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 photon pair, which gives the anharmonic energy ladder. Together with a two-photon parametric drive, this ladder stabilises cat states.

Approximation

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

References

Classes

KerrCavity([freq, kerr, levels, label, T1, ...])

Kerr-nonlinear resonator supporting cat-qubit stabilisation.
class quchip.devices.kerr_cavity.KerrCavity(freq=unbound, kerr=unbound, *, levels=30, label=None, T1=None, T2=None, thermal_occupation=None)[source]

Bases: FockDevice

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 and makes the cavity anharmonic. 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) – Positive cavity frequency \(\omega\) in GHz. Can be a JAX tracer for sweeps / gradients.

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

  • levels (int) – Fock-space truncation dimension. To prevent truncation artefacts, choose at least 4 * (eps2 / K) + 10. Default 30.

  • label (str | None) – Human-readable label. None gives an automatic label kerr_cavity_0, kerr_cavity_1, …

  • T1 (float or None, default None) – Energy-relaxation time in ns. None disables T1 relaxation.

  • T2 (float or None, default None) – Total 0-1 coherence time in ns. If both are set, T2 <= 2*T1.

  • thermal_occupation (float or None, default None) – Dimensionless mean bath occupation. None disables absorption.

Notes

This Hamiltonian is diagonal in the Fock basis and does not itself define a computational subspace. With a two-photon parametric drive, you can engineer the steady state into a cat-code manifold spanned by the even and odd cat states \(|C^+_\alpha\rangle\) and \(|C^-_\alpha\rangle\). Bit-flip errors in 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

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')

Parameters eligible for inverse design. DeviceModel derives these from declared fields unless the class or an ancestor supplies a tuple. Explicit tuples remain authoritative when inherited; an empty tuple excludes the device from inverse design. Plain BaseDevice subclasses default to an empty tuple without derivation.

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=unbound, positive=True, nonnegative=False, serialize=True, unit='GHz', symbol='\\omega', noise=False, kw_only=False, required=False)
kerr: Scalar = Parameter(default=unbound, positive=False, nonnegative=True, serialize=True, unit='GHz', symbol='K', noise=False, kw_only=False, required=False)
local_hamiltonian(op, p)[source]

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:
physics_notes()[source]

Return declared Kerr-cavity approximation notes.