quchip.devices.kerr_cavity

KerrCavity — Kerr-nonlinear resonator model.

Hamiltonian:

\[H = \omega \, \hat{n} - K \, \hat{n}(\hat{n} - I)\]

where \(\omega\) is the cavity frequency (GHz, ordinary) and \(K\) is the Kerr nonlinearity (GHz, positive). Eigenvalues are:

\[E_n = \omega n - K n(n-1)\]

The Kerr term shifts higher Fock levels down by \(K\) per pair of photons, creating the anharmonic energy ladder that stabilises cat states when combined with a two-photon parametric drive.

Approximation

This is an effective single-mode model after adiabatic elimination of the SNAIL or STS-SQUID that provides the nonlinearity. The Kerr coefficient \(K\) captures the leading-order nonlinearity; higher-order corrections are neglected. The Hilbert space is truncated at levels Fock states — choose levels >= 4 * (eps2 / K) + 10 to avoid truncation artefacts.

References

[1]

Grimm et al., Stabilization and operation of a Kerr-cat qubit, Nature 584, 205 (2020). arXiv:1907.12131.

[2]

Hajr et al., High-Coherence Kerr-Cat Qubit in 2D Architecture, PRX Quantum 5, 020347 (2024). arXiv:2404.16697.

Classes

KerrCavity(freq, kerr, *[, levels, label, ...])

Kerr-nonlinear resonator supporting cat-qubit stabilisation.

class quchip.devices.kerr_cavity.KerrCavity(freq, kerr, *, levels=30, label=None, T1=None, T2=None, thermal_population=None)

Bases: DeviceModel

Kerr-nonlinear resonator supporting cat-qubit stabilisation.

Hamiltonian:

\[H = \omega \, \hat{n} - K \, \hat{n}(\hat{n} - I)\]

The nonlinearity \(K\) shifts the photon-number eigenenergies, making the cavity anharmonic. Combined with a two-photon parametric drive at \(2\omega\), the steady state becomes a cat state with amplitude \(\alpha = \sqrt{\varepsilon_2 / K}\).

Parameters:

• freq (float) – Cavity frequency \(\omega\) in GHz. Must be positive. May be a JAX tracer for sweeps / gradients.

• kerr (float) – Kerr nonlinearity \(K\) in GHz. Non-negative; positive value shifts even-photon levels downward. Typically 1–100 MHz in superconducting circuits.

• levels (int) – Fock-space truncation dimension. Choose at least 4 * (eps2 / K) + 10 to avoid truncation artefacts. Default 30.

• label (str | None) – Human-readable label. None → auto-generated kerr_cavity_0, kerr_cavity_1, …

• **noise_kwargs – Forwarded to BaseDevice: T1, T2, thermal_population, etc.

Notes

This Hamiltonian is diagonal in the Fock basis and does not itself define a computational subspace. Combined with a two-photon parametric drive, the steady state can be engineered into a cat-code manifold spanned by the even cat state \(|C^+_\alpha\rangle\) and the odd cat state \(|C^-_\alpha\rangle\). Bit-flip errors within that manifold are exponentially suppressed, \(\sim e^{-2|\alpha|^2}\), in the stabilized regime. This class’s inherited Pauli surface (computational is False) addresses the bare Fock |0>, |1> subspace; see physics_notes() for the caveat.

References

[1]

Grimm et al., Nature 584, 205 (2020). arXiv:1907.12131.

[2]

Hajr et al., PRX Quantum 5, 020347 (2024). arXiv:2404.16697.

Examples

>>> from quchip.devices.kerr_cavity import KerrCavity
>>> cav = KerrCavity(freq=5.0, kerr=1.0, levels=10, label="cav")
>>> cav.freq, cav.kerr, cav.levels
(5.0, 1.0, 10)

tunable_param_names = ('freq', 'kerr')

Bare parameters this device exposes as differentiable / tunable scalars. fit_a_dress walks this tuple to discover what it is allowed to optimize on each device, decoupling the inverse-design surface from any specific device model. Three states, keyed on whether the value is explicitly declared:

• No explicit declaration anywhere in the DeviceModel lineage — the default is derived: every declared parameter() field, in declaration order (see DeviceModel.__init_subclass__).

• Explicit tuple on the class or an ancestor — exact curation, validated at class-definition time; authoritative and inherited until a subclass explicitly replaces it.

• Explicit empty tuple — deliberately freezes the device (and its subclasses, until one replaces it) out of inverse design.

On a plain (non-DeviceModel) BaseDevice subclass there is no derivation; the default stays empty unless the subclass declares its own tuple — e.g. Fluxonium uses ("E_C", "E_J", "E_L", "phi_ext").

approximation = 'Kerr-nonlinear cavity effective single-mode model; SNAIL/STS-SQUID adiabatically eliminated.'

Declared approximation-regime statement surfaced by physics_notes() — the mechanism that keeps a model’s stated validity range attached to the class rather than buried in a docstring a caller may not read.

computational = False

Whether this device represents a computational qubit, as opposed to e.g. a bus resonator or a coupler element.

freq: Scalar = Parameter(default=<object object>, positive=True, nonnegative=False, serialize=True, unit='GHz')

kerr: Scalar = Parameter(default=<object object>, positive=False, nonnegative=True, serialize=True, unit='GHz')

local_hamiltonian(op)

Return \(H = \omega \hat{n} - K \hat{n}(\hat{n} - I)\).

The Kerr term \(\hat{n}(\hat{n}-I) = \hat{n}^2 - \hat{n}\) gives eigenvalue contributions \(-K n(n-1)\) for the \(n\)-photon Fock state.

Returns:

Declarative expression for the Hermitian operator H = omega*n - K*n*(n-1) (GHz), diagonal in the Fock basis.

Return type:

PhysicsExpr

Parameters:

op (LocalOps)

physics_notes()

Return declared Kerr-cavity approximation notes.

Return type:

list[str]