hqs_qorrelator_app.NMRCorrelator

class hqs_qorrelator_app.NMRCorrelator

Create a new NMRCorrelator to calculate the correlation functions for NMR experiments.

The user can access the following options in order to tailor the NMRCorrelator class: * parallelization_blocks: whether to use parallelization_blocks noise insertion mode,

or the all_qubits noise insertion mode (default)

algorithm: the algorithm used for simulating the time evolution of a spin Hamiltonian on the quantum computer
initialisation: the type of initialisation to prepare the infinite temperature state
number_measurements: the number of measurements used in the circuit
b_field_direction: the direction of the external magnetic field for the NMR simulation
decomposition_blocks: whether to use decomposition blocks in the circuits

These can be changed using setters, as shown in the example below.

Example

>>> from hqs_qorrelator_app import NMRCorrelator
... correlator = NMRCorrelator()
... correlator.algorithm = "ParityBased"

Returns:: A new NMRCorrelator object.

__init__()

Methods

`__init__`()
`estimate_decoherence_rate`(trotter_timestep, ...)	Calculates an estimate of the overall decoherence rate of the problem.
`from_bincode`()	Convert the bincode representation of the NMRCorrelator to a NMRCorrelator using the [bincode] crate.
`from_json`()	Convert the json representation of a NMRCorrelator to a NMRCorrelator.
`insert_noise`(device, noise_models)	Insert noise Pragmas into Quantum porgram according to chosen noise model
`noisy_algorithm_model`(trotter_timestep, ...)	Returns the effective noise model derived from the circuit of one Trotterstep.
`spectrum_program_fixed_step`(...)	Creates a QuantumProgram to measure time dependent NMR Magnetization correlators.
`thermalization_fidelity`(trotter_timestep, ...)	Returns the thermalization_fidelity when applying one trotter timestep under the Hamiltonian
`to_bincode`()	Return the bincode representation of the NMRCorrelator using the [bincode] crate.
`to_json`()	Return the json representation of the NMRCorrelator.

Attributes

`algorithm`	Setter for the algorithm option for NMRCorrelator.
`b_field_direction`	Setter for the b_field_direction option of NMRCorrelator.
`decomposition_blocks`	Setter for the decomposition_blocks option of the NMRCorrelator.
`initialisation`	Setter for the initialisation option of NMRCorrelator.
`number_measurements`	Setter for the number of projective measurements used when measuring observables.
`number_samples`	Setter for the number of samples of initial states for the RandomStates initialization option.
`parallelization_blocks`	Setter for the parallelization blocks for noise insertion.

algorithm

Setter for the algorithm option for NMRCorrelator.

Four options are available:

ParityBased: An algorithm that implements the time evolution under a product of PauliOperators: via the total Parity of the set of involved qubits. The total parity is perpared in the last involved qubit.
QSWAP: Terms in the Hamiltonian involving two qubits are implemented using a swap network: that reorders the terms. Uses the ParityBased algorithm for multi qubit terms.
QSWAPMolmerSorensen: The QSWAP algorithm using variable angle Mølmer Sørensen XX interaction: gates
VariableMolmerSorensen: An algorithm that implements terms in the Hamiltonian: involving two qubits with a basis change and variable angle Mølmer Sørensen gates

Parameters:: algorithm (str) -- The option for the algorithm that is set.

b_field_direction

Setter for the b_field_direction option of NMRCorrelator.

This is the direction of the external magnetic field for the NMR simulation. If the field direction in the input Hamiltonian does not match this option, the NMRCorrelator will transform the Hamiltonian accordingly.

Parameters:: initialisation (str) -- The option for the b_field_direction that is set. Available options are X and Z.
Raises:: ValueError -- Option not available.

decomposition_blocks

Setter for the decomposition_blocks option of the NMRCorrelator.

Parameters:: decomposition_blocks (bool) -- Whether to activate the decomposition blocks option.

estimate_decoherence_rate(trotter_timestep, device, noise_models)

Calculates an estimate of the overall decoherence rate of the problem.

