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, k
from proveit.logic import InSet
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import ModAdd, SubIndexed, _alpha, _b_floor, _delta_b_floor, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(LessEq(Exp(Abs(SubIndexed(_alpha, [ModAdd(_b_floor, k)])), two), frac(one, Mult(four, Exp(subtract(k, Mult(_two_pow_t, _delta_b_floor)), two)))), InSet(k, _pos_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|\alpha_{b_{\textit{f}} \oplus k}\right|^{2} \leq \frac{1}{4 \cdot \left(k - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } k \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\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: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	41, 9
7	Operation	operator: 51 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 55
11	Literal
12	ExprTuple	43, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 19 operand: 24
16	Operation	operator: 47 operands: 21
17	Operation	operator: 38 operands: 22
18	Operation	operator: 51 operands: 23
19	Literal
20	ExprTuple	24
21	ExprTuple	25, 26
22	ExprTuple	27, 43
23	ExprTuple	55, 28
24	Operation	operator: 29 operand: 33
25	Literal
26	Operation	operator: 51 operands: 31
27	Variable
28	Operation	operator: 38 operands: 32
29	Literal
30	ExprTuple	33
31	ExprTuple	34, 55
32	ExprTuple	56, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 44 operand: 43
36	Literal
37	ExprTuple	57, 41
38	Literal
39	ExprTuple	41, 42
40	ExprTuple	43
41	Variable
42	Operation	operator: 44 operand: 46
43	Literal
44	Literal
45	ExprTuple	46
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Operation	operator: 51 operands: 52
50	Operation	operator: 53 operand: 57
51	Literal
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	57
55	Literal
56	Literal
57	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 ¶