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, m
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _alpha_m, _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Equals(_alpha_m, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), domain = _m_domain))), InSet(m, _m_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\{\alpha_{m} = \left(\frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right)\right)\right) \textrm{ if } m \in \{0~\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: 22 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	57, 26
6	Operation	operator: 8 operand: 57
7	Operation	operator: 50 operands: 10
8	Literal
9	ExprTuple	57
10	ExprTuple	11, 12
11	Operation	operator: 43 operands: 13
12	Operation	operator: 14 operand: 16
13	ExprTuple	49, 48
14	Literal
15	ExprTuple	16
16	Lambda	parameter: 56 body: 18
17	ExprTuple	56
18	Conditional	value: 19 condition: 20
19	Operation	operator: 50 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	56, 26
24	Operation	operator: 52 operands: 27
25	Operation	operator: 52 operands: 28
26	Operation	operator: 29 operands: 30
27	ExprTuple	32, 31
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	34, 35
31	Operation	operator: 45 operand: 40
32	Literal
33	Operation	operator: 50 operands: 37
34	Literal
35	Operation	operator: 38 operands: 39
36	ExprTuple	40
37	ExprTuple	58, 54, 55, 41, 56
38	Literal
39	ExprTuple	48, 42
40	Operation	operator: 43 operands: 44
41	Literal
42	Operation	operator: 45 operand: 49
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49
47	Operation	operator: 50 operands: 51
48	Operation	operator: 52 operands: 53
49	Literal
50	Literal
51	ExprTuple	58, 54, 55, 56, 57
52	Literal
53	ExprTuple	58, 59
54	Literal
55	Literal
56	Variable
57	Variable
58	Literal
59	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 ¶