This will not perform full noise mapping but estimate the overall decoherence rate of the problem by summing up the decoherence rates of the individual noise contributions between the unitary gates, using the fact that the trace over the decoherence matris is invariant under unitary transformations.

Example

>>> from hqs_qorrelator_app import NMRCorrelator
... from struqture_py import spins
... import numpy as np
... from qoqo.devices import AllToAllDevice
...
... number_qubits = 2
... coupling = 1.0
... shift = 1.0
...
... hamiltonian = spins.PauliHamiltonian()
... for i in range(number_qubits):
...     hamiltonian.add_operator_product(spins.PauliProduct().z(i), -shift * i)
... for i in range(number_qubits - 1):
...     hamiltonian.add_operator_product(spins.PauliProduct().x(i).x(i + 1), coupling)
...     hamiltonian.add_operator_product(spins.PauliProduct().y(i).y(i + 1), coupling)
... device = AllToAllDevice(number_qubits, ["RotateX", "RotateZ"], ["CNOT"], 1.0).add_dephasing_all(0.001);
... correlator = NMRCorrelator()
...
... rate = correlator.estimate_decoherence_rate(hamiltonian, 0.1, device)

Parameters:

hamiltoninan (PauliHamiltonian) -- The quantum circuit simulating one Trotterstep.
trotter_timestep (float) -- The Trotter timestep that is simulated by the circuit.
device (qoqo.Device) -- The device representing the connectivity.
noise_models (List[NoiseModel]) -- Noise models determining noise properties.

Returns:

The estimated noise rate.

Return type:

CaclulatorFloat

Raises:

TypeError -- circuit argument cannot be converted to qoqo Circuit.
RuntimeError -- Extracting effective noise model failed.

from_bincode()

Convert the bincode representation of the NMRCorrelator to a NMRCorrelator using the [bincode] crate.

Parameters:

input (ByteArray) -- The serialized NMRCorrelator (in [bincode] form).

Returns:

The deserialized NMRCorrelator.

Return type:

NMRCorrelator

Raises:

TypeError -- Input cannot be converted to byte array.
ValueError -- Input cannot be deserialized to NMRCorrelator.

from_json()

Convert the json representation of a NMRCorrelator to a NMRCorrelator.

Parameters:: input (str) -- The serialized NMRCorrelator in json form.
Returns:: The deserialized NMRCorrelator.
Return type:: NMRCorrelator
Raises:: ValueError -- Input cannot be deserialized to NMRCorrelator.

initialisation

Setter for the initialisation option of NMRCorrelator.

Please note that, while the following options exist, only the all_initial_states option is currently supported: active_reset, measurement, dephasing, local_operator_measurement, all_initial_states.

Parameters:: initialisation (str) -- The option for the initialisation that is set.
Raises:: ValueError -- Option not available.

insert_noise(device, noise_models)

Insert noise Pragmas into Quantum porgram according to chosen noise model

Parameters:

program (qoqo.QuantumProgram)
device (qoqo.Device)
noise_models (List[NoiseModel]) -- Noise models determining noise properties.

Returns:

The QuantumProgram with noise inserted.

Return type:

QuantumProgram

Raises:

TypeError -- Input could not be converted to QuantumProgram.
TypeError -- Input could not be converted to qoqo Device.
TypeError -- Input could not be converted to List[NoiseModel].
RuntimeError -- Could not insert noise into the QuantumProgram.

noisy_algorithm_model(trotter_timestep, device, noise_models)

Returns the effective noise model derived from the circuit of one Trotterstep.

In this function the circuit simulating the time evolution for one Trotterstep is constructed from the provided Hamiltonian, the provied length of a Trotterstep and all internal parameters of the NMRCorrelator.

