Theorem _sample_space_bijection of type InSet

from the theory of proveit.physics.quantum.QPE

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.QPE import _sample_space_bijection

# check that the built expression is the same as the stored expression
assert _sample_space_bijection.expr == stored_expr
assert _sample_space_bijection.expr._style_id == stored_expr._style_id
print("Passed sanity check: _sample_space_bijection matches stored_expr")

Passed sanity check: _sample_space_bijection matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left[m \mapsto \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)\right] \in \left[\{0~\ldotp \ldotp~2^{t} - 1\} \xrightarrow[\text{onto}]{\text{1-to-1}} \Omega\right]

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	Lambda	parameter: 97 body: 6
4	Operation	operator: 7 operands: 8
5	ExprTuple	97
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15, 16
11	Operation	operator: 80 operands: 17
12	Literal
13	ExprTuple	18, 19
14	ExprTuple	20, 21
15	ExprTuple	22, 23
16	ExprTuple	24, 25
17	ExprTuple	26, 27
18	ExprRange	lambda_map: 28 start_index: 98 end_index: 99
19	ExprRange	lambda_map: 29 start_index: 98 end_index: 100
20	ExprRange	lambda_map: 30 start_index: 98 end_index: 99
21	ExprRange	lambda_map: 30 start_index: 87 end_index: 88
22	ExprRange	lambda_map: 31 start_index: 98 end_index: 99
23	ExprRange	lambda_map: 32 start_index: 98 end_index: 100
24	ExprRange	lambda_map: 33 start_index: 98 end_index: 99
25	ExprRange	lambda_map: 34 start_index: 98 end_index: 100
26	Literal
27	Operation	operator: 94 operands: 35
28	Lambda	parameter: 86 body: 36
29	Lambda	parameter: 86 body: 37
30	Lambda	parameter: 86 body: 38
31	Lambda	parameter: 86 body: 39
32	Lambda	parameter: 86 body: 40
33	Lambda	parameter: 86 body: 41
34	Lambda	parameter: 86 body: 43
35	ExprTuple	44, 45
36	Operation	operator: 72 operands: 46
37	Operation	operator: 53 operands: 47
38	Operation	operator: 53 operands: 48
39	Operation	operator: 49 operands: 50
40	Operation	operator: 73 operands: 51
41	Operation	operator: 53 operands: 52
42	ExprTuple	86
43	Operation	operator: 53 operands: 54
44	Operation	operator: 55 operands: 56
45	Operation	operator: 57 operand: 98
46	NamedExprs	state: 59
47	NamedExprs	element: 60 targets: 68
48	NamedExprs	element: 61 targets: 62
49	Literal
50	NamedExprs	basis: 63
51	NamedExprs	operation: 64
52	NamedExprs	element: 65 targets: 66
53	Literal
54	NamedExprs	element: 67 targets: 68
55	Literal
56	ExprTuple	69, 99
57	Literal
58	ExprTuple	98
59	Operation	operator: 70 operand: 82
60	Operation	operator: 72 operands: 79
61	Operation	operator: 73 operands: 74
62	Operation	operator: 80 operands: 75
63	Literal
64	Literal
65	Operation	operator: 78 operands: 76
66	Operation	operator: 80 operands: 77
67	Operation	operator: 78 operands: 79
68	Operation	operator: 80 operands: 81
69	Literal
70	Literal
71	ExprTuple	82
72	Literal
73	Literal
74	NamedExprs	operation: 83 part: 86
75	ExprTuple	98, 88
76	NamedExprs	state: 84 part: 86
77	ExprTuple	98, 99
78	Literal
79	NamedExprs	state: 85 part: 86
80	Literal
81	ExprTuple	87, 88
82	Literal
83	Operation	operator: 89 operands: 90
84	Operation	operator: 91 operands: 92
85	Literal
86	Variable
87	Operation	operator: 94 operands: 93
88	Operation	operator: 94 operands: 95
89	Literal
90	ExprTuple	96, 99
91	Literal
92	ExprTuple	97, 99
93	ExprTuple	99, 98
94	Literal
95	ExprTuple	99, 100
96	Literal
97	Variable
98	Literal
99	Literal
100	Literal