Basic workflow

To perform Quantum Phase Estimation with the toolbox, take the following steps:

1. The Hamiltonian class describes the qubit Hamiltonian. Chose a system:

   1.1. Spin model with e.g. heisenberg_hamiltonian or a custom Hamiltonian instance.

   1.2. Molecule with chemistry_hamiltonian; see the tutorial on Chemistry to qubit Hamiltonians.

2. Prepare an initial state as a Matrix Product State. Two methods are available:

   2.1. Density Matrix Renormalization Group (DMRG) - see the tutorial on Chemistry to qubit Hamiltonians.

   2.2. Parametrized circuit optimization - see the tutorial on Variational circuit preparation.

3. Encode \(\hat{H}\) into a unitary via either:

   3.1. Exact time evolution or Trotterization, available as methods of the Hamiltonian class - see the tutorial on Trotterization.

   3.2. Block encoding functions from the lcu_walk_operator module - see the tutorial on Linear Combination of Unitaries.

4. Initialize circuit. From circuit.initialization, chose between:

   4.1. make_circ to create a Tensor Network representation of the circuit.

   4.2. make_circMPS to store the state as an MPS and iteratively apply the gates.

   See the tutorials on Building circuits, MPS performance and Hyperoptimization for an introduction on circuit simulation with quimb.

5. Run QPE: in estimation module, chose between

   5.1. Textbook QPE: phase_estimation - see this tutorial.

   5.2. Robust Phase Estimation, a version of QPE with a single ancilla and circuit repetitions: robust_phase_estimation - see the corresponding tutorial.