Performing a Standard FAST-VQE Convergence Study
In this example, we plot the convergence of a FAST Variational Quantum Eigensolver (FAST-VQE) calculation.
Full Script
The script below shows the full script, which is then explained section by section.
1"""Demonstrate FAST-VQE convergence plotting on LiH molecule."""
2# ruff: noqa # ruff: ignore[noqa-comments]
3
4from pathlib import Path
5
6import matplotlib.pyplot as plt
7import numpy as np
8
9import qrunch as qc
10
11
12def plot_energies(
13 fast_energies: list[float],
14 reference_energy: float,
15 *,
16 outdir: Path = Path("dist"),
17 show: bool = False,
18) -> None:
19 """
20 Plot VQE energy convergence and log-scale error vs reference energy.
21
22 Args:
23 fast_energies: Sequence of total energies per VQE iteration.
24 reference_energy: Reference total energy (e.g., FCI) to compare against.
25 outdir: Output directory where plots are written. Defaults to "dist".
26 show: Whether to display the figures interactively after saving.
27 """
28 # Convert to a NumPy array for safe numeric operations and validation.
29 energies = np.asarray(list(fast_energies), dtype=float)
30
31 # Basic validation to help catch silent failures early.
32 if energies.size == 0:
33 msg = "fast_energies must contain at least one value."
34 raise ValueError(msg)
35 if not np.isfinite(energies).all():
36 msg = "fast_energies contains non-finite values."
37 raise ValueError(msg)
38 if not np.isfinite(reference_energy):
39 msg = "reference_energy must be finite."
40 raise ValueError(msg)
41
42 # Prepare x-axis as 1-based iteration indices for readability.
43 iterations = np.arange(1, energies.size + 1, dtype=int)
44
45 # Ensure output directory exists.
46 outdir.mkdir(parents=True, exist_ok=True)
47
48 # -----------------------------
49 # Figure 1: Energies vs Iteration
50 # -----------------------------
51 fig1 = plt.figure()
52 plt.plot(iterations, energies, "-*", color="darkgreen", label="FAST-VQE") # points to visualize steps
53 plt.axhline(reference_energy, linestyle="--", color="black", label="Reference")
54 plt.xlabel("Iteration number")
55 plt.ylabel("Total energy [Hartree]")
56 plt.title("FAST-VQE convergence")
57 plt.legend()
58 plt.tight_layout()
59
60 convergence_plot = outdir / "vqe_convergence.png"
61 fig1.savefig(convergence_plot, dpi=200, bbox_inches="tight")
62
63 # -----------------------------
64 # Figure 2: |Energy - Reference| (log scale)
65 # -----------------------------
66 # Use absolute error; add a tiny epsilon to avoid log(0) if we hit the reference exactly.
67 eps = np.finfo(float).eps
68 abs_error = np.abs(energies - reference_energy) + eps
69
70 fig2 = plt.figure()
71 plt.semilogy(iterations, abs_error, "-*", color="darkgreen", label="|E - E_ref|")
72 plt.xlabel("Iteration number")
73 plt.ylabel("Absolute error [Hartree]")
74 plt.title("FAST-VQE error vs reference")
75 plt.legend()
76 plt.tight_layout()
77
78 error_convergence_plot = outdir / "vqe_error_semilogy.png"
79 fig2.savefig(error_convergence_plot, dpi=200, bbox_inches="tight")
80
81 if show:
82 plt.show()
83 else:
84 # Close figures to free memory when running in batch contexts.
85 plt.close(fig1)
86 plt.close(fig2)
87
88
89
90
91def main() -> list[float]:
92 """Run FAST-VQE on LiH as the first script."""
93 path_to_molecule_xyz_file = Path().absolute() / "qrunch" / "tests" / "demo_scripts" / "lih.xyz"
94 # Build Lithium Hydride (LiH) molecular configuration from xyz file.
95 molecular_configuration = qc.build_molecular_configuration(
96 molecule=Path(path_to_molecule_xyz_file),
97 basis_set="sto3g",
98 spin_difference=0,
99 charge=0,
100 units="angstrom",
101 )
102
103 # Build the ground state problem.
