[Review & Implementation] SCS quantum circuit with deterministic Dicke states implemented in blueqatSDK

Yuichiro Minato

2022/11/07 02:53

We will actually build a quantum circuit about Dicke state generation. the previous article is here.

https://blueqat.com/yuichiro_minato2/4190e59f-4f2a-4593-b880-c336b177b3f5

the reference is

https://arxiv.org/pdf/1904.07358.pdf

I would like to start by creating a 01/10 Dicke state from the classic bit of 01.

The circuit is going to use CX and CRY, the angles are

RY(2cos^{-1}\sqrt{l/n})

Let's use numpy backend to get state vec. I forgot to implement CRY into TN backend...

$SCS_{2,1}$

|0> -----C--RY--C--
         |  |   |
|0> --X--X--C---X--


from blueqat import Circuit
import numpy as np

l=1
n=2

circ = Circuit(2).x[1].cx[0,1].cry(2*np.arccos(np.sqrt(l/n)))[1,0].cx[0,1]
circ.run(backend="numpy")

array([0.        +0.j, 0.70710678+0.j, 0.70710678+0.j, 0.        +0.j])


circ.m[:].run(backend="numpy",shots=1000)

Counter({'10': 530, '01': 470})

done! next!

$U_{3,1} => SCS_{3,1} + SCS_{2,1}$

|001> + |010> + |100>

|0> ---------------C--RY--C--
                   |  |   |
|0> -----C--RY--C--X--C---X--
         |  |   |
|0> --X--X--C---X------------


circ2 = Circuit(3).x[2].cx[1,2].cry(2*np.arccos(np.sqrt(1/3)))[2,1].cx[1,2].cx[0,1].cry(2*np.arccos(np.sqrt(1/2)))[1,0].cx[0,1]
circ2.run(backend="numpy")

array([0.        +0.j, 0.57735027+0.j, 0.57735027+0.j, 0.        +0.j,

       0.57735027+0.j, 0.        +0.j, 0.        +0.j, 0.        +0.j])


circ2.m[:].run(backend="numpy",shots=1000)

Counter({'100': 360, '001': 299, '010': 341})

Done! Next we try $U_{3,2}$

$U_{3,2} => SCS_{3,2} + SCS_{2,1}$

|011> + |110> + |101>

|0> ---------------C--RY--C--C--RY--C--
                   |  |   |  |  |   |
|0> --X--C--RY--C--|--C---|--X--C---X--
         |  |   |  |  |   |
|0> --X--X--C---X--X--C---X------

I havent prepare CCRY, so instead we use CCRY = RY(theta)-CCX-RY(-theta)-CCX

https://qiita.com/gyu-don/items/7c52c0d20f9998022803


circ3 = Circuit(3).x[1,2].cx[1,2].cry(2*np.arccos(np.sqrt(1/3)))[2,1].cx[1,2].cx[0,2].ry(np.arccos(np.sqrt(2/3)))[0].ccx[2,1,0].ry(-np.arccos(np.sqrt(2/3)))[0].ccx[2,1,0].cx[0,2].cx[0,1].cry(2*np.arccos(np.sqrt(1/2)))[1,0].cx[0,1]
circ3.run(backend="numpy")

array([0.        +0.j, 0.        +0.j, 0.        +0.j, 0.57735027+0.j,

       0.        +0.j, 0.57735027+0.j, 0.57735027+0.j, 0.        +0.j])


circ3.m[:].run(backend="numpy",shots=1000)

Counter({'101': 314, '011': 339, '110': 347})

Done! Perfect.