Variational Quantum Circuit

Table of Contents

• Introduction
• Batch Generation of QCircuit
  • Constructing a VQCircuit object
  • Predefined Parameter Update Methods
  • Constructing Ansatz
    • Add QGate
    • Add QCircuit
    • Add VQGate
  • Show Ansatz
  • Parameters to QCircuits
    • Disable layer mechanism
    • Enable layer mechanism
• Post-processing of Results
  • Obtain QCircuits
  • Calculate theoretical Hamiltonian expectation
    • Batch process
    • Non-batch process
  • Calculate Hamiltonian expectation with noise model
    • Batch process
    • Non-batch process
  • Calculate theoretical Pauli Operators expectation
    • Batch process
    • Non-batch process
  • Calculate Pauli Operators expectation with noise model
    • Batch process
    • Non-batch process
• An Example

Prev Tutorial: PauliOperator
Next Tutorial: Quantum State

---

Introduction

QPanda3 uses VQCircuit to support variational quantum circuits. Provide placeholder support for setting variable parameters for logic gates in Ansatz using multidimensional arrays, support for generating QCircuit in batches based on multidimensional arrays, and support for calculating the expected values of Hamiltonians/Pauli operators for the generated QCircuit. In addition, VQCircuit also supports enabling the layer mechanism to better generate QCircuits composed of multiple quantum circuits with the same structure connected in series.

Batch Generation of QCircuit

Constructing a VQCircuit object

Here is API doc

Python

 
from pyqpanda3.vqcircuit import VQCircuit
vqc = VQCircuit()
 

Predefined Parameter Update Methods

Here is API doc for VQCircuit.set_Param

Python

 
#The parameter transmission form of the agreed layer line

vqc.set_Param([3,2])
 

Constructing Ansatz

Here is API doc

Add QGate

Add the parameters of variable quantum logic gates with parameters one by one and fix them.

Python

 
vqc << H(0)<<X(0)<<CP(1,2,3.14)
 

Add QCircuit

Add variable sub-circuit logic gates in batches, with parameters fixed for gates with parameters.

Python

 
cir = QCircuit()
cir << Y(0)<<U2(1,4.14,5.14)
vqc << cir
 

Add VQGate

Add variable quantum logic gates one by one, with parameters of the parameterized gates being variable.

Here is API doc for VQCircuit.Param

Python

 
#<1> qbit 0, <2> the element with index 0, 0 in the array with shape (3, 2) is used as the parameter of the gate, and the parameter with index 0, 0 is assigned the name "theta"
vqc << RX(0,vqc.Param([0,0],"theta"))
 
# The element corresponding to the name "theta" in qbit 2 is used as the parameter of the gate, which corresponds to the element with index 0,0 in the array with shape (3,2)
vqc << RX(2,vqc.Param("theta"))
 
 
#<1> qbit 1, <2> the element with index 1,0 in the array with shape (3,2) is used as the parameter of the gate
vqc << RX(1,vqc.Param([1,0]))
 

Show Ansatz

Display Ansatz related information.

Here is API doc for VQCircuit.display_ansatz

Python

 
# Print information of circuit template
vqc.display_ansatz()
 

Parameters to QCircuits

Batch updating parameters in multidimensional arrays.

Here is API doc for apply params

Disable layer mechanism

Here is API doc for VQCircuit.disable_layer

Python

 
# Prepare test parameters
# Prepare fixed shape array
data = np.zeros((2,3,2,3,2))
# Prepare test data
for i0 in range(2):
    for i1 in range(3):
        for i2 in range(2):
            for i3 in range(3):
                for i4 in range(2):
                    data[i0][i1][i2][i3][i4] = (i0+1)*10000+(i1+1)*1000+(i2+1)*100+(i3+1)*10+(i4+1)
# Print test data
print("data.shape",data.shape)
print("data")
print(data)
# Disable layer mechanism
vqc.disable_layer()
# Apply the parameter data to generate multiple QCircuits in batch and store them in cirs
# Here, 2*3*2 QCircuits are generated, totaling 12 QCircuits. Each QCircuit is updated by VQC based on the last two dimensions of data, which is an array with a shape of (3,2)
res = vqc(data)
 

