Expression of type Prob

from the theory of proveit.physics.quantum.circuits

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit.physics.quantum.circuits import phase_kickback_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Prob(phase_kickback_circuit)

expr:

# 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

# 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} & \control{} \qw \qwx[1] & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U} & \qout{\lvert u \rangle}
} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7, 8
6	ExprTuple	9, 10
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	Operation	operator: 46 operands: 15
10	ExprRange	lambda_map: 16 start_index: 82 end_index: 21
11	Operation	operator: 37 operands: 17
12	ExprRange	lambda_map: 18 start_index: 82 end_index: 21
13	Operation	operator: 52 operands: 19
14	ExprRange	lambda_map: 20 start_index: 82 end_index: 21
15	NamedExprs	state: 22
16	Lambda	parameter: 61 body: 23
17	NamedExprs	element: 24 targets: 25
18	Lambda	parameter: 61 body: 26
19	NamedExprs	state: 27
20	Lambda	parameter: 61 body: 29
21	Operation	operator: 67 operands: 30
22	Operation	operator: 78 operand: 39
23	Operation	operator: 37 operands: 32
24	Literal
25	Operation	operator: 33 operand: 85
26	Operation	operator: 37 operands: 35
27	Operation	operator: 65 operands: 36
28	ExprTuple	61
29	Operation	operator: 37 operands: 38
30	ExprTuple	73, 82
31	ExprTuple	39
32	NamedExprs	element: 40 targets: 45
33	Literal
34	ExprTuple	85
35	NamedExprs	element: 41 targets: 45
36	ExprTuple	42, 43
37	Literal
38	NamedExprs	element: 44 targets: 45
39	Literal
40	Operation	operator: 46 operands: 53
41	Operation	operator: 47 operands: 48
42	Operation	operator: 74 operands: 49
43	Operation	operator: 50 operands: 51
44	Operation	operator: 52 operands: 53
45	Operation	operator: 54 operands: 55
46	Literal
47	Literal
48	NamedExprs	operation: 56 part: 61
49	ExprTuple	82, 57
50	Literal
51	ExprTuple	58, 59
52	Literal
53	NamedExprs	state: 60 part: 61
54	Literal
55	ExprTuple	85, 62
56	Variable
57	Operation	operator: 76 operands: 63
58	Operation	operator: 78 operand: 70
59	Operation	operator: 65 operands: 66
60	Variable
61	Variable
62	Operation	operator: 67 operands: 68
63	ExprTuple	85, 69
64	ExprTuple	70
65	Literal
66	ExprTuple	71, 72
67	Literal
68	ExprTuple	73, 85
69	Operation	operator: 74 operands: 75
70	Literal
71	Operation	operator: 76 operands: 77
72	Operation	operator: 78 operand: 82
73	Variable
74	Literal
75	ExprTuple	82, 85
76	Literal
77	ExprTuple	80, 81
78	Literal
79	ExprTuple	82
80	Literal
81	Operation	operator: 83 operands: 84
82	Literal
83	Literal
84	ExprTuple	85, 86, 87, 88
85	Literal
86	Literal
87	Literal
88	Variable