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_on_register_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Prob(phase_kickback_on_register_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] & \qw & \gate{\cdots} \qwx[1] & \qw & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert + \rangle} & \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qout{\vdots} \\
\qin{\lvert + \rangle} & \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \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_{t}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U_{1}} & \gate{U_{2}} & \gate{\cdots} & \gate{U_{t}} & \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	ExprRange	lambda_map: 11 start_index: 105 end_index: 104
8	ExprTuple	12, 13
9	ExprRange	lambda_map: 14 start_index: 105 end_index: 104
10	ExprRange	lambda_map: 15 start_index: 105 end_index: 88
11	Lambda	parameter: 87 body: 16
12	ExprRange	lambda_map: 17 start_index: 105 end_index: 104
13	ExprRange	lambda_map: 18 start_index: 105 end_index: 88
14	Lambda	parameter: 114 body: 19
15	Lambda	parameter: 114 body: 20
16	ExprTuple	21, 22
17	Lambda	parameter: 114 body: 23
18	Lambda	parameter: 114 body: 24
19	Operation	operator: 38 operands: 25
20	Operation	operator: 63 operands: 26
21	ExprRange	lambda_map: 27 start_index: 105 end_index: 104
22	ExprRange	lambda_map: 28 start_index: 105 end_index: 88
23	Operation	operator: 43 operands: 29
24	Operation	operator: 63 operands: 30
25	NamedExprs	state: 31
26	NamedExprs	element: 32 targets: 49
27	Lambda	parameter: 114 body: 33
28	Lambda	parameter: 114 body: 34
29	NamedExprs	state: 35
30	NamedExprs	element: 36 targets: 49
31	Operation	operator: 98 operand: 45
32	Operation	operator: 38 operands: 44
33	Operation	operator: 39 operands: 40
34	Operation	operator: 63 operands: 41
35	Operation	operator: 83 operands: 42
36	Operation	operator: 43 operands: 44
37	ExprTuple	45
38	Literal
39	Literal
40	ExprTuple	46, 47
41	NamedExprs	element: 48 targets: 49
42	ExprTuple	50, 51
43	Literal
44	NamedExprs	state: 52 part: 114
45	Literal
46	Conditional	value: 53 condition: 54
47	Conditional	value: 55 condition: 56
48	Operation	operator: 66 operands: 57
49	Operation	operator: 58 operands: 59
50	Operation	operator: 94 operands: 60
51	Operation	operator: 61 operands: 62
52	Variable
53	Operation	operator: 63 operands: 64
54	Operation	operator: 65 operands: 69
55	Operation	operator: 66 operands: 67
56	Operation	operator: 68 operands: 69
57	NamedExprs	operation: 70 part: 114
58	Literal
59	ExprTuple	93, 71
60	ExprTuple	105, 72
61	Literal
62	ExprTuple	73, 74
63	Literal
64	NamedExprs	element: 75 targets: 76
65	Literal
66	Literal
67	NamedExprs	operation: 77
68	Literal
69	ExprTuple	87, 114
70	IndexedVar	variable: 78 index: 87
71	Operation	operator: 100 operands: 80
72	Operation	operator: 96 operands: 81
73	Operation	operator: 98 operand: 90
74	Operation	operator: 83 operands: 84
75	Literal
76	Operation	operator: 85 operand: 93
77	Literal
78	Variable
79	ExprTuple	87
80	ExprTuple	104, 88
81	ExprTuple	108, 89
82	ExprTuple	90
83	Literal
84	ExprTuple	91, 92
85	Literal
86	ExprTuple	93
87	Variable
88	Variable
89	Operation	operator: 94 operands: 95
90	Literal
91	Operation	operator: 96 operands: 97
92	Operation	operator: 98 operand: 105
93	Operation	operator: 100 operands: 101
94	Literal
95	ExprTuple	105, 108
96	Literal
97	ExprTuple	102, 103
98	Literal
99	ExprTuple	105
100	Literal
101	ExprTuple	104, 105
102	Literal
103	Operation	operator: 106 operands: 107
104	Variable
105	Literal
106	Literal
107	ExprTuple	108, 109, 110, 111
108	Literal
109	Literal
110	Literal
111	IndexedVar	variable: 112 index: 114
112	Variable
113	ExprTuple	114
114	Variable