Different outputs for U3Gate and QasmUGate

[ArfatSalman]

Description of the issue

These two equivalent circuits show different outputs.

How to reproduce the issue

Qiskit (version 0.37)

from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
from qiskit import Aer, transpile, execute
from qiskit.circuit.library.standard_gates import U3Gate

qr = QuantumRegister(1, name='qr')
cr = ClassicalRegister(1, name='cr')
qc = QuantumCircuit(qr, cr, name='qc')

qc.append(U3Gate(4.690513260097172,1.1919742794819272,2.1795142072537406), qargs=[qr[0]], cargs=[])

qc.measure(qr, cr)

qc = transpile(qc)

backend = Aer.get_backend('qasm_simulator')
counts = execute(qc, backend=backend, shots=7838).result().get_counts(qc)
# {'0': 3731, '1': 4107}

import cirq
from cirq.circuits.qasm_output import QasmUGate
from functools import reduce

qr = [cirq.NamedQubit('q' + str(i)) for i in range(1)]
circuit = cirq.Circuit(
  QasmUGate(4.690513260097172, 1.1919742794819272, 2.1795142072537406)(qr[0]), 
  cirq.measure(qr[0], key='cr0')
)

simulator = cirq.Simulator()
result = simulator.run(circuit, repetitions=7838)
result_dict = dict(result.multi_measurement_histogram(keys=['cr0']))
# {(1,): 6137, (0,): 1701}

The documentation here at Gate conversion rules states that QASM u3(θ,φ,λ) is equaivalent to QasmUGate(θ,φ,λ) (as far as I could tell). So I'm not sure why the outputs are different. Interestingly, if I use circuit_from_qasm, and generate a circuit from qiskit's QASM, I get correct (in this case, similar to qiskit) result.

The documentation (and also this issue) leads me to believe that the u3 and QasmUGate are equivalent. Using circuit_from_qasm works, but using the gate directly doesn't seem to. Am I missing something?

Cirq version
1.0.0

[daxfohl]

I'm not a maintainer but I believe qiskit is in radians whereas cirq is in half-turns. Try dividing the angles by pi?

[viathor]

As @daxfohl said, QasmUGate takes half-turns, not radians, so the angles must be divided by pi. To confirm, I ran

import numpy as np

import cirq
from cirq.circuits.qasm_output import QasmUGate

from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
from qiskit import Aer, transpile, execute
from qiskit.circuit.library.standard_gates import U3Gate

theta = 4.690513260097172
phi = 1.1919742794819272
lmbda = 2.1795142072537406

# Cirq:
qr = [cirq.NamedQubit('q' + str(i)) for i in range(1)]
circuit = cirq.Circuit(
    QasmUGate(theta / np.pi, phi / np.pi, lmbda / np.pi)(qr[0]),
    cirq.measure(qr[0], key='cr0'),
)
u1 = cirq.unitary(circuit)
print('unitary according to cirq:')
print(u1)

# Qiskit:
qr = QuantumRegister(1, name='qr')
cr = ClassicalRegister(1, name='cr')
qc = QuantumCircuit(qr, cr, name='qc')
qc.append(U3Gate(theta, phi, lmbda), qargs=[qr[0]], cargs=[])
qc = transpile(qc)
backend = Aer.get_backend('unitary_simulator')
u2 = execute(qc, backend).result().get_unitary(qc)
print('unitary according to qiskit:')
print(u2)

# Comparison:
print('equal up to global phase?')
print(cirq.equal_up_to_global_phase(u1, u2))

and got

unitary according to cirq:
[[ 0.08020966+0.69471535j -0.62941756-0.33877799j]
 [ 0.62941756-0.33877799j  0.08020966-0.69471535j]]
unitary according to qiskit:
Operator([[-0.6993304 +8.56432739e-17j,  0.40873333-5.86407753e-01j],
          [ 0.2643513 +6.64120002e-01j,  0.68093112+1.59360684e-01j]],
         input_dims=(2,), output_dims=(2,))
equal up to global phase?
True

[viathor]

Note that documentation is explicit about the units.

[viathor]

Actually, not everywhere.