Expression of type Conditional ¶

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, e, l
from proveit.logic import Equals, InSet
from proveit.numbers import Abs, Add, Exp, Sum, two
from proveit.physics.quantum.QPE import Pfail, _e_domain, _neg_domain, _pos_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(Abs(_rel_indexed_alpha), two)
expr = Conditional(Equals(Pfail(e), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _pos_domain))), InSet(e, _e_domain))

# 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\{\left[P_{\rm fail}\right]\left(e\right) = \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right)\right) \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 32 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	57, 8
6	Operation	operator: 9 operand: 57
7	Operation	operator: 64 operands: 11
8	Operation	operator: 40 operands: 12
9	Literal
10	ExprTuple	57
11	ExprTuple	13, 14
12	ExprTuple	70, 15
13	Operation	operator: 17 operand: 20
14	Operation	operator: 17 operand: 21
15	Operation	operator: 64 operands: 19
16	ExprTuple	20
17	Literal
18	ExprTuple	21
19	ExprTuple	56, 22
20	Lambda	parameter: 59 body: 23
21	Lambda	parameter: 59 body: 25
22	Operation	operator: 68 operand: 62
23	Conditional	value: 28 condition: 27
24	ExprTuple	59
25	Conditional	value: 28 condition: 29
26	ExprTuple	62
27	Operation	operator: 32 operands: 30
28	Operation	operator: 60 operands: 31
29	Operation	operator: 32 operands: 33
30	ExprTuple	59, 34
31	ExprTuple	35, 62
32	Literal
33	ExprTuple	59, 36
34	Operation	operator: 40 operands: 37
35	Operation	operator: 38 operand: 44
36	Operation	operator: 40 operands: 41
37	ExprTuple	42, 43
38	Literal
39	ExprTuple	44
40	Literal
41	ExprTuple	50, 56
42	Operation	operator: 64 operands: 45
43	Operation	operator: 68 operand: 50
44	Operation	operator: 47 operand: 51
45	ExprTuple	49, 70
46	ExprTuple	50
47	Literal
48	ExprTuple	51
49	Operation	operator: 68 operand: 56
50	Operation	operator: 64 operands: 53
51	Operation	operator: 54 operands: 55
52	ExprTuple	56
53	ExprTuple	57, 70
54	Literal
55	ExprTuple	58, 59
56	Operation	operator: 60 operands: 61
57	Variable
58	Literal
59	Variable
60	Literal
61	ExprTuple	62, 63
62	Literal
63	Operation	operator: 64 operands: 65
64	Literal
65	ExprTuple	66, 67
66	Literal
67	Operation	operator: 68 operand: 70
68	Literal
69	ExprTuple	70
70	Literal

Expression of type Conditional¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type Conditional ¶

from the theory of proveit.physics.quantum.QPE ¶