Example

>>> from hqs_qorrelator_app import NMRCorrelator
... from struqture_py import spins
... import numpy as np
... from qoqo.devices import AllToAllDevice
...
... number_qubits = 2
... coupling = 1.0
... shift = 1.0
...
... hamiltonian = spins.PauliHamiltonian()
... for i in range(number_qubits):
...     hamiltonian.add_operator_product(spins.PauliProduct().z(i), -shift * i)
... for i in range(number_qubits - 1):
...     hamiltonian.add_operator_product(spins.PauliProduct().x(i).x(i + 1), coupling)
...     hamiltonian.add_operator_product(spins.PauliProduct().y(i).y(i + 1), coupling)
... device = AllToAllDevice(number_qubits, ["RotateX", "RotateZ"], ["CNOT"], 1.0).add_dephasing_all(0.001);
... correlator = NMRCorrelator()
...
... noise_model = correlator.noisy_algorithm_model(hamiltonian, 0.1, device)

Note that the superoperator corresponds to the continuous time evolution of a density matrix but has been derived from a Trotterstep with a discrete time-step. This approximation is only valid if the time-step is short enough compared to the energy scales in the system that the Trotterization errors of the unitary evolution and the noise terms are small.

Parameters:

hamiltoninan (PauliHamiltonian) -- The quantum circuit simulating one Trotterstep.
trotter_timestep (float) -- The Trotter timestep that is simulated by the circuit.
device (qoqo.Device) -- The device representing the connectivity.
noise_models (List[NoiseModel]) -- Noise models determining noise properties.

Returns:

the effective noise system operator derived from the circuit of one Trotterstep.

Return type:

PauliLindbladNoiseOperator

Raises:

TypeError -- circuit argument cannot be converted to qoqo Circuit.
RuntimeError -- Extracting effective noise model failed.

number_measurements

Setter for the number of projective measurements used when measuring observables.

Parameters:: number_measurements (int) -- The new number of measurements

number_samples

Setter for the number of samples of initial states for the RandomStates initialization option.

Parameters:: number_samples (int) -- The new number of samples

parallelization_blocks

Setter for the parallelization blocks for noise insertion.

This controls the noise_mode of the NMRCorrelator:

If the parallelization input is false: the noise mode remains as AllQubits, which: is the default. In this case, the noise model adds noise on all qubits that are involved in the whole quantum circuit after each gate operation.
If the parallelization input is true, the noise mode is changed to: ParallelizationBlocks. In this case, the noise model adds noise on the qubits that are involved in a block or parallel operations. This noise is added after a PragmaStopParallelBlock that notifies the end of the parallel operations in a qoqo circuit.

Parameters:: parallelization (bool) -- The boolean indicating whether to use parallelization blocks for noise insertion, instead of noise on all qubits.

spectrum_program_fixed_step(trotter_timestep, gyromagnetic_factors, device)

Creates a QuantumProgram to measure time dependent NMR Magnetization correlators.

This method uses a fixed Trotter time-step and uses number-trottersteps as a free parameter.

The Hamiltonian of NRM systems contain different frequency scales. A large frequency Zeeman splitting and on a much lower frequency scale the chemical shifts of the on-site PauliZ terms and the interaction between spins.

This function assumes that the Spin-Hamiltonian has already been processed reduce the system to spins very close in Zeeman frequency and that the Rotating Wave Approximation (RWA) has been applied.

The Hamiltonian will have the form

H = sum gj * B * dj * B * Zj + sum Jjk (Xk Xk + YjYk + ZjZk)

where Zj, Yj and Xj are the Pauli Z, Y and X operators on site j and the sum goes over all indices. gj is the gyromagnetic factor dj are the chemical shifts and Jjk is the coupling between spins.

The quantity one is interested in in NMR is the correlator

C(t) = Tr(Splus(t) Sminus(0) rho)

where Splus is the plus magnetization operator Splus = sum gj (Xj - i Yj) / 4 and Sminus is the minus magnetization operator Sminus = sum gj (Xj + i Yj) / 4 and rho is the density matrix. Here we assume the system to be at infinite temperature compared to all other energy scales in the problem and rho is the identity matrix.

The quantum computer cannot simulate the evolution of Hamiltonians with a large separation of frequency scales accurately. The large energy scale (gj * B) is already eliminated from the Hamiltonian in the rotating wave approximation. The function will construct a quantum program that calculates the real and imaginary parts of C(t) which only involves simmulating the long time / low frequency part of the problem on the quantum computer.

