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 Conditional, Lambda, m
from proveit.logic import Equals, InSet
from proveit.physics.quantum.QPE import _alpha_m_sqrd, _m_domain, _phase_est_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Equals(Prob(_phase_est_circuit), _alpha_m_sqrd), InSet(m, _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())

m \mapsto \left\{\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} \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 107 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	107, 10
8	Operation	operator: 11 operand: 15
9	Operation	operator: 41 operands: 13
10	Operation	operator: 90 operands: 14
11	Literal
12	ExprTuple	15
13	ExprTuple	16, 52
14	ExprTuple	17, 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 28
17	Literal
18	Operation	operator: 104 operands: 23
19	Literal
20	ExprTuple	24, 25, 26, 27
21	Literal
22	ExprTuple	28
23	ExprTuple	29, 30
24	ExprTuple	31, 32
25	ExprTuple	33, 34
26	ExprTuple	35, 36
27	ExprTuple	37, 38
28	Operation	operator: 39 operand: 107
29	Operation	operator: 41 operands: 42
30	Operation	operator: 43 operand: 108
31	ExprRange	lambda_map: 45 start_index: 108 end_index: 109
32	ExprRange	lambda_map: 46 start_index: 108 end_index: 110
33	ExprRange	lambda_map: 47 start_index: 108 end_index: 109
34	ExprRange	lambda_map: 47 start_index: 97 end_index: 98
35	ExprRange	lambda_map: 48 start_index: 108 end_index: 109
36	ExprRange	lambda_map: 49 start_index: 108 end_index: 110
37	ExprRange	lambda_map: 50 start_index: 108 end_index: 109
38	ExprRange	lambda_map: 51 start_index: 108 end_index: 110
39	Literal
40	ExprTuple	107
41	Literal
42	ExprTuple	52, 109
43	Literal
44	ExprTuple	108
45	Lambda	parameter: 96 body: 53
46	Lambda	parameter: 96 body: 54
47	Lambda	parameter: 96 body: 55
48	Lambda	parameter: 96 body: 56
49	Lambda	parameter: 96 body: 57
50	Lambda	parameter: 96 body: 58
51	Lambda	parameter: 96 body: 60
52	Literal
53	Operation	operator: 82 operands: 61
54	Operation	operator: 68 operands: 62
55	Operation	operator: 68 operands: 63
56	Operation	operator: 64 operands: 65
57	Operation	operator: 83 operands: 66
58	Operation	operator: 68 operands: 67
59	ExprTuple	96
60	Operation	operator: 68 operands: 69
61	NamedExprs	state: 70
62	NamedExprs	element: 71 targets: 79
63	NamedExprs	element: 72 targets: 73
64	Literal
65	NamedExprs	basis: 74
66	NamedExprs	operation: 75
67	NamedExprs	element: 76 targets: 77
68	Literal
69	NamedExprs	element: 78 targets: 79
70	Operation	operator: 80 operand: 92
71	Operation	operator: 82 operands: 89
72	Operation	operator: 83 operands: 84
73	Operation	operator: 90 operands: 85
74	Literal
75	Literal
76	Operation	operator: 88 operands: 86
77	Operation	operator: 90 operands: 87
78	Operation	operator: 88 operands: 89
79	Operation	operator: 90 operands: 91
80	Literal
81	ExprTuple	92
82	Literal
83	Literal
84	NamedExprs	operation: 93 part: 96
85	ExprTuple	108, 98
86	NamedExprs	state: 94 part: 96
87	ExprTuple	108, 109
88	Literal
89	NamedExprs	state: 95 part: 96
90	Literal
91	ExprTuple	97, 98
92	Literal
93	Operation	operator: 99 operands: 100
94	Operation	operator: 101 operands: 102
95	Literal
96	Variable
97	Operation	operator: 104 operands: 103
98	Operation	operator: 104 operands: 105
99	Literal
100	ExprTuple	106, 109
101	Literal
102	ExprTuple	107, 109
103	ExprTuple	109, 108
104	Literal
105	ExprTuple	109, 110
106	Literal
107	Variable
108	Literal
109	Literal
110	Literal