Expression of type Image

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 import Lambda, m
from proveit.logic import Image
from proveit.physics.quantum.QPE import _m_domain, _phase_est_circuit

# build up the expression from sub-expressions
expr = Image(Lambda(m, _phase_est_circuit), _m_domain)

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())

\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]^{\rightarrow}(\{0~\ldotp \ldotp~2^{t} - 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',)

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