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instability in kak decomposition

See original GitHub issue

In some cases the kak decomposition appears to have an instability in the sign of the ZZ coefficient. Consider the following example:

a, b = cirq.LineQubit(0), cirq.LineQubit(1)

theta = 0.3
circuit_1 = cirq.Circuit()
circuit_1.append(cirq.ISWAP.on(a, b))
circuit_1.append(
    cirq.ZZPowGate(exponent=2 * theta / numpy.pi, global_shift=-0.5).on(a, b))
print(cirq.kak_decomposition(cirq.unitary(circuit_1)).interaction_coefficients)

theta += 0.001
circuit_2 = cirq.Circuit()
circuit_2.append(cirq.ISWAP.on(a, b))
circuit_2.append(
    cirq.ZZPowGate(exponent=2 * theta / numpy.pi, global_shift=-0.5).on(a, b))
print(cirq.kak_decomposition(cirq.unitary(circuit_2)).interaction_coefficients)

print(numpy.amax(numpy.absolute(cirq.unitary(circuit_1) - cirq.unitary(circuit_2))))

returns

(0.7853981633974483, 0.7853981633974483, -0.2999999999999998)
(0.7853981633974482, 0.7853981633974482, 0.30099999999999993)
0.0009999999583333466

And thus we see that despite the fact the unitaries are very similar, the kak decomposition gives a seemingly random sign on the ZZ interaction coefficient. Is this a bug?

Issue Analytics

State:
Created 4 years ago
Comments:48 (13 by maintainers)

Top GitHub Comments

1reaction

vtomolecommented, May 21, 2019

@Strilanc I’m currently stepping through the bad and good machine at the moment.

0reactions

Strilanccommented, Jun 27, 2019

I asked @babbush and he said it’s no longer blocking him, therefore it’s good to close.

and… clo-

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