Transpiler misses control pattern simplification #15348
Description
Environment
- Qiskit: 2.2.1
- Python: 3.14.0
What is happening?
Two multi-controlled RX gates with control patterns '11' and '10' should combine into a single controlled gate, but the transpiler produces 6x more gates.
Reproduction
import numpy as np
from qiskit import QuantumCircuit, transpile
from qiskit.circuit.library import RXGate
from qiskit.quantum_info import Statevector, state_fidelity
theta = np.pi / 4
qc = QuantumCircuit(3)
qc.append(RXGate(theta).control(2, ctrl_state='11'), [0, 1, 2])
qc.append(RXGate(theta).control(2, ctrl_state='01'), [0, 1, 2])
qc_opt = transpile(qc, basis_gates=['cx', 'u3'], optimization_level=3)
print(f"Transpiled: {len(qc_opt.data)} gates") # Output: 31 gatesExpected behavior
Patterns '11' (q0=1 AND q1=1) and '10' (q0=1 AND q1=0) are complementary - they cover all cases where q0=1. They should combine into a single CRX controlled by q0:
optimal = QuantumCircuit(3)
optimal.append(RXGate(theta).control(1, ctrl_state='1'), [0, 2])
optimal_opt = transpile(optimal, basis_gates=['cx', 'u3'], optimization_level=3)
print(f"Optimal: {len(optimal_opt.data)} gates") # Output: 5 gatesExpected: 5 gates
Actual: 31 gates (26 extra, 520% overhead)
Verification
Both circuits are equivalent (fidelity=1.0 on all 8 computational basis states):
for i in range(8):
init = QuantumCircuit(3)
for q in range(3):
if (i >> q) & 1:
init.x(q)
test1, test2 = init.copy(), init.copy()
test1.compose(qc, inplace=True)
test2.compose(optimal, inplace=True)
fid = state_fidelity(Statevector.from_instruction(test1),
Statevector.from_instruction(test2))
print(f"|{i:03b}>: {fid:.10f}") # All: 1.0000000000Impact
This pattern appears in Hamiltonian simulation, variational algorithms, and any multi-controlled gate circuits. The overhead significantly impacts NISQ devices where gate count is critical.
References
- Atallah et al., "Graph Matching Trotterization for Continous Time Quantum Walk Circuit Simulation", Proceedings of IEEE Quantum Computing and Engineering, (QCE) 2025.
- Gonzalez et al.: "Efficient sparse state preparation via quantum walks", npj Quantum Information (2025).
- Amy et al., "Fast synthesis of depth-optimal quantum circuits", IEEE TCAD 32.6 (2013).
- Shende & Markov, "On the CNOT-cost of TOFFOLI gates", arXiv:0803.2316 (2008).
- Barenco et al., "Elementary gates for quantum computation", Phys. Rev. A 52.5 (1995).