Improve the performance of the ProductFormula synthesizers

[mrossinek]

Summary

This PR implements the suggestion made in #12021 (comment).

Details and comments

I ran a very simple benchmark to showcase the performance improvements of this PR. Below you can see that we get a ~30x performance improvement (note the logarithmic y axis).

Here is the code which builds a heavy-hex graph of a given size, constructs an XYZ model Hamiltonian on its connectivity, and builds a LieTrotter and SuzukiTrotter circuit.

import sys
import time

import numpy as np
import rustworkx as rx
from qiskit import QuantumCircuit, transpile
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.quantum_info import SparsePauliOp
from qiskit.synthesis import LieTrotter, SuzukiTrotter

for size in range(3, 10, 2):
    graph = rx.generators.heavy_hex_graph(size, multigraph=False)

    num_qubits = graph.num_nodes()

    sparse_pauli_list = []
    for edge in graph.edge_list():
        for p in ("XX", "YY", "ZZ"):
            sparse_pauli_list.append((p, [edge[0], edge[1]], 1.0))
    for qubit in range(num_qubits):
        for p in "XYZ":
            sparse_pauli_list.append((p, [qubit], 1.0))

    hamil = SparsePauliOp.from_sparse_list(sparse_pauli_list, num_qubits=num_qubits)

    print("starting LieTrotter with 10 reps", file=sys.stderr)
    t1 = time.time()
    circuit = QuantumCircuit(num_qubits)
    circuit.append(
        PauliEvolutionGate(hamil, time=0.5, synthesis=LieTrotter(reps=10)),
        qargs=circuit.qubits,
    )
    transpiled = transpile(circuit, basis_gates=["rz", "x", "sx", "cx"])
    t2 = time.time()
    lie = t2 - t1
    print(f"took {lie}s", file=sys.stderr)

    print("starting SuzukiTrotter with 10 reps", file=sys.stderr)
    t1 = time.time()
    circuit = QuantumCircuit(num_qubits)
    circuit.append(
        PauliEvolutionGate(hamil, time=0.5, synthesis=SuzukiTrotter(reps=10)),
        qargs=circuit.qubits,
    )
    transpiled = transpile(circuit, basis_gates=["rz", "x", "sx", "cx"])
    t2 = time.time()
    suzuki = t2 - t1
    print(f"took {suzuki}s", file=sys.stderr)

As part of this improvement, I also aligned the implementations of LieTrotter and SuzukiTrotter which partially diverged in #12021. I also handle the wrapping of the individually time-evolved Pauli terms in a new way, which results in a different (but imo improved) visualization of a circuit. Below you can see the same circuit drawn with Qiskit 1.1.1 and this PR, side by side:

Qiskit 1.1.1	This PR

Here is the code to plot the circuit above

import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.quantum_info import SparsePauliOp
from qiskit.synthesis import LieTrotter, SuzukiTrotter

num_qubits = 10
edges = [(i, i + 1) for i in range(0, num_qubits - 1, 2)]
edges += [(i, i + 1) for i in range(1, num_qubits - 1, 2)]

sparse_pauli_list = []
for edge in edges:
    for p in ("XX", "YY", "ZZ"):
        sparse_pauli_list.append((p, [edge[0], edge[1]], 1.0))
for qubit in range(num_qubits):
    for p in "XYZ":
        sparse_pauli_list.append((p, [qubit], 1.0))

hamil = SparsePauliOp.from_sparse_list(sparse_pauli_list, num_qubits=num_qubits)

circuit = QuantumCircuit(num_qubits)
circuit.append(
    PauliEvolutionGate(hamil, time=0.5, synthesis=LieTrotter(wrap=True)),
    qargs=circuit.qubits,
)
circuit = circuit.decompose()
circuit.draw("mpl", filename="circuit_branch.png")

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Cryoris
• @Qiskit/terra-core
• @ajavadia

[coveralls]

Pull Request Test Coverage Report for Build 9796156398

Details

• 94 of 99 (94.95%) changed or added relevant lines in 6 files are covered.
• 24 unchanged lines in 2 files lost coverage.
• Overall coverage decreased (-0.008%) to 89.824%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/quantumcircuit.py	3	4	75.0%
qiskit/synthesis/evolution/lie_trotter.py	11	12	91.67%
qiskit/synthesis/evolution/suzuki_trotter.py	9	10	90.0%
qiskit/synthesis/evolution/product_formula.py	62	64	96.88%

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	6	91.35%
crates/qasm2/src/parse.rs	18	96.69%

Totals
Change from base Build 9794304676:	-0.008%
Covered Lines:	65206
Relevant Lines:	72593

---

💛 - Coveralls

[Cryoris]

This looks great, both performance and visualization wise, thanks for the effort! 🙂 I just have a few minor comments below.

[coveralls]

Pull Request Test Coverage Report for Build 9806942643

Details

• 95 of 100 (95.0%) changed or added relevant lines in 6 files are covered.
• 22 unchanged lines in 3 files lost coverage.
• Overall coverage decreased (-0.007%) to 89.835%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/quantumcircuit.py	3	4	75.0%
qiskit/synthesis/evolution/lie_trotter.py	11	12	91.67%
qiskit/synthesis/evolution/suzuki_trotter.py	10	11	90.91%
qiskit/synthesis/evolution/product_formula.py	62	64	96.88%

Files with Coverage Reduction	New Missed Lines	%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	88.35%
crates/qasm2/src/lex.rs	8	91.6%
crates/qasm2/src/parse.rs	12	97.15%

Totals
Change from base Build 9806112690:	-0.007%
Covered Lines:	65214
Relevant Lines:	72593

---

💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 9842266493

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 95 of 100 (95.0%) changed or added relevant lines in 6 files are covered.
• 34 unchanged lines in 3 files lost coverage.
• Overall coverage decreased (-0.07%) to 89.765%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/quantumcircuit.py	3	4	75.0%
qiskit/synthesis/evolution/lie_trotter.py	11	12	91.67%
qiskit/synthesis/evolution/suzuki_trotter.py	10	11	90.91%
qiskit/synthesis/evolution/product_formula.py	62	64	96.88%

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	5	92.11%
crates/qasm2/src/parse.rs	12	96.69%
crates/circuit/src/slice.rs	17	83.85%

Totals
Change from base Build 9825985118:	-0.07%
Covered Lines:	59209
Relevant Lines:	65960

---

💛 - Coveralls

[Cryoris]

Great improvement, thanks a lot for the work! 🚤 💨