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__u_Akl_v, circuit__u_Akl_v__psi_m
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Equals(Prob(circuit__u_Akl_v), Prob(circuit__u_Akl_v__psi_m)).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{
\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} \\
\qin{\lvert \psi \rangle} & { /^{m} } \qw & { /^{m} } \qw & \gate{\cdots} & { /^{m} } \qw & \qout{\lvert \psi \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	20
14	ExprRange	lambda_map: 19 start_index: 78 end_index: 23
15	ExprTuple	24
16	ExprTuple	20, 21
17	ExprRange	lambda_map: 22 start_index: 78 end_index: 23
18	ExprTuple	24, 25
19	Lambda	parameter: 68 body: 26
20	ExprRange	lambda_map: 27 start_index: 78 end_index: 79
21	ExprRange	lambda_map: 28 start_index: 78 end_index: 80
22	Lambda	parameter: 68 body: 30
23	Variable
24	ExprRange	lambda_map: 31 start_index: 78 end_index: 79
25	ExprRange	lambda_map: 32 start_index: 78 end_index: 80
26	ExprTuple	35
27	Lambda	parameter: 72 body: 33
28	Lambda	parameter: 72 body: 34
29	ExprTuple	68
30	ExprTuple	35, 36
31	Lambda	parameter: 72 body: 37
32	Lambda	parameter: 72 body: 38
33	Operation	operator: 44 operands: 39
34	Operation	operator: 44 operands: 40
35	ExprRange	lambda_map: 41 start_index: 78 end_index: 79
36	ExprRange	lambda_map: 42 start_index: 78 end_index: 80
37	Operation	operator: 44 operands: 43
38	Operation	operator: 44 operands: 45
39	NamedExprs	element: 46 targets: 52
40	NamedExprs	element: 47 targets: 54
41	Lambda	parameter: 72 body: 48
42	Lambda	parameter: 72 body: 50
43	NamedExprs	element: 51 targets: 52
44	Literal
45	NamedExprs	element: 53 targets: 54
46	Operation	operator: 56 operands: 55
47	Operation	operator: 56 operands: 64
48	IndexedVar	variable: 57 indices: 58
49	ExprTuple	72
50	Operation	operator: 59 operands: 60
51	Operation	operator: 63 operands: 61
52	Operation	operator: 65 operands: 62
53	Operation	operator: 63 operands: 64
54	Operation	operator: 65 operands: 66
55	NamedExprs	state: 67 part: 72
56	Literal
57	Variable
58	ExprTuple	68, 72
59	Literal
60	NamedExprs	operation: 69
61	NamedExprs	state: 70 part: 72
62	ExprTuple	78, 79
63	Literal
64	NamedExprs	state: 71 part: 72
65	Literal
66	ExprTuple	73, 74
67	Variable
68	Variable
69	Literal
70	Variable
71	Variable
72	Variable
73	Operation	operator: 76 operands: 75
74	Operation	operator: 76 operands: 77
75	ExprTuple	79, 78
76	Literal
77	ExprTuple	79, 80
78	Literal
79	Variable
80	Variable