Parameters:

hamiltonian (PauliHamiltonian) -- The Hamiltonian of the Spin system, already in RWA form.
trotter_timestep (float) -- One Trotterstep propagates the system under the hamiltonian for this time. Smallest time increment when running simulations.
gyromagnetic_factors (List[float]) -- The gyromagnetic factors for scaling the magnetization operators.
device (qoqo.Device) -- The device for which to create the QuantumProgram.

Returns:

A qoqo QuantumProgram for calculating the correlation function for a time.: The program takes time as the free parameter.

Return type:

QuantumProgram

Raises:

TypeError -- Input could not be converted to PauliHamiltonian.
TypeError -- Input could not be converted to qoqo Device.
RuntimeError -- Creating the QuantumProgram failed.

Example

>>> from hqs_qorrelator_app import NMRCorrelator
... from struqture_py import spins
... import numpy as np
... from qoqo_quest import backend
... from qoqo.devices import AllToAllDevice
...
...
... gyromagnetic = 1.0
... number_qubits = 2
... time = np.pi/4
... coupling = 1.0
... shift = 1.0
... gyromagnetic_factors = [gyromagnetic for _ in range(number_qubits)]
...
... hamiltonian = spins.PauliHamiltonian()
... for i in range(number_qubits):
...     hamiltonian.add_operator_product(spins.PauliProduct().z(i), -shift * i)
... for i in range(number_qubits - 1):
...     hamiltonian.add_operator_product(spins.PauliProduct().x(i).x(i + 1), coupling)
...     hamiltonian.add_operator_product(spins.PauliProduct().y(i).y(i + 1), coupling)
...
... nmr = NMRCorrelator()
... device = AllToAllDevice(number_qubits, ["RotateX", "RotateZ"], ["CNOT"], 1.0).add_dephasing_all(0.001);
... trotter_timestep = 0.01
... program = nmr.spectrum_program_fixed_step(hamiltonian, trotter_timestep, gyromagnetic_factors, device)
... backend = Backend(number_qubits)
... result = program.run([time], backend)
...
...

thermalization_fidelity(trotter_timestep, device, noise_models)

Returns the thermalization_fidelity when applying one trotter timestep under the Hamiltonian

During the calculation of the time-resolved correlation functions, the quantum computer propagates the state with a trotterization algorithm. The noise of the physical quantum computer leads to an effective hamiltonian noise model. In the ideal case, this effective noise will correspond to infinite temperature thermalization. In general, however, the effective noise model will not exactly correspond to infinite temperature. The noise model can contain biased noise rates that drive the system towards a state that is not the fully mixed state (which corresponding to infinite temperature). The thermalization fidelity is an approximate measure for the quality of the effective noise. It is given by 1 - sum of biased rates / sum of unbiased rates. A thermalization fidelity of 1 corresponds to a noise model closely matching infinite temperature environments and a thermalization fidelity of 0 corresponds to an environment that is far away from infinite temperature.

When calculating the thermalization fidelity, not all rates are categorized into biased or unbiased rates. These rates are discarded. The discarded weight gives the ratio between the discarded rates and all rates. A value of 0 corresponds to a reliable value for the thermalization fidelity.

Parameters:

hamiltonian (PauliHamiltonian) -- The Hamiltonian for which thermalization fidelity is calculated.
trotter_timestep (float) -- The Trotter timestep
device (qoqo.Device) -- The device determining the connectivity.
noise_models (List[NoiseModel]) -- Noise models determining noise properties.

Returns:

(infinite temperature thermalization fidelity, discarded weight)

Raises:

TypeError -- Input could not be converted to PauliHamiltonian.
TypeError -- Input could not be converted to qoqo Device.
TypeError -- Input could not be converted to List[NoiseModel].
RuntimeError -- Extracting effective noise model failed.

to_bincode()

Return the bincode representation of the NMRCorrelator using the [bincode] crate.

Returns:: The serialized NMRCorrelator (in [bincode] form).
Return type:: ByteArray
Raises:: ValueError -- Cannot serialize NMRCorrelator to bytes.

to_json()

Return the json representation of the NMRCorrelator.

Returns:: The serialized form of NMRCorrelator.
Return type:: str
Raises:: ValueError -- Cannot serialize NMRCorrelator to json.