Enable layer mechanism

Here is API doc for VQCircuit.enable_layer

Python

 
# Prepare test parameters
# Prepare fixed shape array
data = np.zeros((2,3,2,3,2))
# Prepare test data
for i0 in range(2):
    for i1 in range(3):
        for i2 in range(2):
            for i3 in range(3):
                for i4 in range(2):
                    data[i0][i1][i2][i3][i4] = (i0+1)*10000+(i1+1)*1000+(i2+1)*100+(i3+1)*10+(i4+1)
# Print test data
print("data.shape",data.shape)
print("data")
print(data)
# Enable layer mechanism
vqc.enable_layer()
# Apply the parameter data to generate multiple QCircuits in batches and store them in cirs
# Here, 2*3 QCircuits consisting of two layers of sub-circuits are generated, for a total of 6 QCircuits,
# Each QCircuit is generated by VQC by updating parameters based on the last 3-dimensional data, specifically an array with a shape of (2, 3, 2).
# Each QCircuit is composed of two layers of sub-circuits connected in series, and each sub-circuit layer is obtained by setting specific parameters for the Ansatz based on the last two-dimensional data, which is an array with a shape of (3, 2).
res = vqc(data)
 

Post-processing of Results

Obtain QCircuits

Obtaining QCircuits using multidimensional indexing.

Here is API doc for VQCResult.at

Python

 
# Prepare test parameters
# Prepare fixed shape array
data = np.zeros((2,3,2,3,2))
# Prepare test data
for i0 in range(2):
    for i1 in range(3):
        for i2 in range(2):
            for i3 in range(3):
                for i4 in range(2):
                    data[i0][i1][i2][i3][i4] = (i0+1)*10000+(i1+1)*1000+(i2+1)*100+(i3+1)*10+(i4+1)
# Print test data
print("data.shape",data.shape)
print("data")
print(data)
# Disable layer mechanism
vqc.disable_layer()
# Apply the parameter data to generate multiple QCircuits in batch and store them in cirs
# Here, 2*3*2 QCircuits are generated, totaling 12 QCircuits. Each QCircuit is updated by VQC based on the last two dimensions of data, which is an array with a shape of (3,2)
res = vqc(data)
# Obtaining Results Using Multidimensional Indexing 
for i0 in range(2):
    for i1 in range(3):
        for i2 in range(2):
            cir = res.at([i0,i1,i2]) #at method, the input parameter is a list of multi-dimensional subscript indexes
 
 

Calculate theoretical Hamiltonian expectation

Calculating theoretical expectation values of hamiltonians.

Batch process

Calculate the expected values of all QCircuits in batch.

Here is API doc for VQCResult.expval_hamiltonian

Please use VQCResult.expval_at to get every expectation val

Python

 
# Constructing the Hamiltonian
Ha = Hamiltonian(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
# Calculate the Hamiltonian expectation of all QCircuits in res in batch
# The parameter exp_type specifies the method for solving the Hamiltonian.
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
expectations = res.expval_hamiltonian(hamiltonian=Ha,backend='CPU') 
#res is the same as the previous example
 
# Obtain results
for i0 in range(2):
    for i1 in range(3):
            expectation = res.expval_at([i0,i1])# The expval_at method takes a list of multi-dimensional subscript indexes as input parameters
            print(expectation)
 

Non-batch process

Calculate the expected non-batch processing method corresponding to a single QCircuit.

Here is API doc for VQCResult.expval_hamiltonian

Python

 
# Constructing the Hamiltonian
Ha = Hamiltonian(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
 
# The expected value of the Hamiltonian Ha corresponding to the QCircuit of res.at([1,2]).
# The parameter exp_type specifies the method for solving the Hamiltonian. 
# res is the same as the previous example
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
expectation = res.expval_hamiltonian(hamiltonian=Ha,idx_s=[1,2],backend='CPU')
# Print result
print("expectation:",expectation)
 

Calculate Hamiltonian expectation with noise model

Calculating expectation values of hamiltonians with noise model

Batch process

Calculate the expected values of all QCircuits in batch.

