Common Hamiltonians (quanguru.QuantumToolbox.Hamiltonians)#

Contains functions to create some standard Hamiltonians.

Functions#

qubCavFreeHam(qubFreq, cavFreq, cavDim)

Creates Qubit + Cavity Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a}\) for given frequencies and truncated cavity dimension.

RabiHam(qubFreq, cavFreq, g, cavDim)

Creates Rabi Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a} + g\hat{\sigma}_{x}(\hat{a}^{\dagger} + \hat{a})\) for given frequencies, coupling strength, and truncated cavity dimension.

JCHam(qubFreq, cavFreq, g, cavDim)

Creates Jaynes-Cummings Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a} + g(\hat{\sigma}_{-}\hat{a}^{\dagger} + \hat{\sigma}_{+}\hat{a})\) for given frequencies, coupling strength, and truncated cavity dimension.

aJCHam(qubFreq, cavFreq, g, cavDim)

Creates anti-Jaynes-Cummings Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a} + g(\hat{\sigma}_{+}\hat{a}^{\dagger} + \hat{\sigma}_{-}\hat{a})\) for given frequencies, coupling strength, and truncated cavity dimension.

UJC(wq, wc, g, t, dimC[, sparse])

Analytical implementation of the time independante Jaynes-Cummings Unitary evolution

Function Name

Docstrings

Examples

Unit Tests

Tutorials

qubCavFreeHam

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RabiHam

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JCHam

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aJCHam

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UJC

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qubCavFreeHam(qubFreq: float, cavFreq: float, cavDim: int) → Tuple[spmatrix | ndarray, spmatrix | ndarray][source]#

Creates Qubit + Cavity Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a}\) for given frequencies and truncated cavity dimension.

Hilbert space ordering is \(Qubit\otimes Cavity\), i.e. qubit first.

Parameters:

  • qubFreq (float) – qubit frequency

  • cavFreq (float) – cavity frequency

  • cavDim (int) – (truncated) dimension for cavity

Returns:

Qubit + Cavity Hamiltonian for given frequencies and truncated cavity dimension.

Return type:

Matrix

Examples

# TODO

RabiHam(qubFreq: float, cavFreq: float, g: float, cavDim: int) → spmatrix | ndarray[source]#

Creates Rabi Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a} + g\hat{\sigma}_{x}(\hat{a}^{\dagger} + \hat{a})\) for given frequencies, coupling strength, and truncated cavity dimension.

Parameters:

  • cavFreq (float) – cavity frequency

  • qubFreq (float) – qubit frequency

  • g (float) – coupling strength

  • cavDim (int) – (truncated) dimension for cavity

Returns:

Rabi Hamiltonian for given frequencies

Return type:

Matrix

Examples

# TODO Create some examples both in here and the demo script

JCHam(qubFreq: float, cavFreq: float, g: float, cavDim: int) → spmatrix | ndarray[source]#

Creates Jaynes-Cummings Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a} + g(\hat{\sigma}_{-}\hat{a}^{\dagger} + \hat{\sigma}_{+}\hat{a})\) for given frequencies, coupling strength, and truncated cavity dimension.

Parameters:

  • cavFreq (float) – cavity frequency

  • qubFreq (float) – qubit frequency

  • g (float) – coupling strength

  • cavDim (int) – (truncated) dimension for cavity

Returns:

Jaynes-Cummings Hamiltonian for given frequencies

Return type:

Matrix

Examples

# TODO Create some examples both in here and the demo script

aJCHam(qubFreq: float, cavFreq: float, g: float, cavDim: int) → spmatrix | ndarray[source]#

Creates anti-Jaynes-Cummings Hamiltonian \(\frac{\omega_{q}}{2}\hat{\sigma}_{z} + \omega_{c}\hat{a}^{\dagger}\hat{a} + g(\hat{\sigma}_{+}\hat{a}^{\dagger} + \hat{\sigma}_{-}\hat{a})\) for given frequencies, coupling strength, and truncated cavity dimension.

Parameters:

  • cavFreq (float) – cavity frequency

  • qubFreq (float) – qubit frequency

  • g (float) – coupling strength

  • cavDim (int) – (truncated) dimension for cavity

Returns:

anti-Jaynes-Cummings Hamiltonian for given frequencies

Return type:

Matrix

Examples

# TODO Create some examples both in here and the demo script

UJC(wq: float, wc: float, g: float, t: float, dimC: int, sparse=False) → spmatrix | ndarray[source]#
Analytical implementation of the time independante Jaynes-Cummings Unitary evolution

see Stenholm 1973 (https://doi.org/10.1016/0370-1573(73)90011-2) #TODO: explain the basis

Parameters:

  • wq (float) – qubit frequency

  • wc (float) – cavity frequency

  • g (float) – coupling strength

  • t (float) – evolution time

  • dimC (int) – cavity dimention

Returns:

Unitary matrix describing free evolution of the Jaynes-Cummings model

Return type:

Matrix

Examples

# TODO Create some examples both in here and the demo script