubit	qubit	demonstrated
transmon	qubit	demonstrated
xmon	qubit	demonstrated

Composition

• coupling: 1
• encoding: 2
• infrastructure: 1
• qubit: 17

Conceptual anchors

• charge-noise-in-superconducting-qubits and charge-noise-sweet-spot explain the CPB → transmon → protected-superconducting arc.
• josephson-junction-as-nonlinear-element is the common circuit primitive behind nearly every qubit in this family.
• jaynes-cummings-in-circuits, dispersive-readout-mechanism, and resonator-as-quantum-bus are the shared circuit-QED infrastructure layer.
• bosonic-code-hierarchy explains why cat-codes, gkp-codes, and binomial-codes are related but not interchangeable.

Four-branch reading map

Branch	What it is really optimizing	Best entry points	Evergreen lens
Baseline circuit-QED branch	Fast microwave control, scalable readout, and tunable two-qubit gates in a weakly anharmonic artificial atom stack	transmon, xmon, gmon, tunable-coupler, circuit-qed	josephson-junction-as-nonlinear-element, dispersive-readout-mechanism, resonator-as-quantum-bus
Protected-circuit branch	Suppress sensitivity before decoding by reshaping the circuit landscape or exploiting duality	fluxonium, heavy-fluxonium-qubit, blochnium, 0-pi-qubit, cos2phi-qubit	charge-noise-sweet-spot, coherence-time-hierarchy, noise-bias-and-asymmetric-error-channels
Bosonic / oscillator branch	Push error correction partly into a long-lived cavity mode instead of a single anharmonic junction mode	bosonic-qubit, cat-codes, kerr-cat-qubit, gkp-codes, binomial-codes	bosonic-code-hierarchy, noise-bias-and-asymmetric-error-channels, erasure-error-vs-pauli-error
Rail / erasure branch	Turn dominant relaxation or leakage events into flagged faults that the decoder can exploit	dual-rail-superconducting-qubit	erasure-error-vs-pauli-error, threshold-theorem

A useful routing rule is that circuit-qed is infrastructure, not a peer qubit. Enter it when the live question is about readout, coupling, resonators, or cavity-mediated control. Enter transmon, fluxonium, blochnium, or the bosonic-code notes when the live question is what degree of freedom is actually carrying the logical information.

Hardware-assisted fault-tolerance routes

• transmon, xmon, gmon, flux-qubit, and the broader circuit-QED stack are the baseline branch: improve raw gate and measurement fidelity, then hand off to surface-code-logical-qubit or color-code-logical-qubit for architecture-level scaling.
• bosonic-qubit, cat-codes, kerr-cat-qubit, gkp-codes, and binomial-codes are the oscillator branch: the hardware itself already starts behaving like a logical primitive, so route first through bosonic-code-hierarchy and then ask whether the win comes from general cavity QEC or from biased-noise protection.
• 0-pi-qubit, cos2phi-qubit, blochnium, and heavy-fluxonium-qubit are the protected-circuit branch, but they are not interchangeable. The real split is whether the design is buying protection from a sweet-spot-plus-matrix-element strategy, from a duality regime, or from a symmetry-engineered multi-axis potential.
• dual-rail-superconducting-qubit is the erasure-conversion branch: the dominant relaxation event is supposed to leave the codespace in a flagged way, so compare it through erasure-error-vs-pauli-error rather than only through bare gate fidelity.

Protected-circuit routing

• heavy-fluxonium-qubit is the nearest-term coherence-first branch. It still lives squarely inside familiar fluxonium control and readout practice, but uses disjoint-support wavefunctions and sweet-spot operation to suppress matrix elements before the error ever reaches the decoder.
• blochnium is the duality branch. Read it when the interesting claim is quasicharge physics, large anharmonicity, and flux-dispersion flattening, not maximal passive protection in the 0-π sense.
• 0-pi-qubit and cos2phi-qubit are the symmetry-engineered protection branch. They belong together because both aim for multi-axis protection by reshaping the circuit potential itself, even though 0-pi-qubit is experimentally ahead and cos2phi-qubit is still a more aspirational construction.
• dual-rail-superconducting-qubit should sit adjacent to this branch, not inside it: the payoff is still lower logical overhead, but via flagged leakage and erasure structure rather than suppressed in-code-space matrix elements.

Boundary with the super-semi family

Route superconducting descendants to super-semi-moc only when the semiconductor weak link or Andreev physics becomes part of the qubit’s defining control story. If the central claim is still protected superconducting-circuit design, cavity coupling, or oscillator-level encoding, keep it here even when the fabrication stack overlaps materially with hybrid devices.

Editorial note

This family mixes bare qubits, bosonic encodings, and enabling infrastructure. Keep the generated table exhaustive, but use the evergreen layer to prevent the family page from becoming a flat list.