Here is API doc for VQCResult.expval_hamiltonian

Please use VQCResult.expval_at to get every expectation val

Python

 
# Constructing the Hamiltonian
Ha = Hamiltonian(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
# Calculate the Hamiltonian expectation of all QCircuits in res in batch
# The parameter exp_type specifies the method for solving the Hamiltonian.
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
# You should set an appropriate noise model for the input parameter 'model'. NoiseModel() represents no noise.
expectations = res.expval_hamiltonian(hamiltonian=Ha,backend='CPU',shots= 1000, model=NoiseModel())
#res is the same as the previous example
 
# Obtain results
for i0 in range(2):
    for i1 in range(3):
            expectation = res.expval_at([i0,i1])# The expval_at method takes a list of multi-dimensional subscript indexes as input parameters
            print(expectation)
 

Non-batch process

Calculate the expected non-batch processing method corresponding to a single QCircuit.

Here is API doc for VQCResult.expval_hamiltonian

Python

 
from pyqpanda3.core import NoiseModel
 
# Constructing the Hamiltonian
Ha = Hamiltonian(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
 
# The expected value of the Hamiltonian Ha corresponding to the QCircuit of res.at([1,2]).
# The parameter exp_type specifies the method for solving the Hamiltonian. 
# res is the same as the previous example
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
# You should set an appropriate noise model for the input parameter 'model'. NoiseModel() represents no noise.
expectation = res.expval_hamiltonian(hamiltonian=Ha, idx_s=[2],backend='CPU',shots= 1000, model=NoiseModel())
# Print result
print("expectation:",expectation)
 

Calculate theoretical Pauli Operators expectation

Calculating theoretical expectation values of pauli operators.

Batch process

Calculate the expected values of all QCircuits PauliOperators in batch.

Here is API doc for VQCResult.expval_pauli_operator Please use VQCResult.expval_at to get every expectation val

Python

 
# Constructing the PauliOperator
op = PauliOperator(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
# Calculate the PauliOperator expectation of all QCircuits in res in batch
# The parameter exp_type specifies the method for solving the PauliOperator.
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
expectations = res.expval_pauli_operator(pauli_operator=op,backend='CPU')#res is the same as the previous example
 
# Obtain results
for i0 in range(2):
    for i1 in range(3):
            expectation = res.expval_at([i0,i1])# The expval_at method takes a list of multi-dimensional subscript indexes as input parameters
            print(expectation)
 
 

Non-batch process

Calculate the expected non-batch processing method corresponding to a single QCircuit pauli.

Here is API doc for VQCResult.expval_pauli_operator

Python

 
# Constructing the PauliOperator
op = PauliOperator(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
 
# The expected value of the PauliOperator op corresponding to the QCircuit of res.at([1,2]).
# The parameter exp_type specifies the method for solving the PauliOperator. 
# res is the same as the previous example
 
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
expectation = res.expval_pauli_operator(pauli_operator=op,idx_s=[1,2],backend='CPU')
# Print result
print("expectation:",expectation)
 

Calculate Pauli Operators expectation with noise model

Calculating theoretical expectation values of pauli operators with noise model

Batch process

Calculate the expected values of all QCircuits PauliOperators in batch.

Here is API doc for VQCResult.expval_pauli_operator Please use VQCResult.expval_at to get every expectation val

Python

 
# Constructing the PauliOperator
op = PauliOperator(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
# Calculate the PauliOperator expectation of all QCircuits in res in batch
# The parameter exp_type specifies the method for solving the PauliOperator.
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
# You should set an appropriate noise model for the input parameter 'model'. NoiseModel() represents no noise.
expectations = res.expval_pauli_operator(pauli_operator=pauli,backend='CPU',shots= 1000, model=NoiseModel())
 
# Obtain results
for i0 in range(2):
    for i1 in range(3):
            expectation = res.expval_at([i0,i1])# The expval_at method takes a list of multi-dimensional subscript indexes as input parameters
            print(expectation)
 
 

Non-batch process

Calculate the expected non-batch processing method corresponding to a single QCircuit pauli.

