Any way to get consistent average photon values for Gaussian Boson Sampling for same rotations?

Photonic Software Strawberry Fields
1

Tried implementing GBS as per this circuit diagram (https://medium.com/xanaduai/introducing-the-strawberry-fields-applications-layer-b61f55c82689) and using the circuits in the X8 tutorial.

I have tried increasing the number of shots, but I still get very different average photon values for outputs for a set of rotations when running different times. Any way to help make the averages more in accordance with one another?

Thanks!

2

Hi @Samarth_Sandeep ā€” Could you share the code you are using to generate the samples?

3 
    ops.S2gate(1.0) | (q[0], q[4])
    ops.S2gate(1.0) | (q[1], q[5])
    ops.S2gate(1.0) | (q[2], q[6])
    ops.S2gate(1.0) | (q[3], q[7])

    ops.Interferometer(unitary_mat) | (q[0], q[1], q[2], q[3])
    ops.Rgate(math.pi/2) | q[0]
    ops.Rgate(math.pi/2) | q[1]
    ops.Rgate(math.pi/2) | q[2]
    ops.Rgate(math.pi/2) | q[3]
    ops.BSgate(math.pi/4, math.pi/2) | (q[1], q[0])
    ops.BSgate(math.pi/4, math.pi/2) | (q[2], q[3])
    ops.Rgate(math.pi/2) | q[1]
    ops.Rgate(math.pi/2) | q[2]
    ops.Rgate(rmath.pi/2) | q[0]
    ops.BSgate(math.pi/4, math.pi/2) | (q[1], q[2])
    ops.Rgate(math.pi/2) | q[3]
    ops.Rgate(math.pi/2) | q[1]
    ops.Rgate(math.pi/2) | q[2]
    ops.BSgate(math.pi/4, math.pi/2) | (q[1], q[0])
    ops.BSgate(math.pi/4, math.pi/2) | (q[2], q[3])
    ops.Rgate(math.pi/2) | q[1]
    ops.Rgate(math.pi/2) | q[2]
    ops.BSgate(math.pi/4, math.pi/2) | (q[1], q[2])


    ops.Interferometer(unitary_mat) | (q[4], q[5], q[6], q[7])
    ops.Rgate(math.pi/2) | q[4]
    ops.Rgate(math.pi/2) | q[5]
    ops.Rgate(math.pi/2) | q[6]
    ops.Rgate(math.pi/2) | q[7]
    ops.BSgate(math.pi/4, math.pi/2) | (q[4], q[5])
    ops.BSgate(math.pi/4, math.pi/2) | (q[6], q[7])
    ops.Rgate(math.pi/2) | q[5]
    ops.Rgate(math.pi/2) | q[6]
    ops.Rgate(math.pi/2) | q[4]
    ops.BSgate(math.pi/4, math.pi/2) | (q[5], q[6])
    ops.Rgate(math.pi/2) | q[7]
    ops.Rgate(math.pi/2) | q[5]
    ops.Rgate(math.pi/2) | q[6]
    ops.BSgate(math.pi/4, math.pi/2) | (q[4], q[5])
    ops.BSgate(math.pi/4, math.pi/2) | (q[6], q[7])
    ops.Rgate(math.pi/2) | q[5]
    ops.Rgate(math.pi/2) | q[6]
    ops.BSgate(math.pi/4, math.pi/2) | (q[5], q[6])

    ops.MeasureFock() | q
4

Hi @Samarth_Sandeep ---- How many samples are you using to calculate averages? Also, are you doing a simulation or are you using the hardware?

5

Iā€™m using the hardware and was doing 1000 shots.

6

Can you also post the results that you got and that seem inconsistent?

7

These both are using the same interferometer angles and same rotation angles, but the photon averages are very different:

Trial 1:
[[1 0 2 ā€¦ 0 2 3]
[0 1 0 ā€¦ 0 1 1]
[1 0 2 ā€¦ 1 1 0]
ā€¦
[0 3 0 ā€¦ 1 2 1]
[2 0 4 ā€¦ 1 3 1]
[0 0 0 ā€¦ 0 0 4]]
[0.98 1. 0.925 0.82 0.905 0.84 1.085 0.895]

Trial 2:
[[0 3 0 ā€¦ 1 2 0]
[2 1 3 ā€¦ 1 3 3]
[0 0 2 ā€¦ 1 1 0]
ā€¦
[0 0 0 ā€¦ 0 0 0]
[0 0 3 ā€¦ 2 1 0]
[4 0 0 ā€¦ 0 0 2]]
[1.03 0.87 0.93 0.975 1. 0.89 0.91 1.005]

8

Hi @Samarth_Sandeep ā€” From a quick statistical analysis the means you report have a relative difference

\text{rel_dif} = \frac{|\text{mean1} - \text{mean2}|}{\tfrac12 (\text{mean1} + \text{mean2})}

of at most 17% . This is a bit too high but is not wholly inconsistent with a simple estimate that will predict a relative difference of on the order of 1/\sqrt{M} \sim 3\% for M=1000 thousand samples.

Can I suggest you use more samples to estimate these averages. If you increase the number of samples by one-hundred fold, you should expect to decrease the relative difference by one order of magnitude.

Hope this helps,

Nicolas

9

Thanks for the answer @Nicolas_Quesada! Will give it a shot (no pun intended). That makes sense.

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