Model

class Model(name=None)

Represent a coupled spin system.

This class provides a high-level abstraction for simulating quantum systems consisting of multiple coupled spins. It supports adding spins, interactions, static and driving magnetic fields. The model allows calculation of energy levels and eigenstates. In addition, it provides methods for computing parameters required to define control pulses (e.g. splittings, Rabi-frequencies, …). It enables the simulation of the system’s time evolution under the influence of driving fields and additional noise. It is especially suitable for modeling systems like nitrogen-vacancy centers.

The model owns the lifecycle of attached components. Spins, interactions, static fields, and driving fields should be attached using the corresponding add_spin(), add_interaction(), add_static_field(), and add_driving_field() methods, and removed using the matching remove_...() methods. After a component is attached, updating one of its physically relevant attributes automatically affects future accesses to derived model quantities such as the static Hamiltonian, eigensystem, or driving operators.

Rotating-frame frequencies, virtual phases, and pulse lists remain directly editable runtime settings unless a model-level rotating-frame setter is attached.

Initialize a model.

Parameters:

name (str) – Name of the model.

Hint

For example, to initialize a model for a nitrogen-vacancy center including the intrinsic nitrogen nuclear spin, one can use:

model = simphony.default_nv_model(nitrogen_isotope=14)

add_driving_field	Add a driving field to the model.
add_interaction	Add a spin-spin interaction to the model.
add_spin	Add a spin to the model.
add_static_field	Add a static field to the model.
basis	Product-basis labels of the full Hilbert space.
basis_qubit_subspace	Product-basis labels restricted to the qubit subspace of each spin.
dimension	Total dimension of the spin model.
driving_field	Return the instance of the driving field specified by name.
driving_field_names	Names of the driving fields.
driving_fields	Driving fields attached to the model.
driving_operators	Time-independent operator parts of the driving Hamiltonian.
eigenbasis	Eigenstates of static_hamiltonian expressed in the product basis.
eigenenergies	Eigenenergies of static_hamiltonian labeled by basis.
eigenenergy	Return the eigenenergy of a labeled eigenstate.
eigenstate	Return the static-Hamiltonian eigenstate assigned to the local-\(S_z\) product-basis state.
initial_state	Initial state used when state_only=True simulations are requested.
interactions	Interactions attached to the model.
last_pulse_end	Latest pulse end time across all driving fields.
local_quasistatic_noise_operators	Time-independent operators of the local quasistatic-noise Hamiltonian.
matrix_element	Return the matrix element of the effective driving operator between two states.
n_spins	Number of the spins.
name	Name of the model.
operator_from_string	Return tensor product operator from an extended operator string.
plot_driving_fields	Plot the pulses of the driving fields.
plot_levels	Plot the energy spectrum with optionally zoomed electron subpanels.
productstate	Return the product-basis state for the given per-spin quantum numbers.
project_to_qubit_subspace	Project an operator or batch of operators into the qubit subspace.
pulses	Concatenated pulse list from all driving fields.
rabi_amplitude	Return the driving-field amplitude for a single Rabi cycle.
rabi_amplitude_qubit	Return the driving-field amplitude for a single Rabi cycle.
rabi_period	Return the period time of a Rabi cycle.
rabi_period_qubit	Return the period time of a Rabi cycle.
remove_all_pulses	Remove all pulses from every driving field and reset virtual z-phases.
remove_driving_field	Remove a driving field from the model.
remove_interaction	Remove an interaction from the model.
remove_spin	Remove a spin from the model.
remove_static_field	Remove a static field from the model.
rotating_frame	Optional rotating-frame setter that owns per-spin frame frequencies.
rotating_frame_frequencies	Per-spin rotating-frame frequencies used by 'local_qubit_z'.
rotating_frame_hamiltonian	Hamiltonian used to construct the rotating-frame operator.
rotating_frame_operator	Return the rotating-frame operator defined by rotating_frame_hamiltonian.
simulate_time_evolution	Simulate the model's time evolution under its driving fields and noise.
spin	Return the instance of the spin specified by name.
spin_names	Names of the spins.
spins	Spins attached to the model.
splitting	Return the energy splitting between the two eigenstates of the model.
splitting_qubit	Return the energy splitting between the two eigenstates of the model.
state	Return the state of the model corresponding to the given quantum numbers.
static_fields	Static fields attached to the model.
static_hamiltonian	Static part of the Hamiltonian in the model's full Hilbert space.
subdimensions	Dimensions of the spins.
test_labeling	Inspect eigenstate labeling quality in the local-\(S_z\) product basis.
virtual_phases	Per-spin virtual z-phases.
virtual_phases_operator	Return the operator corresponding to the virtual z-phases:

Overview

name	Name of the model.
n_spins	Number of the spins.
dimension	Total dimension of the spin model.
subdimensions	Dimensions of the spins.
spin_names	Names of the spins.
driving_field_names	Names of the driving fields.