104 problem_builder = qc.problem_builder_creator().ground_state().standard().create()
105 ground_state_problem = problem_builder.build_unrestricted(molecular_configuration)
106
107 adaptive_vqe_options = qc.options.IterativeVqeOptions(
108 max_iterations=100, # Increase the maximum number of iterations
109 gates_per_iteration=1, # Add one gate per iteration (Recommended)
110 force_all_iterations=True, # Force all iterations to run, independent of convergence.
111 )
112
113 # Build the user-configured VQE calculator instance
114 fast_vqe_calculator = (
115 qc
116 .calculator_creator() # Start creating a calculator
117 .vqe() # Narrow: pick Variational quantum eigensolver (VQE)
118 .iterative() # Narrow: pick the iterative VQE
119 .standard() # Narrow: pick the standard iterative VQE (FAST-VQE)
120 .with_options(adaptive_vqe_options) # Use the user-defined iterative VQE options
121 .choose_minimizer() # Start sub-choice: Choose the gate parameter minimizer
122 .quick_default() # Perform the sub-choice selection - Here we pick the greedy and quick minimizer
123 .create() # Create the calculator instance
124 )
125
126 result = fast_vqe_calculator.calculate(ground_state_problem)
127
128 # We can get a nice timings report.
129 print(qc.get_execution_times_report())
130
131 # Extract FAST-VQE energies for plotting
132 fast_energies = result.total_energy_per_macro_iteration_with_initial_energy_and_final_energy.values
133
134 # Build a Full Configuration Interaction (FCI) calculator
135 full_configuration_interaction_calculator = (
136 qc
137 .calculator_creator() # Start creating a calculator
138 .configuration_interaction() # Narrow: pick Configuration Interaction (CI)
139 .standard() # Narrow: pick standard CI (not paired version)
140 .create() # Create the calculator instance
141 )
142
143 # Calculate the FCI result for reference energy
144 fci_result = full_configuration_interaction_calculator.calculate(ground_state_problem)
145
146 # Plot the convergence and error relative to FCI reference.
147 plot_energies(fast_energies, reference_energy=fci_result.total_energy.value, show=True)
148
149 return fast_energies
150
151
152if __name__ == "__main__":
153 main()
The script requires an XYZ file specifying the molecule: Download lih.xyz
Explanation
Import Kvantify Qrunch
from pathlib import Path import matplotlib.pyplot as plt import numpy as np import qrunch as qc
This code snippet loads the python packages we need. The public and stable Kvantify Qrunch API is loaded as
import qrunch as qc. This is the only import you need for most tasks, and the only one that is guaranteed to be supported across versions. In addition, we usematplotlib,numpy, andPath(frompathlib).The plotting method
def plot_energies( fast_energies: list[float], reference_energy: float, *, outdir: Path = Path("dist"), show: bool = False, ) -> None: """ Plot VQE energy convergence and log-scale error vs reference energy. Args: fast_energies: Sequence of total energies per VQE iteration. reference_energy: Reference total energy (e.g., FCI) to compare against. outdir: Output directory where plots are written. Defaults to "dist". show: Whether to display the figures interactively after saving. """ # Convert to a NumPy array for safe numeric operations and validation. energies = np.asarray(list(fast_energies), dtype=float) # Basic validation to help catch silent failures early. if energies.size == 0: msg = "fast_energies must contain at least one value." raise ValueError(msg) if not np.isfinite(energies).all(): msg = "fast_energies contains non-finite values." raise ValueError(msg) if not np.isfinite(reference_energy): msg = "reference_energy must be finite." raise ValueError(msg) # Prepare x-axis as 1-based iteration indices for readability. iterations = np.arange(1, energies.size + 1, dtype=int) # Ensure output directory exists. outdir.mkdir(parents=True, exist_ok=True) # ----------------------------- # Figure 1: Energies vs Iteration # ----------------------------- fig1 = plt.figure() plt.plot(iterations, energies, "-*", color="darkgreen", label="FAST-VQE") # points to visualize steps plt.axhline(reference_energy, linestyle="--", color="black", label="Reference") plt.xlabel("Iteration number") plt.ylabel("Total energy [Hartree]") plt.title("FAST-VQE convergence") plt.legend() plt.tight_layout() convergence_plot = outdir / "vqe_convergence.png" fig1.savefig(convergence_plot, dpi=200, bbox_inches="tight") # ----------------------------- # Figure 2: |Energy - Reference| (log scale) # ----------------------------- # Use absolute error; add a tiny epsilon to avoid log(0) if we hit the reference exactly. eps = np.finfo(float).eps abs_error = np.abs(energies - reference_energy) + eps fig2 = plt.figure() plt.semilogy(iterations, abs_error, "-*", color="darkgreen", label="|E - E_ref|") plt.xlabel("Iteration number") plt.ylabel("Absolute error [Hartree]") plt.title("FAST-VQE error vs reference") plt.legend() plt.tight_layout() error_convergence_plot = outdir / "vqe_error_semilogy.png" fig2.savefig(error_convergence_plot, dpi=200, bbox_inches="tight") if show: plt.show() else: # Close figures to free memory when running in batch contexts. plt.close(fig1) plt.close(fig2)
This code plot the convergence of the VQE energy and the error relative to the reference full configuration interaction (FCI) energy.
