Scale SQD chemistry workflows with the SBD eigensolver

This guide shows how to use the SBD eigensolver as an alternative selected configuration interaction (SCI) solver to diagonalize larger fermionic problems beyond what the default PySCF solver can support. SBD (Selected Basis Diagonalization) runs in-process, is parallelized with MPI, and offers both CPU and CUDA backends. For information on how to install and use it, see the SBD documentation.

SBD compiles a C++ extension against the MPI and BLAS libraries available on the machine, so you must install both before you install the sbd extra:

pip install qiskit-addon-sqd[sbd]

Because solve_sci_batch already matches the solver interface that diagonalize_fermionic_hamiltonian expects, you can pass it directly to sci_solver after you bind its configuration options with functools.partial. To run on a CUDA-capable GPU instead of the CPU, pass device_config=DeviceConfig.gpu() from sbd.device_config.

For more details on the SQD code used in this example, see the chemistry Hamiltonian tutorial.

from functools import partial

import numpy as np
import pyscf
import pyscf.cc
import pyscf.mcscf
from qiskit_addon_sqd.counts import generate_bit_array_uniform
from qiskit_addon_sqd.fermion import diagonalize_fermionic_hamiltonian
from sbd.sbd_solver import solve_sci_batch

# Specify molecule properties
num_orbitals = 16
num_elec_a = num_elec_b = 5
spin_sq = 0

# Build N2 molecule
mol = pyscf.gto.Mole()
mol.build(
    atom=[["N", (0, 0, 0)], ["N", (1.0, 0, 0)]],
    basis="6-31g",
    symmetry="Dooh",
)

# Define active space
n_frozen = 2
active_space = range(n_frozen, mol.nao_nr())

# Get molecular integrals
scf = pyscf.scf.RHF(mol).run()
num_orbitals = len(active_space)
n_electrons = int(sum(scf.mo_occ[active_space]))
num_elec_a = (n_electrons + mol.spin) // 2
num_elec_b = (n_electrons - mol.spin) // 2
cas = pyscf.mcscf.CASCI(scf, num_orbitals, (num_elec_a, num_elec_b))
mo = cas.sort_mo(active_space, base=0)
hcore, nuclear_repulsion_energy = cas.get_h1cas(mo)
eri = pyscf.ao2mo.restore(1, cas.get_h2cas(mo), num_orbitals)

# Compute exact energy
exact_energy = cas.run().e_tot

# Create a seed to control randomness throughout this workflow
rng = np.random.default_rng(24)


# Generate random samples
bit_array = generate_bit_array_uniform(10_000, num_orbitals * 2, rand_seed=rng)

# Bind the SBD solver options. method=0 selects the Davidson eigensolver.
sbd_solver = partial(
    solve_sci_batch,
    sbd_config={"method": 0, "eps": 1e-5, "max_it": 10, "max_nb": 10},
)

# Run SQD
result = diagonalize_fermionic_hamiltonian(
    hcore,
    eri,
    bit_array,
    samples_per_batch=300,
    norb=num_orbitals,
    nelec=(num_elec_a, num_elec_b),
    num_batches=5,
    max_iterations=5,
    sci_solver=sbd_solver,
    symmetrize_spin=True,
    seed=rng,
)

WARN: Unable to to identify input symmetry using original axes.
Different symmetry axes will be used.

converged SCF energy = -108.835236570774
CASCI E = -109.046671778080  E(CI) = -32.8155692383188  S^2 = 0.0000000
Energy = -28.25375765030941
Energy = -28.25375765030941
Energy = -28.25375765030941
Energy = -28.25375765030941
Energy = -28.25375765030941
Energy = -30.63923484895107
Energy = -31.84189676459039
Energy = -32.67859713028513
Energy = -31.68346579646724
Energy = -31.89038148016397
Energy = -32.77440443557443
Energy = -32.7445862988791
Energy = -32.77705680502877
Energy = -32.781393512705
Energy = -32.76632732988578
Energy = -32.80004322621618
Energy = -32.79978483683345
Energy = -32.79978311278118
Energy = -32.79811950451766
Energy = -32.80031839350911
Energy = -32.80388159827887
Energy = -32.80421476938036
Energy = -32.80490490614043
Energy = -32.80449612243751
Energy = -32.80517636244122

print(f"Exact energy: {exact_energy}")
print(f"Estimated energy: {result.energy + nuclear_repulsion_energy}")

Exact energy: -109.04667177808021
Estimated energy: -109.03627890220267