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.numbers import one
from proveit.physics.quantum.circuits import phase_kickback_circuit
from proveit.statistics import Prob

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

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) = 1

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