Barren gadgets

Implementation of perturbative gadgets for the mitigation of Barren plateaus in variational quantum algorithms as presented in this paper.

Main idea

Using a perturbation theory to create a perturbative gadget (inspired from adiabatic computing). The spectrum of a global Hamitlonian of interest is encoded within the low-energy subspace of some specially constructed Hamiltonian on a larger Hilbert space: the gadget Hamiltonian. For more details, see the full paper by Cichy, Fährmann et al..

How to use:

Perturbative gadgets for own applications

The method of main interest to the user will probably be that of automatic generation of the gadget Hamiltonian from a given target Hamiltonian. The method is gadgetize() from the NewPerturbativeGadgets class. To use it, first import the relevant packages

import pennylane as qml
from faehrmann_gadgets import NewPerturbativeGadgets

then create the (global) hamiltonian of interest. It should be built using the qml.Hamiltonian class and strings of single qubit operators. For example, the linear combination of two Pauli words

term1 = qml.operation.Tensor(qml.PauliX(0), qml.PauliX(1), qml.PauliY(2), qml.PauliZ(3))
term2 = qml.operation.Tensor(qml.PauliZ(0), qml.PauliY(1), qml.PauliX(2), qml.PauliX(3))
Hcomp = qml.Hamiltonian([0.4, 0.7], [term1, term2])

Next, create the gadgetizer object with the desired settings and generate the gadget Hamiltonian

gadgetizer = NewPerturbativeGadgets(perturbation_factor=1)
Hgad = gadgetizer.gadgetize(Hamiltonian=Hcomp, target_locality=3)

/!\ WARNING: The automatic gadgetization using our scripts will work for most simple cases and for the numerical examples presented from the paper, but does not cover all the extensions and edge cases presented there. Please check the gadgetized Hamiltonian (e.g. like done in /barren-gadgets/tests/new_gadget_decomposition_tests.py ) before running simulations with it.

Tutorial on how to use our gadgets

For those interested in the topic for whom it is new, we prepared a tutorial based on the Pennylane library. It can be found under /barren-gadgets/Pennylane-tutorial/perturbative_gadgets_for_VQE.ipynb. Just open the notebook and follow the tutorial!

Reproduction of the plots from the paper

This repository also contains the scripts used to generate the figures from the paper. For each, the simulation (hence generation of the data) and plotting are done independently. First of all, set where to save the data. To do so, in /barren-gadgets/src/data_management.py on lines 7, 38 and 95 set the relative path to where the files should be saved.

data_folder = '../path/to/your/storing/location'

To generate the data from figure 1, one needs to run /barren-gadgets/own-experiments/gadget_gradients_faehrmann.py three times, with the right settings on lines 14-22 and. First

# General parameters:
generating_Hamiltonian = "global"
num_samples = 1000
layers_list = [2, 5, 10, 20]
qubits_list = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
lambda_scaling = 1                        # w.r.t. lambda_max
gate_set = [qml.RX, qml.RY, qml.RZ]
newk = 3
seed = 43

for the target global Hamiltonian, then

# General parameters:
generating_Hamiltonian = "gadget"
num_samples = 1000
layers_list = [2, 5, 10, 20]
qubits_list = [4, 5, 6, 7, 8, 9]
lambda_scaling = 1                        # w.r.t. lambda_max
gate_set = [qml.RX, qml.RY, qml.RZ]
newk = 3
seed = 43

for the 3-local gadget construction and finally

# General parameters:
generating_Hamiltonian = "gadget"
num_samples = 1000
layers_list = [2, 5, 10, 20]
qubits_list = [4, 6, 8, 10, 12]
lambda_scaling = 1                        # w.r.t. lambda_max
gate_set = [qml.RX, qml.RY, qml.RZ]
newk = 4
seed = 43

gives the data for the 4-local gadget curves. Then, running /barren-gadgets/plotting/paper_plots.py having changed lines 11 and 186-188 to reflect the respective location of the data files and uncommenting only

variances_plots()

in the main loop will save a pdf of the figure under data_folder + '../plots/variances_new_gadget/variances_for_paper.pdf'.
Note: The data points will not be exactly the same since the data generation has been splitted in several runs due to access to computational resources, hence some data points in the paper resulted from 200 samples batches with different random seeds.

For figure 2, the file to generate the data is /barren-gadgets/own-experiments/gadget_scheduled_training.py with the settings on lines 12 to 20

use_exact_ground_energy = False
plot_data = False
save_data = True

computational_qubits = 5
newk = 3
max_iter = 500
step = 0.3
num_shots = None

and chosing

schedule = soi.linear_ala_new_gad(pf, opt, max_iter, newk, False)

on line 37. Then, to generate the figure itself one can run /barren-gadgets/plotting/paper_plots.py updating line 11 and lines 75 to 109 to reflect the location of the files generated in the previous step and uncommenting only

training_plots_with_statistics()

in the main loop. You will find the file under data_folder + '../plots/training_new_gadget/trainings_for_paper_with_stats.pdf'

Repository structure:

• own-experiments: compilation of scripts and notebooks corresponding to experiments on perturbative gadgets that have been re-written using more abstraction
  • gadget_gradients_faehrmann.py: main script to generate the data on gradient variances.
  • gadget_scheduled_training.py: script to run various kind of training simulations. Strongly relies on src/training/* for the running of the simulation (scheduled_training()) and for the definitions of the simulation settings (SchedulesOfInterest())
• src: folder with the source files containing methods used in the main scripts
  • data_management: methods used for saving, reading and recovering the data from the gradients calculations and training simulations
  • faehrmann_gadgets: automated generation of the gadget Hamiltonian according to Cichy, Fährmann et al. for any given computational Hamiltonian as qml. Hamiltonian
  • hardware_efficient_ansatz: compilation of classes falling under the "hardware efficient ansatz" description. Each has a method self.ansatz() that can be used with qml.ExpvalCost
    • AlternatingLayeredAnsatz(): as used by McClean et al. and Holmes et al..
    • SimplifiedAlternatingLayeredAnsatz(): as used in Cerezo et al., similar to qml.SimplifiedTwoDesign
    • HardwareEfficientAnsatz(): deprecated
  • jordan_gadgets: automated generation of the gadget Hamiltonian according to Jordan & Fahri for any given computational Hamiltonian as qml. Hamiltonian
  • merge_files: script used to merge several data files into a single one when the simulations where splitted into several runs
  • observables_holmes: (deprecated) class to generate the relevant observables related to the application of the perturbative gadgets from Jordan & Fahri to the examples from Holmes et al..
  • trainings: script containing the main method to run training simulations with schedules and a collection of relevant schedules for our work
• plotting: directory containing the notebooks displaying the main results
• tests: some test scripts to make sure that the main source files keep being correct implementations when updating them