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

In [1]:
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 ExprTuple, l
from proveit.numbers import Abs, Exp, Sum, two
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain, _rel_indexed_alpha

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(Abs(_rel_indexed_alpha), two)
expr = ExprTuple(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _pos_domain))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}, \sum_{l = e + 1}^{2^{t - 1}} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 4
operand: 6
2Operationoperator: 4
operand: 7
3ExprTuple6
4Literal
5ExprTuple7
6Lambdaparameter: 43
body: 8
7Lambdaparameter: 43
body: 10
8Conditionalvalue: 12
condition: 11
9ExprTuple43
10Conditionalvalue: 12
condition: 13
11Operationoperator: 16
operands: 14
12Operationoperator: 44
operands: 15
13Operationoperator: 16
operands: 17
14ExprTuple43, 18
15ExprTuple19, 46
16Literal
17ExprTuple43, 20
18Operationoperator: 24
operands: 21
19Operationoperator: 22
operand: 28
20Operationoperator: 24
operands: 25
21ExprTuple26, 27
22Literal
23ExprTuple28
24Literal
25ExprTuple34, 40
26Operationoperator: 48
operands: 29
27Operationoperator: 52
operand: 34
28Operationoperator: 31
operand: 35
29ExprTuple33, 54
30ExprTuple34
31Literal
32ExprTuple35
33Operationoperator: 52
operand: 40
34Operationoperator: 48
operands: 37
35Operationoperator: 38
operands: 39
36ExprTuple40
37ExprTuple41, 54
38Literal
39ExprTuple42, 43
40Operationoperator: 44
operands: 45
41Variable
42Literal
43Variable
44Literal
45ExprTuple46, 47
46Literal
47Operationoperator: 48
operands: 49
48Literal
49ExprTuple50, 51
50Literal
51Operationoperator: 52
operand: 54
52Literal
53ExprTuple54
54Literal