Here is API doc for VQCResult.expval_pauli_operator

Python

 
# Constructing the PauliOperator
op = PauliOperator(pauli_with_coef_s = { 'X0 Z1 ':2 + 0j, 'X1 Y2 ':3 + 0j, })
 
# The expected value of the PauliOperator op corresponding to the QCircuit of res.at([1,2]).
# The parameter exp_type specifies the method for solving the PauliOperator. 
# res is the same as the previous example
 
# If you want to calculate expectation using CPUQVM,please set backend='CPU'.
# If you want to calculate expectation using GPUQVM,please set backend='GPU'
# You should set an appropriate noise model for the input parameter 'model'. NoiseModel() represents no noise.
expectation = res.expval_pauli_operator(pauli_operator=pauli,backend='CPU', idx_s=[1,2],shots= 1000, model=NoiseModel())
# Print result
print("expectation:",expectation)
 

An Example

Python

 
import numpy as np
 
from pyqpanda3.core import QCircuit, H, X, CP, Y, U2, RX, RY, draw_qprog
from pyqpanda3.hamiltonian import PauliOperator, Hamiltonian
from pyqpanda3.vqcircuit import VQCircuit
 
vqc = VQCircuit()
 
vqc.set_Param([3, 2])
 
vqc << H(0) << X(0) << CP(1, 2, 3.14)
 
cir = QCircuit()
cir << Y(0) << U2(1, 4.14, 5.14)
vqc << cir
 
vqc << RX(0, vqc.Param([0, 0], "theta"))
 
vqc << RX(2, vqc.Param("theta"))
 
vqc << RX(1, vqc.Param([1, 0]))
 
vqc << RY(0, vqc.Param([0, 1]))
vqc << U2(1, vqc.Param([1, 1]), 5.55)
vqc << RY(2, vqc.Param([2, 1]))
 
vqc.display_ansatz()
 
data = np.zeros((3, 2, 3, 2))
 
for i1 in range(3):
    for i2 in range(2):
        for i3 in range(3):
            for i4 in range(2):
                data[i1][i2][i3][i4] = (i1 + 1) * 1000 + (i2 + 1) * 100 + (i3 + 1) * 10 + (i4 + 1)
print("data.shape", data.shape)
print("data")
print(data)
 
vqc.disable_layer()
 
 
def test_circuit(cir: QCircuit):
    print(draw_qprog(circuit=cir, param_show=True, expend_map={'all': 2}))
 
 
res = vqc(data)
for i1 in range(3):
    for i2 in range(2):
        cir = res.at([i1, i2])
        test_circuit(cir)
 
print("------------------------------------")
 
vqc.enable_layer()
 
res = vqc(data)
for i1 in range(3):
    cir = res.at([i1])
    test_circuit(cir)
 
Ha = Hamiltonian(pauli_with_coef_s={'X0 Z1 ': 2 + 0j, 'X1 Y2 ': 3 + 0j, })
 
expectation = res.expval_hamiltonian(hamiltonian=Ha, idx_s=[2])
print("expectation:", expectation)
 
pauli = PauliOperator(pauli_with_coef_s={'X0 Z1 ': 2 + 0j, 'X1 Y2 ': 3 + 0j, })
 
expectation = res.expval_pauli_operator(pauli_operator=pauli, idx_s=[2])
print("expectation:", expectation)
 
Ha = Hamiltonian(pauli_with_coef_s={'X0 Z1 ': 2 + 0j, 'X1 Y2 ': 3 + 0j, })
 
expectations = res.expval_hamiltonian(hamiltonian=Ha)
 
for i1 in range(3):
    expectation = res.expval_at([i1])
    print(expectation)
 
pauli = PauliOperator(pauli_with_coef_s={'X0 Z1 ': 2 + 0j, 'X1 Y2 ': 3 + 0j, })
expectations = res.expval_pauli_operator(pauli_operator=pauli)
 
for i1 in range(3):
    expectation = res.expval_at([i1])
    print(expectation)
 
vqc.display_ansatz()
 
dims = vqc.get_Param_dims()
print("dims:", dims)
 
data2 = np.array([
    [11, 12],
    [21, 22],
    [31, 32]
])
res2 = vqc(data2)
cir = res2.at([])
test_circuit(cir)
 
 

