Expression of type Lambda

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.physics.quantum.QPE import _phase_est_circuit

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

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())

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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 78 body: 2
1	ExprTuple	78
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6, 7, 8
5	ExprTuple	9, 10
6	ExprTuple	11, 12
7	ExprTuple	13, 14
8	ExprTuple	15, 16
9	ExprRange	lambda_map: 17 start_index: 79 end_index: 80
10	ExprRange	lambda_map: 18 start_index: 79 end_index: 81
11	ExprRange	lambda_map: 19 start_index: 79 end_index: 80
12	ExprRange	lambda_map: 19 start_index: 68 end_index: 69
13	ExprRange	lambda_map: 20 start_index: 79 end_index: 80
14	ExprRange	lambda_map: 21 start_index: 79 end_index: 81
15	ExprRange	lambda_map: 22 start_index: 79 end_index: 80
16	ExprRange	lambda_map: 23 start_index: 79 end_index: 81
17	Lambda	parameter: 67 body: 24
18	Lambda	parameter: 67 body: 25
19	Lambda	parameter: 67 body: 26
20	Lambda	parameter: 67 body: 27
21	Lambda	parameter: 67 body: 28
22	Lambda	parameter: 67 body: 29
23	Lambda	parameter: 67 body: 31
24	Operation	operator: 53 operands: 32
25	Operation	operator: 39 operands: 33
26	Operation	operator: 39 operands: 34
27	Operation	operator: 35 operands: 36
28	Operation	operator: 54 operands: 37
29	Operation	operator: 39 operands: 38
30	ExprTuple	67
31	Operation	operator: 39 operands: 40
32	NamedExprs	state: 41
33	NamedExprs	element: 42 targets: 50
34	NamedExprs	element: 43 targets: 44
35	Literal
36	NamedExprs	basis: 45
37	NamedExprs	operation: 46
38	NamedExprs	element: 47 targets: 48
39	Literal
40	NamedExprs	element: 49 targets: 50
41	Operation	operator: 51 operand: 63
42	Operation	operator: 53 operands: 60
43	Operation	operator: 54 operands: 55
44	Operation	operator: 61 operands: 56
45	Literal
46	Literal
47	Operation	operator: 59 operands: 57
48	Operation	operator: 61 operands: 58
49	Operation	operator: 59 operands: 60
50	Operation	operator: 61 operands: 62
51	Literal
52	ExprTuple	63
53	Literal
54	Literal
55	NamedExprs	operation: 64 part: 67
56	ExprTuple	79, 69
57	NamedExprs	state: 65 part: 67
58	ExprTuple	79, 80
59	Literal
60	NamedExprs	state: 66 part: 67
61	Literal
62	ExprTuple	68, 69
63	Literal
64	Operation	operator: 70 operands: 71
65	Operation	operator: 72 operands: 73
66	Literal
67	Variable
68	Operation	operator: 75 operands: 74
69	Operation	operator: 75 operands: 76
70	Literal
71	ExprTuple	77, 80
72	Literal
73	ExprTuple	78, 80
74	ExprTuple	80, 79
75	Literal
76	ExprTuple	80, 81
77	Literal
78	Variable
79	Literal
80	Literal
81	Literal