noise_mapper_py.noisy_algorithm_model

noise_mapper_py.noisy_algorithm_model(circuit, hamiltonian, trotter_timestep)

Construct the noisy algorithm model from a circuit with noise operations.

The noisy algorithm model is the static noise model that effectively determines the time propagation when a quantum algorithm for the coherent time propagation under a Hamiltonian is run on a quantum computer with physical noise. For a detailed discussion see also http://arxiv.org/abs/2210.11371.

Parameters:

• circuit (qoqo.Circuit) -- The circuit of one Trotter-Step already annotated with decomposition blocks and noise operations.

• hamiltonian (PauliHamiltonian) -- The Hamiltonian that determines the coherent part of the time evolution.

• trotter_timestep (float) -- The virtual time the circuit propagates a state that has been prepared on the quantum computer.

Example:

>>> from noise_mapper_py import noisy_algorithm_model
... from qoqo import Circuit
... from qoqo import operations as ops
... from struqture_py import spins
...
... circuit = Circuit()
... # To be able to construct the noisy alqorithm model
... # the parts to the circuit simulation the
... circuit += ops.PragmaStartDecompositionBlock([0], {})
... circuit += ops.Hadamard(0)
... circuit += ops.PragmaDamping(0, 1e-3, 1e-3)
... circuit += ops.RotateZ(0, 0.01)
... circuit += ops.PragmaDamping(0, 1e-3, 1e-3)
... circuit += ops.Hadamard(0)
... circuit += ops.PragmaDamping(0, 1e-3, 1e-3)
... circuit += ops.PragmaStopDecompositionBlock([0])
...
... system = spins.PauliHamiltonian()
... system.set(spins.PauliProduct().x(0), 2)
...
... open_sytem = noisy_algorithm_model(circuit, system, 0.01)

Note:

To be as general as possible the noisy-algorithm extraction does not construct the quantum circuit that propagates a state for a virtual time. For the same reason the extraction method does not default to any physical noise model, but uses noise terms that have already been inserted in the circuit. The noise mapper can extract the noise for all circuits that meet the following conditions:

• The circuit implements one Trotter step in a time propagation

• The original Hamiltonian can be written as a sum of partial Hamiltonians

  H = H1 + H2 + ...

• The segments of the circuit that implement the time propagation under

  a partial Hamiltonian Hkare denoted by PragmaStartDecompositionBlock and PragmaStopDecompositionBlock

• The decomposition blocks do not overlap

• The circuit does not have free symbolic parameters

• The circuit already contains the effect of physical device noise

  on the circuit level, represented by qoqo noise operations like PragmaDamping, PragmaDephasing etc.

The method makes the assumption that the trotter-timestep t is short enough so that if LL1 and LL2 are Lindblad superoperators, exp(LL1 t) exp(LL2 t) is approximately equal to exp((LL1 + LL2) t) where exp(LL t) is shorhand for applying the full time propagation under the Lindblad superoperator LL