py_alqorithms.sbtgd_circuit

py_alqorithms.sbtgd_circuit(unitary_circuit, number_system_qubits, system_bath_spin_spin, parameter, interactions, coupling_system_qubits, system_bath_spin_boson=None)

Function to create a system bath thermal gradient descten (SBTGD) circuit candidate

Here we construct test-circuits for running a system-bath-thermal-gradient-descent (SBTGD) method.

In the SBTGD method, we aim to find the a local minimum of a Hamiltonian that is stable under a set of thermal perturbations with a gradient-based approach.

We assume that a system bath coupling is created by the HQS Noise App Bath-Fitter with an XX coupling to produce an approximation of a desired bath.

Note that the algorithm assumes all-to-all-connectivity for now.

Parameters:

  • unitary_circuit (Circuit) -- The unitary circuit that applies a trotterized time evolution under the Spin-Hamiltonian.This is left for the user to construct to allow different algorithms to be used. Please note that thisassumes that the unitary circuit returns all logical qubits to the original order.

  • number_system_qubits (int) -- The number of system qubits.

  • system_bath_spin_spin (MixedHamiltonian) -- The spin-spin Hamiltonian of the system bath approach that has been fitted withthe HQS Noise App Bath-Fitter fit_spin_bath_to_spectral_function method. Needs to only have onesystem-spin and XX coupling. Will be transformed to different coupling candidates by the funciton.

  • parameter (float) -- The parameter determining the time propagation under the circuit. Usually the trotter time step times aa user chosen scaling factor.

  • interactions (Tuple[float, float, float]) -- Note that values like [1.,-1.,0.] are allowed.

  • coupling_system_qubits (List[int]) -- The indices of the system qubits that should couple to the bath.

  • system_bath_spin_boson (MixedLindbaldOpenSystem) -- The optional spin-boson Hamiltonian of the system bath approach that has been fitted with the HQS Noise App Bath-Fitter fit_spin_bath_to_spectral_function method. When this is provided, explicit damping Pragma operations will be inserted into the circuit. The timescale of the damping operations is assumed to be the same as the timescale of the trotter time step. This is useful for theoretical modeling a gradient descent with the optimal damping rates of the bath.

Returns:

The testing circuit for the gradient descent containing the unitary evolution, the

system bath-coupling, and bath time evolution.

Return type:

Circuit