How to build and transpile Qiskit quantum circuits¶

In this guide, we show how to use the ffsim.qiskit module to build and transpile fermionic quantum circuits.

The following code cell imports modules and sets values that will be used in later code cells. Note that the number of qubits is twice the number of spatial orbitals.

[1]:

import numpy as np
from qiskit.circuit import QuantumCircuit, QuantumRegister

import ffsim

# Let's use 4 spatial orbitals with 2 alpha electrons and 2 beta electrons.
norb = 4
nelec = (2, 2)

# Initialize qubits
qubits = QuantumRegister(2 * norb, name="q")

# Initialize random number generator
rng = np.random.default_rng(1234)

Circuit transpilation¶

In this section, we show how to use transpiler passes included in ffsim to optimize quantum circuits built from fermionic gates. As a representative example circuit, we construct a circuit that prepares the Hartree-Fock state and then applies a unitary cluster Jastrow (UCJ) ansatz operator to it.

[2]:

# Construct a random UCJ operator
ucj_op = ffsim.random.random_ucj_op_spin_balanced(norb=norb, n_reps=2, seed=rng)

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

circuit.draw("mpl", scale=0.7)

[2]:

../_images/how-to-guides_qiskit-circuits_3_0.png

We recommend taking the following steps to transpile your quantum circuit:

Generate a staged pass manager using the generate_preset_pass_manager function.
Set the pre_init stage of your staged pass manager to ffsim.qiskit.PRE_INIT.
Run the transpiler pass on your circuit.

The ffsim.qiskit.PRE_INIT constant stores a pass manager with the transpiler passes generated by the pre_init_passes function. These passes decompose gates into orbital rotations and then merges the orbital rotations, resulting in fewer XXPlusYYGates in the final transpiled circuit. See Qubit gate decompositions of fermionic gates for a more detailed explanation of how this works.

[3]:

from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager

# Initialize quantum device backend
backend = GenericBackendV2(2 * norb, basis_gates=["cp", "xx_plus_yy", "p", "x"])

# Create a pass manager for circuit transpilation
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

# Transpile the circuit
transpiled = pass_manager.run(circuit)

transpiled.count_ops()

[3]:

OrderedDict([('cp', 56), ('xx_plus_yy', 32), ('p', 24), ('x', 4)])

Overview of gates¶

In this section, we give an overview of the quantum gates available in ffsim and provide usage examples.

State preparation gates¶

The state preparation gates are meant to be applied to the zero state. Their behavior when applied to other states is not guaranteed.

Prepare Hartree-Fock state¶

[4]:

circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)

[4]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab04c4fbb0>

Prepare Slater determinant¶

[5]:

occupied_orbitals = ([0, 2], [0, 1])
orbital_rotation = ffsim.random.random_unitary(norb, seed=rng)

circuit = QuantumCircuit(qubits)
circuit.append(
    ffsim.qiskit.PrepareSlaterDeterminantJW(
        norb, occupied_orbitals, orbital_rotation=orbital_rotation
    ),
    qubits,
)

[5]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab057148b0>

Unitary transformation gates¶

These gates can be applied to any state.

Orbital rotation¶

[6]:

orbital_rotation = ffsim.random.random_unitary(norb, seed=rng)

circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.OrbitalRotationJW(norb, orbital_rotation), qubits)

[6]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab04c4ed10>

Number operator sum evolution¶

[7]:

coeffs = rng.standard_normal(norb)
circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.NumOpSumEvolutionJW(norb, coeffs, time=1.0), qubits)

[7]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab057fc4c0>

Diagonal Coulomb evolution¶

[8]:

diag_coulomb_mat = ffsim.random.random_real_symmetric_matrix(norb, seed=rng)

circuit = QuantumCircuit(qubits)
circuit.append(
    ffsim.qiskit.DiagCoulombEvolutionJW(norb, diag_coulomb_mat, time=1.0), qubits
)

[8]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab04c4f430>

Spin-balanced unitary cluster Jastrow (UCJ) operator¶

[9]:

ucj_op = ffsim.random.random_ucj_op_spin_balanced(norb=norb, n_reps=2)

circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)

[9]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab05575450>

Spin-unbalanced unitary cluster Jastrow (UCJ) operator¶

[10]:

ucj_op = ffsim.random.random_ucj_op_spin_unbalanced(norb=norb, n_reps=2)

circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.UCJOpSpinUnbalancedJW(ucj_op), qubits)

[10]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab04c4f250>

Trotter simulation of double-factorized Hamiltonian¶

[11]:

df_hamiltonian = ffsim.random.random_double_factorized_hamiltonian(norb, seed=rng)
circuit = QuantumCircuit(qubits)
circuit.append(
    ffsim.qiskit.SimulateTrotterDoubleFactorizedJW(
        df_hamiltonian, time=1.0, n_steps=1, order=0
    ),
    qubits,
)

[11]:

<qiskit.circuit.instructionset.InstructionSet at 0x7fab04c4db10>