Choose an Initial Ansatz Builder

Goal

Select the initial state (reference circuit) that a VQE calculation starts from.

Overview

The initial ansatz is the circuit that prepares the reference state before the adaptive VQE loop starts adding gates. It can be attached to a VQE calculator via the fluent step .choose_initial_ansatz_builder() and then picking one initial ansatz.

import qrunch as qc

calculator = (
    qc.calculator_creator()
    .vqe()
    .iterative()
    .standard()
    .choose_initial_ansatz_builder()
      # .<pick-an-initial-ansatz>(...)
    .create()
)

Available Initial Ansätze

Hartree-Fock (Default)

Uses the Hartree-Fock determinant as the initial state. This is the default reference state and a good choice for most standard problems.

calculator = (
    qc.calculator_creator()
    .vqe()
    .iterative()
    .standard()
    .choose_initial_ansatz_builder()
    .hartree_fock()
    .create()
)

Møller-Plesset 2nd order (MP2)

Uses a circuit that mimics the Møller-Plesset 2nd order (MP2) wave function as the initial state. The MP2 wave function is the first-order correction to the Hartree-Fock wave function, so the MP2 ansatz starts the VQE from a state that already captures some electron correlation.

calculator = (
    qc.calculator_creator()
    .vqe()
    .iterative()
    .standard()
    .choose_initial_ansatz_builder()
    .moller_plesset_2()
    .create()
)

Note

The MP2 initial ansatz is a circuit that mimics the MP2 wave function. It cannot be expected to reproduce the MP2 energy exactly, but it provides a starting state close to it.

When to use the MP2 initial ansatz

The MP2 initial ansatz is recommended whenever MP2 orbitals are used to define the problem, i.e.:

When MP2 is used as the embedded_orbital_calculator of a projective embedding calculation.

When an MP2 molecular_orbital_calculator is chosen for a standard ground-state problem, e.g.:

problem_builder = (
    qc.problem_builder_creator()
    .ground_state()
    .standard()
    .choose_molecular_orbital_calculator()
    .moller_plesset_2()
    .create()
)

You can optionally forward MP2 and beam-search options, and set the amplitude threshold used when constructing the MP2 wave function from the t2 amplitudes:

.choose_initial_ansatz_builder()
.moller_plesset_2(
    mp2_options=my_mp2_options,
    beam_search_options=my_beam_search_options,
    amplitude_threshold=1e-8,
)