Mandacaru

Mandacaru is a Python framework for fermionic quantum simulation with variational quantum algorithms. From an ASE geometry it builds a real-space Hamiltonian, maps it to qubits, and solves it with VQE or ADAPT-VQE on a state-vector simulator or on quantum hardware (IBM Quantum, Amazon Braket).

Installation

pip install mandacaru

# PAW datasets (kept in a separate repository because of their size)
git clone https://github.com/seixas-research/mandacaru-paw.git
mandacaru --link-paw mandacaru-paw

LiH with ASE

from ase import Atoms
from mandacaru import Mandacaru
from mandacaru.optimizers import Optimizer

atoms = Atoms("LiH",
              positions=[[0.0, 0.0, 0.0],
                         [0.0, 0.0, 1.6]],
              cell=[10.0, 10.0, 10.0])
atoms.center()                                      # the cell is the real-space box

atoms.calc = Mandacaru(method="adapt-vqe",                   # "vqe" | "adapt-vqe" | "subspace-vqe" | "subspace-adapt-vqe"
                       basis={"name": "PAW",
                              "size": "DZP",
                              "energy_shift": 0.1},          # pseudopotential family + valence basis
                       h=0.10,                               # grid spacing (Å)
                       pool="fermionic",                     # "fermionic" | "qubit" | "qeb" | "ceo" | "ceo-ovp"
                       mapping="jordan_wigner",              # "jordan_wigner" | "parity" | "parity_reduced" | "bravyi_kitaev"
                       optimizer=Optimizer(method="SLSQP",   # or SPSA | COBYLA | Nelder-Mead | Adam | L-BFGS-B
                                           maxiter=2000,
                                           tol=1e-12),
                       max_iterations=300,                   # at most 300 operators
                       gradient_tolerance=1e-3,              # stop when every pool gradient is smaller
                       device="AER_simulator",               # or an IBM Quantum / Amazon Braket device
                       shots=0,                              # 0 = exact expectation values
                       verbose_operators=False,              # True -> the pool to pool.json
                       verbose_hamiltonian=False)            # True -> hamiltonian.inspect.json

forces = atoms.get_forces()                         # eV/Å, runs the simulation
energy = atoms.get_potential_energy()               # eV, from the same run
result = atoms.calc.result

print(f"E = {energy:.4f} eV with {result.num_operators} operators")
print(f"F(Li) = {forces[0, 2]:+.3f} eV/Å along the bond")

Potential energy surface

import matplotlib.pyplot as plt
import numpy as np
from ase import Atoms
from mandacaru import Mandacaru
from mandacaru.optimizers import Optimizer

distances = np.linspace(1.2, 3.0, 10)
energies = []
for d in distances:
    atoms = Atoms("LiH",
                  positions=[[0.0, 0.0, 0.0],
                             [0.0, 0.0, d]],
                  cell=[10.0, 10.0, 10.0])
    atoms.center()

    atoms.calc = Mandacaru(method="adapt-vqe",
                           basis={"name": "PAW",
                                  "size": "DZP",
                                  "energy_shift": 0.1},
                           h=0.10,
                           pool="fermionic",
                           optimizer=Optimizer(method="L-BFGS-B",
                                               maxiter=2000,
                                               tol=1e-12))
    energies.append(atoms.get_potential_energy())

plt.plot(distances, energies, "o-")
plt.xlabel("Li–H distance (Å)")
plt.ylabel("Energy (eV)")
plt.savefig("lih_pes.png", dpi=150)

Theory

VQE. The variational quantum eigensolver prepares a parameterized state |ψ(θ)⟩ = U(θ)|Φ_HF⟩ on a quantum processor, measures the energy ⟨ψ(θ)|H|ψ(θ)⟩, and lets a classical optimizer update θ to minimize it. By the variational principle the minimum is an upper bound to the ground-state energy, reached exactly when the ansatz can represent the ground state. Mandacaru starts from the Hartree–Fock determinant in the molecular-orbital basis; the fixed ansatz of method="vqe" is UCCSD.

ADAPT-VQE. ADAPT-VQE builds the ansatz during the calculation instead of fixing it in advance. At each iteration it evaluates the energy gradient ⟨ψ|[H, A_k]|ψ⟩ of every generator A_k in an operator pool, appends exp(θ_kA_k) for the largest one, and re-optimizes all parameters. It stops when every gradient falls below gradient_tolerance, producing compact circuits tailored to the molecule.

Operator pools. The pool is the set of anti-Hermitian generators ADAPT-VQE chooses from, and it sets the trade-off between circuit depth and the number of iterations. fermionic holds spin-adapted single and double excitations; qubit splits them into individual Pauli strings (the shallowest gates, more iterations); qeb uses qubit excitations — the same occupation moves without the fermionic sign; ceo couples the qubit excitations that act on the same spin-orbitals, and ceo-ovp keeps that coupling to one parameter per step, roughly halving the two-qubit gate count of qeb. Every pool is built in the encoding you ask for (Jordan–Wigner, parity, reduced parity or Bravyi–Kitaev) and reaches the same ground state. The fermionic and qubit-excitation pools conserve the particle number; the individual Pauli strings of qubit do not, by design.

Classical optimization. The parameters are updated by the optimizer in optimizer= — a method name, or an Optimizer with an explicit iteration budget and tolerance. SLSQP (the default) and L-BFGS-B use gradients and stop in one to two orders of magnitude fewer steps on exact simulators; Nelder–Mead and COBYLA are gradient-free and more robust on a small, nearly-converged problem; SPSA (two energy evaluations per step, whatever the number of parameters) and Adam tolerate the statistical noise of shot-based hardware. Both costs of a run — optimizer steps and energy evaluations — are reported per growth step and in total; see the guide.

License

Mandacaru is released under the MIT License.

Developer: Leandro Seixas Rocha (leandro.rocha@ilum.cnpem.br).

Documentation: mandacaru.readthedocs.io.

We thank financial support from INCT Materials Informatics (Grant No. 406447/2022-5).