Components

spins	Spins attached to the model.
spin(name)	Return the instance of the spin specified by name.
add_spin(spin)	Add a spin to the model.
remove_spin(spin[, include_interactions])	Remove a spin from the model.
interactions	Interactions attached to the model.
add_interaction(interaction)	Add a spin-spin interaction to the model.
remove_interaction(interaction)	Remove an interaction from the model.
static_fields	Static fields attached to the model.
add_static_field(static_field[, target_spins])	Add a static field to the model.
remove_static_field(static_field)	Remove a static field from the model.
driving_fields	Driving fields attached to the model.
driving_field(name)	Return the instance of the driving field specified by name.
add_driving_field(driving_field[, target_spins])	Add a driving field to the model.
remove_driving_field(driving_field)	Remove a driving field from the model.

Bases and Eigensystem

basis	Product-basis labels of the full Hilbert space.
basis_qubit_subspace	Product-basis labels restricted to the qubit subspace of each spin.
state(quantum_nums[, basis, coeffs_basis])	Return the state of the model corresponding to the given quantum numbers.
productstate(quantum_nums)	Return the product-basis state for the given per-spin quantum numbers.
eigenstate(quantum_nums)	Return the static-Hamiltonian eigenstate assigned to the local-\(S_z\) product-basis state.
eigenenergy(quantum_nums)	Return the eigenenergy of a labeled eigenstate.
eigenbasis	Eigenstates of static_hamiltonian expressed in the product basis.
eigenenergies	Eigenenergies of static_hamiltonian labeled by basis.

Hamiltonians, Operators and Frames

static_hamiltonian	Static part of the Hamiltonian in the model's full Hilbert space.
driving_operators	Time-independent operator parts of the driving Hamiltonian.
local_quasistatic_noise_operators	Time-independent operators of the local quasistatic-noise Hamiltonian.
rotating_frame	Optional rotating-frame setter that owns per-spin frame frequencies.
rotating_frame_frequencies	Per-spin rotating-frame frequencies used by 'local_qubit_z'.
rotating_frame_hamiltonian	Hamiltonian used to construct the rotating-frame operator.
rotating_frame_operator(t[, only_diag, ...])	Return the rotating-frame operator defined by rotating_frame_hamiltonian.
virtual_phases	Per-spin virtual z-phases.
virtual_phases_operator([only_diag, ...])	Return the operator corresponding to the virtual z-phases:
operator_from_string(string[, in_qubit_subspace])	Return tensor product operator from an extended operator string.

Transitions and Control

splitting(spin_name, quantum_nums[, ...])	Return the energy splitting between the two eigenstates of the model.
splitting_qubit(spin_name[, rest_quantum_nums])	Return the energy splitting between the two eigenstates of the model.
rabi_amplitude(driving_field_name, ...)	Return the driving-field amplitude for a single Rabi cycle.
rabi_amplitude_qubit(driving_field_name, ...)	Return the driving-field amplitude for a single Rabi cycle.
rabi_period(driving_field_name, amplitude, ...)	Return the period time of a Rabi cycle.
rabi_period_qubit(driving_field_name, ...[, ...])	Return the period time of a Rabi cycle.
matrix_element(driving_field_name, state1, ...)	Return the matrix element of the effective driving operator between two states.

Simulation

simulate_time_evolution([n_shots, start, ...])	Simulate the model's time evolution under its driving fields and noise.
initial_state	Initial state used when state_only=True simulations are requested.
pulses	Concatenated pulse list from all driving fields.
last_pulse_end	Latest pulse end time across all driving fields.
remove_all_pulses()	Remove all pulses from every driving field and reset virtual z-phases.

Visualization

plot_driving_fields([name, function, start, end])	Plot the pulses of the driving fields.
plot_levels([zoom_electron_state, height, ...])	Plot the energy spectrum with optionally zoomed electron subpanels.

Utils

project_to_qubit_subspace(unitary[, ...])	Project an operator or batch of operators into the qubit subspace.
test_labeling([output, return_type, ...])	Inspect eigenstate labeling quality in the local-\(S_z\) product basis.