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Fix QASM Pauli exponential Rz angle #1343

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Fix QASM Pauli exponential Rz angle #1343

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4 changes: 3 additions & 1 deletion src/openfermion/circuits/trotter_exp_to_qgates.py
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Original file line number Diff line number Diff line change
Expand Up @@ -255,7 +255,9 @@ def pauli_exp_to_qasm(qubit_operator_list, evolution_time=1.0, qubit_list=None,
]
else:
if len(qids) > 0:
ret_list = ret_list + ["Rz {} {}".format(term_coeff * evolution_time, qids[-1])]
ret_list = ret_list + [
"Rz {} {}".format(2 * term_coeff * evolution_time, qids[-1])
]
Comment on lines +258 to +260
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@gemini-code-assist gemini-code-assist Bot Jun 6, 2026

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high

While doubling the uncontrolled Rz angle correctly fixes the rotation for the uncontrolled case, the controlled version of the exponentiation (when ancilla is not None on lines 242-255) still contains a sign inversion bug.

Specifically, to implement $\exp(-i \theta P)$ controlled on the ancilla, the relative phase on the ancilla should be $e^{-i \theta \lambda}$ (where $\lambda \in {1, -1}$ is the eigenvalue of the target state):

  • For $\lambda = 1$, we need a relative phase of $e^{-i \theta}$.
  • For $\lambda = -1$, we need a relative phase of $e^{i \theta}$.

With the current implementation:

  • Rz on the ancilla has angle $\theta$, giving a base relative phase of $e^{i \theta}$.
  • C-Phase has angle $-2\theta$, giving an additional phase of $e^{-2i \theta}$ when the target is $|1\rangle$ ($\lambda = -1$).
    This results in:
  • For $\lambda = 1$: relative phase is $e^{i \theta}$ (should be $e^{-i \theta}$).
  • For $\lambda = -1$: relative phase is $e^{-i \theta}$ (should be $e^{i \theta}$).

This means the controlled version implements $\exp(i \theta P)$ instead of $\exp(-i \theta P)$. To fix this, the signs of the angles in the ancilla is not None block should be inverted:

  1. Change the C-Phase angle to 2 * term_coeff * evolution_time.
  2. Change the Rz angle on the ancilla to -1 * term_coeff * evolution_time (both in the if len(qids) > 0 and else branches).

Note that you will also need to update the corresponding tests in trotter_exp_to_qgates_test.py (such as test_qasm_string_Controlled_XYZ and test_qasm_string_Controlled_XYZ_ancilla_list) to reflect the corrected signs.


# 4. Second set of CNOTs
ret_list = ret_list + cnots2
Expand Down
17 changes: 11 additions & 6 deletions src/openfermion/circuits/trotter_exp_to_qgates_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -210,11 +210,16 @@ def test_qasm_string_Z(self):
# Correct string
strcorrect = '''5
CNOT 3 4
Rz 0.6 4
Rz 1.2 4
CNOT 3 4'''

self.assertEqual(qasmstr, strcorrect)

def test_pauli_exp_to_qasm_uses_rz_angle_for_exp_minus_i_theta_z(self):
qasmstr = "\n".join(pauli_exp_to_qasm([QubitOperator('Z0', 0.5)], evolution_time=3))

self.assertEqual(qasmstr, 'Rz 3.0 0')

def test_qasm_string_XYZ(self):
# Testing for correct QASM string output w/ Pauli-{X,Y,Z}
# QubitOperator('X0 Z1 Y3', 0.5)
Expand All @@ -231,7 +236,7 @@ def test_qasm_string_XYZ(self):
Rx 1.5707963267948966 3
CNOT 0 1
CNOT 1 3
Rz 0.5 3
Rz 1.0 3
CNOT 1 3
CNOT 0 1
H 0
Expand Down Expand Up @@ -329,13 +334,13 @@ def test_qasm_string_multiple_operator(self):
# the order in which the operators loop.
strcorrect1 = '''5
CNOT 3 4
Rz 0.6 4
Rz 1.2 4
CNOT 3 4
H 0
Rx 1.5707963267948966 3
CNOT 0 1
CNOT 1 3
Rz 0.5 3
Rz 1.0 3
CNOT 1 3
CNOT 0 1
H 0
Expand All @@ -346,13 +351,13 @@ def test_qasm_string_multiple_operator(self):
Rx 1.5707963267948966 3
CNOT 0 1
CNOT 1 3
Rz 0.5 3
Rz 1.0 3
CNOT 1 3
CNOT 0 1
H 0
Rx -1.5707963267948966 3
CNOT 3 4
Rz 0.6 4
Rz 1.2 4
CNOT 3 4'''
try:
self.assertEqual(qasmstr, strcorrect1)
Expand Down
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