Output

---gates of a layer circuit:
___
gate id:0
gate type:H
qbits:0,
gate's params' total:0
gate's params:
___
gate id:1
gate type:X
qbits:0,
gate's params' total:0
gate's params:
___
gate id:2
gate type:CP
qbits:1,2,
gate's params' total:1
gate's params:
 1th param is fixed. It's val is 3.14
___
gate id:3
gate type:Y
qbits:0,
gate's params' total:0
gate's params:
___
gate id:4
gate type:U2
qbits:1,
gate's params' total:2
gate's params:
 1th param is fixed. It's val is 4.14
 2th param is fixed. It's val is 5.14
___
gate id:5
gate type:RX
qbits:0,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:0,0
   It's label is:theta
___
gate id:6
gate type:RX
qbits:2,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:0,0
   It's label is:theta
___
gate id:7
gate type:RX
qbits:1,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:1,0
   It's label is:
___
gate id:8
gate type:RY
qbits:0,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:0,1
   It's label is:
___
gate id:9
gate type:U2
qbits:1,
gate's params' total:2
gate's params:
 1th param is mutable. 
   It's pos in parameters is:1,1
   It's label is:
 2th param is fixed. It's val is 5.55
___
gate id:10
gate type:RY
qbits:2,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:2,1
   It's label is:
---
data.shape (3, 2, 3, 2)
data
[[[[1111. 1112.]
   [1121. 1122.]
   [1131. 1132.]]
 
  [[1211. 1212.]
   [1221. 1222.]
   [1231. 1232.]]]
 
 
 [[[2111. 2112.]
   [2121. 2122.]
   [2131. 2132.]]
 
  [[2211. 2212.]
   [2221. 2222.]
   [2231. 2232.]]]
 
 
 [[[3111. 3112.]
   [3121. 3122.]
   [3131. 3132.]]
 
  [[3211. 3212.]
   [3221. 3222.]
   [3231. 3232.]]]]
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             ┌─────────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(1111.00000000)├──────────── ┤RY(1112.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ └─────────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(1121.00000000)├ ┤U2(1122.00000000, 5.55000000)├ ─────────────────── 
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                     
q_2:  |0>─┤CP(3.14000000)├ ┤RX(1111.00000000)├───────── ┤RY(1132.00000000)├ ─────────────────────────────── ─────────────────── 
          └──────────────┘ └─────────────────┘          └─────────────────┘                                                     
 c :   / ═
          
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             ┌─────────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(1211.00000000)├──────────── ┤RY(1212.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ └─────────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(1221.00000000)├ ┤U2(1222.00000000, 5.55000000)├ ─────────────────── 
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                     
q_2:  |0>─┤CP(3.14000000)├ ┤RX(1211.00000000)├───────── ┤RY(1232.00000000)├ ─────────────────────────────── ─────────────────── 
          └──────────────┘ └─────────────────┘          └─────────────────┘                                                     
 c :   / ═
          
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             ┌─────────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(2111.00000000)├──────────── ┤RY(2112.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ └─────────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(2121.00000000)├ ┤U2(2122.00000000, 5.55000000)├ ─────────────────── 
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                     
q_2:  |0>─┤CP(3.14000000)├ ┤RX(2111.00000000)├───────── ┤RY(2132.00000000)├ ─────────────────────────────── ─────────────────── 
          └──────────────┘ └─────────────────┘          └─────────────────┘                                                     
 c :   / ═
          
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             ┌─────────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(2211.00000000)├──────────── ┤RY(2212.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ └─────────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(2221.00000000)├ ┤U2(2222.00000000, 5.55000000)├ ─────────────────── 
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                     
q_2:  |0>─┤CP(3.14000000)├ ┤RX(2211.00000000)├───────── ┤RY(2232.00000000)├ ─────────────────────────────── ─────────────────── 
          └──────────────┘ └─────────────────┘          └─────────────────┘                                                     
 c :   / ═
          
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             ┌─────────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(3111.00000000)├──────────── ┤RY(3112.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ └─────────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(3121.00000000)├ ┤U2(3122.00000000, 5.55000000)├ ─────────────────── 
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                     
q_2:  |0>─┤CP(3.14000000)├ ┤RX(3111.00000000)├───────── ┤RY(3132.00000000)├ ─────────────────────────────── ─────────────────── 
          └──────────────┘ └─────────────────┘          └─────────────────┘                                                     
 c :   / ═
          
