Expression of type Equals

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.logic import Equals
from proveit.physics.quantum.circuits import circuit__psi_m__u_Akl_v, circuit__u_Akl_v
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Equals(Prob(circuit__u_Akl_v), Prob(circuit__psi_m__u_Akl_v)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\right) =  \\ \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \rangle} \\
\multiqin{3}{\lvert u \rangle} & \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \multiqout{3}{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \ghostqout{\lvert v \rangle} \\
\ghostqin{\lvert u \rangle} & \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \ghostqout{\lvert v \rangle}
} \end{array}\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14, 15
11	Literal
12	ExprTuple	16, 17, 18
13	ExprTuple	19
14	ExprRange	lambda_map: 20 start_index: 88 end_index: 25
15	ExprTuple	21
16	ExprTuple	22, 23
17	ExprRange	lambda_map: 24 start_index: 88 end_index: 25
18	ExprTuple	26, 27
19	ExprRange	lambda_map: 28 start_index: 88 end_index: 90
20	Lambda	parameter: 79 body: 29
21	ExprRange	lambda_map: 30 start_index: 88 end_index: 90
22	ExprRange	lambda_map: 31 start_index: 88 end_index: 89
23	ExprRange	lambda_map: 32 start_index: 88 end_index: 90
24	Lambda	parameter: 79 body: 34
25	Variable
26	ExprRange	lambda_map: 35 start_index: 88 end_index: 89
27	ExprRange	lambda_map: 36 start_index: 88 end_index: 90
28	Lambda	parameter: 82 body: 37
29	ExprTuple	42
30	Lambda	parameter: 82 body: 38
31	Lambda	parameter: 82 body: 39
32	Lambda	parameter: 82 body: 40
33	ExprTuple	79
34	ExprTuple	41, 42
35	Lambda	parameter: 82 body: 43
36	Lambda	parameter: 82 body: 44
37	Operation	operator: 52 operands: 45
38	Operation	operator: 52 operands: 46
39	Operation	operator: 52 operands: 47
40	Operation	operator: 52 operands: 48
41	ExprRange	lambda_map: 49 start_index: 88 end_index: 89
42	ExprRange	lambda_map: 50 start_index: 88 end_index: 90
43	Operation	operator: 52 operands: 51
44	Operation	operator: 52 operands: 53
45	NamedExprs	element: 56 targets: 54
46	NamedExprs	element: 62 targets: 54
47	NamedExprs	element: 55 targets: 61
48	NamedExprs	element: 56 targets: 63
49	Lambda	parameter: 82 body: 57
50	Lambda	parameter: 82 body: 59
51	NamedExprs	element: 60 targets: 61
52	Literal
53	NamedExprs	element: 62 targets: 63
54	Operation	operator: 75 operands: 64
55	Operation	operator: 65 operands: 71
56	Operation	operator: 65 operands: 66
57	Operation	operator: 67 operands: 68
58	ExprTuple	82
59	IndexedVar	variable: 69 indices: 70
60	Operation	operator: 73 operands: 71
61	Operation	operator: 75 operands: 72
62	Operation	operator: 73 operands: 74
63	Operation	operator: 75 operands: 76
64	ExprTuple	88, 90
65	Literal
66	NamedExprs	state: 77 part: 82
67	Literal
68	NamedExprs	operation: 78
69	Variable
70	ExprTuple	79, 82
71	NamedExprs	state: 80 part: 82
72	ExprTuple	88, 89
73	Literal
74	NamedExprs	state: 81 part: 82
75	Literal
76	ExprTuple	83, 84
77	Variable
78	Literal
79	Variable
80	Variable
81	Variable
82	Variable
83	Operation	operator: 86 operands: 85
84	Operation	operator: 86 operands: 87
85	ExprTuple	89, 88
86	Literal
87	ExprTuple	89, 90
88	Literal
89	Variable
90	Variable