The code generates two PNG files under
dist/:vqe_convergence.pngvqe_error_semilogy.png
Molecule from XYZ file
# Build Lithium Hydride (LiH) molecular configuration from xyz file. molecular_configuration = qc.build_molecular_configuration( molecule=Path(path_to_molecule_xyz_file), basis_set="sto3g", spin_difference=0, charge=0, units="angstrom", )
We load LiH from an XYZ file, set the STO-3G basis, neutral charge, zero spin difference, and specify that the unit is ångström.
Build the ground-state problem
# Build the ground state problem. problem_builder = qc.problem_builder_creator().ground_state().standard().create() ground_state_problem = problem_builder.build_unrestricted(molecular_configuration)
We create a standard ground-state problem using the problem builder. Here we use the unrestricted variant for LiH (spin up and spin down electrons are allowed to occupy different spatial orbitals).
Configure and create the FAST-VQE calculator
adaptive_vqe_options = qc.options.IterativeVqeOptions( max_iterations=100, # Increase the maximum number of iterations gates_per_iteration=1, # Add one gate per iteration (Recommended) force_all_iterations=True, # Force all iterations to run, independent of convergence. ) # Build the user-configured VQE calculator instance fast_vqe_calculator = ( qc .calculator_creator() # Start creating a calculator .vqe() # Narrow: pick Variational quantum eigensolver (VQE) .iterative() # Narrow: pick the iterative VQE .standard() # Narrow: pick the standard iterative VQE (FAST-VQE) .with_options(adaptive_vqe_options) # Use the user-defined iterative VQE options .choose_minimizer() # Start sub-choice: Choose the gate parameter minimizer .quick_default() # Perform the sub-choice selection - Here we pick the greedy and quick minimizer .create() # Create the calculator instance )
We specify that we want a maximum of 100 iterations, one gate per iteration, and we force all iterations to be executed, independent of any stopping criteria.
We then build the adaptive VQE calculator with the specified options, where we choose a quick default gate parameter optimization method, optimizing only the parameter of the last gate in every iteration.
Run and extract energies
result = fast_vqe_calculator.calculate(ground_state_problem)
We run the VQE calculation, and here we also print a timing report for profiling:
# We can get a nice timings report. print(qc.get_execution_times_report())
Compute a high-accuracy FCI reference
# Build a Full Configuration Interaction (FCI) calculator full_configuration_interaction_calculator = ( qc .calculator_creator() # Start creating a calculator .configuration_interaction() # Narrow: pick Configuration Interaction (CI) .standard() # Narrow: pick standard CI (not paired version) .create() # Create the calculator instance ) # Calculate the FCI result for reference energy fci_result = full_configuration_interaction_calculator.calculate(ground_state_problem)
We build a FCI calculator and calculate the FCI energy for the same problem.
Make the plots
# Plot the convergence and error relative to FCI reference. plot_energies(fast_energies, reference_energy=fci_result.total_energy.value, show=True)
We plot the VQE convergence and the error relative to the FCI reference, by calling the plotting function defined above.
Running the Example
After saving the script as run_vqe_convergence.py,
you can run it directly from the command line:
$ python run_vqe_convergence.py
You should see 2 plots:
