BEAST with PT2 Correction

This guide explains how to use BEAST augmented with a second-order perturbative correction (often referred to as BEAST-PT2) in Kvantify Qrunch.

The perturbative correction improves the accuracy of the BEAST-VQE energy by recovering correlation effects that are not captured in the paired-electron ansatz.

The correction is inspired by:

Overview

BEAST-PT2 extends the standard BEAST-VQE calculation with a second-order perturbation theory correction computed from additional measurements.

This provides:

  • improved accuracy

  • reduced bias from the paired-electron approximation

  • access to physics beyond the seniority-zero model

When to use BEAST-PT2

The BEAST ansatz assumes all electrons are paired. While efficient, this introduces systematic limitations:

  • pair breaking effects are not described

  • single excitations are not included

  • dynamic correlation is partially missing

BEAST-PT2 addresses these limitations by incorporating perturbative corrections from additional excitation channels.

This typically yields energies closer to full configuration interaction (FCI) while retaining the efficiency of BEAST-VQE.

Minimal Example

adaptive_vqe_options = qc.options.IterativeVqeOptions(
    max_iterations=100,
    force_all_iterations=True,
)

estimator = (
    qc.estimator_creator()
    .excitation_gate()
    .choose_grouper()
    .beast()
    .choose_estimator_error_mitigator()
    .symmetry_adapted()
    .with_total_particle_conservation()
    .with_parallel_setting("parallel")
    .create()
)

beast_vqe_calculator = (
    qc.calculator_creator()
    .vqe()
    .iterative()
    .beast()
    .with_options(adaptive_vqe_options)
    .choose_minimizer()
    .quick_default()
    .with_second_order_corrector(estimator)
    .create()
)

This runs a standard BEAST-VQE calculation and augments the final energy with a second-order perturbative correction.

Correction Modes

Different perturbative models can be selected using the optional correction_mode argument:

.with_second_order_corrector(estimator, correction_mode)

Available modes:

“standard”

Includes pair-breaking excitations beyond the paired-electron space.

“singles”

Includes single excitations to recover missing orbital relaxation effects.

“standard_and_singles”

Combines both pair-breaking and single excitation corrections.

Example:

.with_second_order_corrector(
    estimator,
    correction_mode="standard_and_singles",
)

The perturbative correction requires additional measurements to construct reduced density matrices and therefore increases computational cost compared to standard BEAST-VQE.

However, the cost remains significantly lower than increasing the ansatz expressibility or using more general quantum chemistry methods.

Relationship to OO-BEAST-VQE

BEAST-PT2 and OO-BEAST-VQE address different limitations:

  • BEAST-PT2 adds perturbative correlation corrections.

  • OO-BEAST-VQE improves the orbital basis.

The two methods can be complementary.

See Also

References