# from the theory of proveit.physics.quantum.QPE¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit.physics.quantum.QPE import _Psi_circuit
from proveit.statistics import Prob

In [2]:
# build up the expression from sub-expressions
expr = Prob(_Psi_circuit)

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7, 8
6ExprTuple9, 10
7ExprTuple11, 12
8ExprTuple13, 14
9ExprRangelambda_map: 15
start_index: 65
end_index: 66
10ExprRangelambda_map: 16
start_index: 65
end_index: 67
11ExprRangelambda_map: 17
start_index: 65
end_index: 66
12ExprRangelambda_map: 17
start_index: 57
end_index: 58
13ExprRangelambda_map: 18
start_index: 65
end_index: 66
14ExprRangelambda_map: 19
start_index: 65
end_index: 67
15Lambdaparameter: 56
body: 20
16Lambdaparameter: 56
body: 21
17Lambdaparameter: 56
body: 22
18Lambdaparameter: 56
body: 23
19Lambdaparameter: 56
body: 25
20Operationoperator: 42
operands: 26
21Operationoperator: 30
operands: 27
22Operationoperator: 30
operands: 28
23Operationoperator: 30
operands: 29
24ExprTuple56
25Operationoperator: 30
operands: 31
27NamedExprselement: 33
targets: 39
28NamedExprselement: 34
targets: 35
29NamedExprselement: 36
targets: 37
30Literal
31NamedExprselement: 38
targets: 39
32Operationoperator: 40
operand: 52
33Operationoperator: 42
operands: 49
34Operationoperator: 43
operands: 44
35Operationoperator: 50
operands: 45
36Operationoperator: 48
operands: 46
37Operationoperator: 50
operands: 47
38Operationoperator: 48
operands: 49
39Operationoperator: 50
operands: 51
40Literal
41ExprTuple52
42Literal
43Literal
44NamedExprsoperation: 53
part: 56
45ExprTuple65, 58
part: 56
47ExprTuple65, 66
48Literal
part: 56
50Literal
51ExprTuple57, 58
52Literal
53Operationoperator: 59
operands: 60
54Literal
55Literal
56Variable
57Operationoperator: 62
operands: 61
58Operationoperator: 62
operands: 63
59Literal
60ExprTuple64, 66
61ExprTuple66, 65
62Literal
63ExprTuple66, 67
64Literal
65Literal
66Literal
67Literal