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, Integer, Mult, Sum, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _alpha_m_mod_two_pow_t, _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(Equals(_alpha_m_mod_two_pow_t, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Exp(Exp(e, Mult(two, pi, i, subtract(_phase, frac(m, _two_pow_t)))), k), domain = _m_domain))), InSet(m, Integer))

# 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 ~\textup{mod}~ 2^{t}} = \left(\frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\varphi - \frac{m}{2^{t}}\right)})^{k}\right)\right) \textrm{ if } m \in \mathbb{Z}\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: 25 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	55, 8
6	Operation	operator: 9 operand: 12
7	Operation	operator: 37 operands: 11
8	Literal
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14
12	Operation	operator: 15 operands: 54
13	Operation	operator: 53 operands: 16
14	Operation	operator: 17 operand: 19
15	Literal
16	ExprTuple	49, 56
17	Literal
18	ExprTuple	19
19	Lambda	parameter: 28 body: 21
20	ExprTuple	28
21	Conditional	value: 22 condition: 23
22	Operation	operator: 57 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 57 operands: 30
28	Variable
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Literal
34	Operation	operator: 37 operands: 38
35	Literal
36	Operation	operator: 44 operands: 39
37	Literal
38	ExprTuple	59, 40, 41, 42
39	ExprTuple	56, 43
40	Literal
41	Literal
42	Operation	operator: 44 operands: 45
43	Operation	operator: 50 operand: 49
44	Literal
45	ExprTuple	47, 48
46	ExprTuple	49
47	Literal
48	Operation	operator: 50 operand: 52
49	Literal
50	Literal
51	ExprTuple	52
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Variable
56	Operation	operator: 57 operands: 58
57	Literal
58	ExprTuple	59, 60
59	Literal
60	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 ¶