NuclearSpin

class NuclearSpin(dimension, name, qubit_subspace, gyromagnetic_ratio, quadrupole_splitting=0.0, anisotropy_axis=None, local_quasistatic_noise=None, quantization_axis='global_z')

Spin representation tailored for nuclear spins.

Parameters:

dimension (int) – Dimension, must be 2 for spin-1/2, 3 for spin-1, etc.
name (str) – Name of the spin.
qubit_subspace (Tuple[float, float]) – The quantum numbers that define the qubit subspace.
gyromagnetic_ratio (float) – Gyromagnetic ratio (in \(\text{MHz}/\text{T}\)).
quadrupole_splitting (float) – Quadrupole splitting parameter (in \(\text{MHz}\)).
anisotropy_axis (List[float] | None) – Local anisotropy axis of the spin, given in the global coordinate system.
local_quasistatic_noise (List[float] | None) – Local-quasistatic noise components of the spin (in \(\text{MHz}\)).
quantization_axis (str | Sequence[float]) – Quantization axis of the spin, given by the keyword 'global_z', 'local_static_field', or 'anisotropy_axis', or by an explicit vector in the global coordinate system. It determines which direction is treated as the spin’s local z-axis when building operators and states for that spin.

Raises:

SimphonyError – If an invalid dimension or qubit subspace is provided.

Note

Hamiltonian of the nuclear spin reads

\[H_n = -\gamma_n \mathbf{B} \cdot \mathbf{I} + Q \left( I_{z'}^2-\frac{I(I+1)}{3} \right),\]

where \(\gamma_n\) is the gyromagnetic_ratio, \(Q\) is quadrupole_splitting. The quadrupole term is written in the principal axis frame \((x',y',z'),\) that is defined by the anisotropy_axis.

Attributes

`anisotropy_axis`	Local anisotropy axis of the spin, given in the global coordinate system.
`anisotropy_tensor`	Anisotropy tensor in the global coordinate system (in \(\text{MHz}\)).
`dimension`	Dimension, it is 2 for spin-1/2, 3 for spin-1, etc.
`gyromagnetic_ratio`	Gyromagnetic ratio (in \(\text{MHz}/\text{T}\)).
`local_quasistatic_noise`	Local quasistatic noise components.
`name`	Name of the spin.
`operator`	Spin operator.
`operator_qubit_subspace`	Pauli operators defined on the qubit subspace.
`quadrupole_splitting`	Quadrupole splitting parameter (in \(\text{MHz}\)).
`quantization_axis`	Quantization axis of the spin.
`quantum_nums`	Quantum numbers corresponding to spin operator.
`qubit_subspace`	Qubit subspace that is defined by a two-length subset of the `quantum_nums`.
`rotating_frame_frequency`	Rotating frame frequency (in \(\text{MHz}\)).
`virtual_phase`	Virtual z-phase of the spin.
`ZEEMAN_SIGN`	Sign of the Zeeman term.