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             ┌─────────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(3211.00000000)├──────────── ┤RY(3212.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ └─────────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(3221.00000000)├ ┤U2(3222.00000000, 5.55000000)├ ─────────────────── 
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                     
q_2:  |0>─┤CP(3.14000000)├ ┤RX(3211.00000000)├───────── ┤RY(3232.00000000)├ ─────────────────────────────── ─────────────────── 
          └──────────────┘ └─────────────────┘          └─────────────────┘                                                     
 c :   / ═
          
 
 
------------------------------------
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             >
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(1111.00000000)├──────────── >
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ >
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(1121.00000000)├ ┤U2(1122.00000000, 5.55000000)├ >
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘ >
q_2:  |0>─┤CP(3.14000000)├ ┤RX(1111.00000000)├───────── ┤RY(1132.00000000)├ ─────────────────────────────── >
          └──────────────┘ └─────────────────┘          └─────────────────┘                                 >
 c :   / ═
          
 
         ┌─────────────────┐ ┌─┐                          ┌─┐                 ┌─┐                             ┌─────────────────┐ ┌─────────────────┐ 
q_0:  |0>┤RY(1112.00000000)├ ┤H├───────────────────────── ┤X├──────────────── ┤Y├──────────────────────────── ┤RX(1211.00000000)├ ┤RY(1212.00000000)├ 
         └─────────────────┘ ├─┴────────────────────────┐ ├─┴───────────────┐ ├─┴───────────────────────────┐ └─────────────────┘ └─────────────────┘ 
q_1:  |0>────────*────────── ┤U2(4.14000000, 5.14000000)├ ┤RX(1221.00000000)├ ┤U2(1222.00000000, 5.55000000)├ ─────────────────── ─────────────────── 
         ┌───────┴──────┐    ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                                         
q_2:  |0>┤CP(3.14000000)├─── ┤RX(1211.00000000)├───────── ┤RY(1232.00000000)├ ─────────────────────────────── ─────────────────── ─────────────────── 
         └──────────────┘    └─────────────────┘          └─────────────────┘                                                                         
 c :   / 
         
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             >
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(2111.00000000)├──────────── >
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ >
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(2121.00000000)├ ┤U2(2122.00000000, 5.55000000)├ >
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘ >
q_2:  |0>─┤CP(3.14000000)├ ┤RX(2111.00000000)├───────── ┤RY(2132.00000000)├ ─────────────────────────────── >
          └──────────────┘ └─────────────────┘          └─────────────────┘                                 >
 c :   / ═
          
 
         ┌─────────────────┐ ┌─┐                          ┌─┐                 ┌─┐                             ┌─────────────────┐ ┌─────────────────┐ 
q_0:  |0>┤RY(2112.00000000)├ ┤H├───────────────────────── ┤X├──────────────── ┤Y├──────────────────────────── ┤RX(2211.00000000)├ ┤RY(2212.00000000)├ 
         └─────────────────┘ ├─┴────────────────────────┐ ├─┴───────────────┐ ├─┴───────────────────────────┐ └─────────────────┘ └─────────────────┘ 
q_1:  |0>────────*────────── ┤U2(4.14000000, 5.14000000)├ ┤RX(2221.00000000)├ ┤U2(2222.00000000, 5.55000000)├ ─────────────────── ─────────────────── 
         ┌───────┴──────┐    ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                                         
q_2:  |0>┤CP(3.14000000)├─── ┤RX(2211.00000000)├───────── ┤RY(2232.00000000)├ ─────────────────────────────── ─────────────────── ─────────────────── 
         └──────────────┘    └─────────────────┘          └─────────────────┘                                                                         
 c :   / 
         
 
 
 
          ┌─┐              ┌─┐                          ┌─┐                 ┌─────────────────┐             >
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├──────────────── ┤RX(3111.00000000)├──────────── >
          └─┘              ├─┴────────────────────────┐ ├─┴───────────────┐ ├─────────────────┴───────────┐ >
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(3121.00000000)├ ┤U2(3122.00000000, 5.55000000)├ >
          ┌───────┴──────┐ ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘ >
q_2:  |0>─┤CP(3.14000000)├ ┤RX(3111.00000000)├───────── ┤RY(3132.00000000)├ ─────────────────────────────── >
          └──────────────┘ └─────────────────┘          └─────────────────┘                                 >
 c :   / ═
          
