How to build Qiskit circuits for the LUCJ ansatz

This guide provides some examples of building and transpiling Qiskit circuits to implement the LUCJ ansatz.

import pyscf
from qiskit.circuit import QuantumCircuit, QuantumRegister
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager

import ffsim

LUCJ circuit for a closed-shell molecule

For a closed-shell system, use the spin-balanced LUCJ ansatz. This example creates an LUCJ circuit for a nitrogen molecule in the 6-31g basis.

# 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 data and Hamiltonian
scf = pyscf.scf.RHF(mol).run()
mol_data = ffsim.MolecularData.from_scf(scf, active_space=active_space)
norb, nelec = mol_data.norb, mol_data.nelec
mol_hamiltonian = mol_data.hamiltonian
print(f"norb = {norb}")
print(f"nelec = {nelec}")

# Get CCSD t2 amplitudes for initializing the ansatz
ccsd = pyscf.cc.CCSD(
    scf, frozen=[i for i in range(mol.nao_nr()) if i not in active_space]
).run()

# Use 2 ansatz layers
n_reps = 2
# Use interactions implementable on a square lattice
pairs_aa = [(p, p + 1) for p in range(norb - 1)]
pairs_ab = [(p, p) for p in range(norb)]
ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes(
    ccsd.t2, t1=ccsd.t1, n_reps=n_reps, interaction_pairs=(pairs_aa, pairs_ab)
)

# Construct circuit
qubits = QuantumRegister(2 * norb)
circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)
circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)
circuit.measure_all()

# Create a generic backend and transpile the circuit to it
backend = GenericBackendV2(2 * norb, basis_gates=["cp", "xx_plus_yy", "p", "x"])
pass_manager = generate_preset_pass_manager(optimization_level=3, backend=backend)
# Set the pre-initialization stage of the pass manager with passes suggested by ffsim
pass_manager.pre_init = ffsim.qiskit.PRE_INIT
transpiled = pass_manager.run(circuit)

transpiled.count_ops()

converged SCF energy = -108.835236570775
norb = 16
nelec = (5, 5)
E(CCSD) = -109.0398256929734  E_corr = -0.2045891221988307

OrderedDict([('xx_plus_yy', 582),
             ('p', 64),
             ('cp', 52),
             ('measure', 32),
             ('x', 10),
             ('barrier', 1)])

LUCJ circuit for an open-shell molecule

For an open-shell system, use the spin-unbalanced LUCJ ansatz. This example creates an LUCJ circuit for a hydroxyl radical in the 6-31g basis.

# Build HO molecule
mol = pyscf.gto.Mole()
mol.build(
    atom=[["H", (0, 0, 0)], ["O", (0, 0, 1.1)]],
    basis="6-31g",
    spin=1,
    symmetry="Coov",
)

# Get molecular data and Hamiltonian
scf = pyscf.scf.ROHF(mol).run()
mol_data = ffsim.MolecularData.from_scf(scf)
norb, nelec = mol_data.norb, mol_data.nelec
mol_hamiltonian = mol_data.hamiltonian
print(f"norb = {norb}")
print(f"nelec = {nelec}")

# Get CCSD t2 amplitudes for initializing the ansatz
ccsd = pyscf.cc.CCSD(scf).run()

# Use 4 layers from opposite-spin amplitudes and 2 layers from same-spin amplitudes
n_reps = (4, 2)
# Use interactions implementable on a square lattice
pairs_aa = [(p, p + 1) for p in range(norb - 1)]
pairs_ab = [(p, p) for p in range(norb)]
pairs_bb = [(p, p + 1) for p in range(norb - 1)]
ucj_op = ffsim.UCJOpSpinUnbalanced.from_t_amplitudes(
    ccsd.t2, t1=ccsd.t1, n_reps=n_reps, interaction_pairs=(pairs_aa, pairs_ab, pairs_bb)
)

# Construct circuit
qubits = QuantumRegister(2 * norb)
circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)
circuit.append(ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op), qubits)
circuit.measure_all()

# Create a generic backend and transpile the circuit to it
backend = GenericBackendV2(2 * norb, basis_gates=["cp", "xx_plus_yy", "p", "x"])
pass_manager = generate_preset_pass_manager(optimization_level=3, backend=backend)
# Set the pre-initialization stage of the pass manager with passes suggested by ffsim
pass_manager.pre_init = ffsim.qiskit.PRE_INIT
transpiled = pass_manager.run(circuit)

transpiled.count_ops()

SCF not converged.
SCF energy = -75.3484557079827
norb = 11
nelec = (5, 4)

WARN: RCCSD method does not support ROHF method. ROHF object is converted to UHF object and UCCSD method is called.

E(UCCSD) = -75.45619739109992  E_corr = -0.1077416831172149

OrderedDict([('xx_plus_yy', 696),
             ('p', 112),
             ('cp', 108),
             ('measure', 22),
             ('x', 9),
             ('barrier', 1)])