Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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.QPE import _alpha_m_sqrd, _phase_est_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Equals(Prob(_phase_est_circuit), _alpha_m_sqrd)

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} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) = \left|\alpha_{m}\right|^{2}

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.	()	()	('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: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operand: 20
11	Literal
12	Literal
13	ExprTuple	16, 17, 18, 19
14	Literal
15	ExprTuple	20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprTuple	27, 28
20	Operation	operator: 29 operand: 92
21	ExprRange	lambda_map: 31 start_index: 93 end_index: 94
22	ExprRange	lambda_map: 32 start_index: 93 end_index: 95
23	ExprRange	lambda_map: 33 start_index: 93 end_index: 94
24	ExprRange	lambda_map: 33 start_index: 82 end_index: 83
25	ExprRange	lambda_map: 34 start_index: 93 end_index: 94
26	ExprRange	lambda_map: 35 start_index: 93 end_index: 95
27	ExprRange	lambda_map: 36 start_index: 93 end_index: 94
28	ExprRange	lambda_map: 37 start_index: 93 end_index: 95
29	Literal
30	ExprTuple	92
31	Lambda	parameter: 81 body: 38
32	Lambda	parameter: 81 body: 39
33	Lambda	parameter: 81 body: 40
34	Lambda	parameter: 81 body: 41
35	Lambda	parameter: 81 body: 42
36	Lambda	parameter: 81 body: 43
37	Lambda	parameter: 81 body: 45
38	Operation	operator: 67 operands: 46
39	Operation	operator: 53 operands: 47
40	Operation	operator: 53 operands: 48
41	Operation	operator: 49 operands: 50
42	Operation	operator: 68 operands: 51
43	Operation	operator: 53 operands: 52
44	ExprTuple	81
45	Operation	operator: 53 operands: 54
46	NamedExprs	state: 55
47	NamedExprs	element: 56 targets: 64
48	NamedExprs	element: 57 targets: 58
49	Literal
50	NamedExprs	basis: 59
51	NamedExprs	operation: 60
52	NamedExprs	element: 61 targets: 62
53	Literal
54	NamedExprs	element: 63 targets: 64
55	Operation	operator: 65 operand: 77
56	Operation	operator: 67 operands: 74
57	Operation	operator: 68 operands: 69
58	Operation	operator: 75 operands: 70
59	Literal
60	Literal
61	Operation	operator: 73 operands: 71
62	Operation	operator: 75 operands: 72
63	Operation	operator: 73 operands: 74
64	Operation	operator: 75 operands: 76
65	Literal
66	ExprTuple	77
67	Literal
68	Literal
69	NamedExprs	operation: 78 part: 81
70	ExprTuple	93, 83
71	NamedExprs	state: 79 part: 81
72	ExprTuple	93, 94
73	Literal
74	NamedExprs	state: 80 part: 81
75	Literal
76	ExprTuple	82, 83
77	Literal
78	Operation	operator: 84 operands: 85
79	Operation	operator: 86 operands: 87
80	Literal
81	Variable
82	Operation	operator: 89 operands: 88
83	Operation	operator: 89 operands: 90
84	Literal
85	ExprTuple	91, 94
86	Literal
87	ExprTuple	92, 94
88	ExprTuple	94, 93
89	Literal
90	ExprTuple	94, 95
91	Literal
92	Variable
93	Literal
94	Literal
95	Literal