 
         ┌─────────────────┐ ┌─┐                          ┌─┐                 ┌─┐                             ┌─────────────────┐ ┌─────────────────┐ 
q_0:  |0>┤RY(3112.00000000)├ ┤H├───────────────────────── ┤X├──────────────── ┤Y├──────────────────────────── ┤RX(3211.00000000)├ ┤RY(3212.00000000)├ 
         └─────────────────┘ ├─┴────────────────────────┐ ├─┴───────────────┐ ├─┴───────────────────────────┐ └─────────────────┘ └─────────────────┘ 
q_1:  |0>────────*────────── ┤U2(4.14000000, 5.14000000)├ ┤RX(3221.00000000)├ ┤U2(3222.00000000, 5.55000000)├ ─────────────────── ─────────────────── 
         ┌───────┴──────┐    ├─────────────────┬────────┘ ├─────────────────┤ └─────────────────────────────┘                                         
q_2:  |0>┤CP(3.14000000)├─── ┤RX(3211.00000000)├───────── ┤RY(3232.00000000)├ ─────────────────────────────── ─────────────────── ─────────────────── 
         └──────────────┘    └─────────────────┘          └─────────────────┘                                                                         
 c :   / 
         
 
 
expectation: -1.928947450418577
expectation: -1.928947450418577
-1.2142270395620407
0.12937804539398867
-1.9289474504185768
-1.2142270395620407
0.12937804539398867
-1.9289474504185768
---gates of a layer circuit:
___
gate id:0
gate type:H
qbits:0,
gate's params' total:0
gate's params:
___
gate id:1
gate type:X
qbits:0,
gate's params' total:0
gate's params:
___
gate id:2
gate type:CP
qbits:1,2,
gate's params' total:1
gate's params:
 1th param is fixed. It's val is 3.14
___
gate id:3
gate type:Y
qbits:0,
gate's params' total:0
gate's params:
___
gate id:4
gate type:U2
qbits:1,
gate's params' total:2
gate's params:
 1th param is fixed. It's val is 4.14
 2th param is fixed. It's val is 5.14
___
gate id:5
gate type:RX
qbits:0,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:0,0
   It's label is:theta
___
gate id:6
gate type:RX
qbits:2,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:0,0
   It's label is:theta
___
gate id:7
gate type:RX
qbits:1,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:1,0
   It's label is:
___
gate id:8
gate type:RY
qbits:0,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:0,1
   It's label is:
___
gate id:9
gate type:U2
qbits:1,
gate's params' total:2
gate's params:
 1th param is mutable. 
   It's pos in parameters is:1,1
   It's label is:
 2th param is fixed. It's val is 5.55
___
gate id:10
gate type:RY
qbits:2,
gate's params' total:1
gate's params:
 1th param is mutable. 
   It's pos in parameters is:2,1
   It's label is:
---
dims: [3, 2]
 
          ┌─┐              ┌─┐                          ┌─┐               ┌───────────────┐             ┌───────────────┐ 
q_0:  |0>─┤H├───────────── ┤X├───────────────────────── ┤Y├────────────── ┤RX(11.00000000)├──────────── ┤RY(12.00000000)├ 
          └─┘              ├─┴────────────────────────┐ ├─┴─────────────┐ ├───────────────┴───────────┐ └───────────────┘ 
q_1:  |0>─────────*─────── ┤U2(4.14000000, 5.14000000)├ ┤RX(21.00000000)├ ┤U2(22.00000000, 5.55000000)├ ───────────────── 
          ┌───────┴──────┐ ├───────────────┬──────────┘ ├───────────────┤ └───────────────────────────┘                   
q_2:  |0>─┤CP(3.14000000)├ ┤RX(11.00000000)├─────────── ┤RY(32.00000000)├ ───────────────────────────── ───────────────── 
          └──────────────┘ └───────────────┘            └───────────────┘                                                 
 c :   / ═