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 InSet
from proveit.numbers import Add, Exp, LessEq, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail, _diff_l_scaled_delta_floor, _e_domain, _neg_domain, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Conditional(LessEq(Pfail(e), Mult(frac(one, four), 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) \leq \left(\frac{1}{4} \cdot \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\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: 38 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	61, 8
6	Operation	operator: 9 operand: 61
7	Operation	operator: 64 operands: 11
8	Operation	operator: 45 operands: 12
9	Literal
10	ExprTuple	61
11	ExprTuple	13, 14
12	ExprTuple	81, 15
13	Operation	operator: 36 operands: 16
14	Operation	operator: 69 operands: 17
15	Operation	operator: 69 operands: 18
16	ExprTuple	81, 19
17	ExprTuple	20, 21
18	ExprTuple	60, 22
19	Literal
20	Operation	operator: 24 operand: 27
21	Operation	operator: 24 operand: 28
22	Operation	operator: 79 operand: 76
23	ExprTuple	27
24	Literal
25	ExprTuple	28
26	ExprTuple	76
27	Lambda	parameter: 55 body: 29
28	Lambda	parameter: 55 body: 31
29	Conditional	value: 33 condition: 32
30	ExprTuple	55
31	Conditional	value: 33 condition: 34
32	Operation	operator: 38 operands: 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	ExprTuple	55, 40
36	Literal
37	ExprTuple	81, 41
38	Literal
39	ExprTuple	55, 42
40	Operation	operator: 45 operands: 43
41	Operation	operator: 71 operands: 44
42	Operation	operator: 45 operands: 46
43	ExprTuple	47, 48
44	ExprTuple	49, 76
45	Literal
46	ExprTuple	54, 60
47	Operation	operator: 69 operands: 50
48	Operation	operator: 79 operand: 54
49	Operation	operator: 69 operands: 52
50	ExprTuple	53, 81
51	ExprTuple	54
52	ExprTuple	55, 56
53	Operation	operator: 79 operand: 60
54	Operation	operator: 69 operands: 58
55	Variable
56	Operation	operator: 79 operand: 62
57	ExprTuple	60
58	ExprTuple	61, 81
59	ExprTuple	62
60	Operation	operator: 71 operands: 63
61	Variable
62	Operation	operator: 64 operands: 65
63	ExprTuple	76, 66
64	Literal
65	ExprTuple	67, 68
66	Operation	operator: 69 operands: 70
67	Operation	operator: 71 operands: 72
68	Operation	operator: 73 operand: 78
69	Literal
70	ExprTuple	77, 75
71	Literal
72	ExprTuple	76, 77
73	Literal
74	ExprTuple	78
75	Operation	operator: 79 operand: 81
76	Literal
77	Literal
78	Literal
79	Literal
80	ExprTuple	81
81	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 ¶