# 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.
# import Expression classes needed to build the expression
from proveit import e, l
from proveit.numbers import Abs, Add, Exp, Interval, Neg, Sum, one, subtract, two
from proveit.physics.quantum.QPE import _rel_indexed_alpha, _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
expr = Sum(index_or_indices = [l], summand = Exp(Abs(_rel_indexed_alpha), two), domain = Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one)))

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())

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

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 32
body: 5
4ExprTuple32
5Conditionalvalue: 6
condition: 7
6Operationoperator: 35
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 37
9Literal
10ExprTuple32, 12
11Operationoperator: 13
operand: 17
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17
15Literal
16ExprTuple18, 19
17Operationoperator: 20
operand: 24
18Operationoperator: 39
operands: 22
19Operationoperator: 39
operands: 23
20Literal
21ExprTuple24
22ExprTuple25, 45
23ExprTuple26, 42
24Operationoperator: 27
operands: 28
25Operationoperator: 43
operand: 33
26Operationoperator: 43
operand: 34
27Literal
28ExprTuple31, 32
29ExprTuple33
30ExprTuple34
31Literal
32Variable
33Operationoperator: 35
operands: 36
34Variable
35Literal
36ExprTuple37, 38
37Literal
38Operationoperator: 39
operands: 40
39Literal
40ExprTuple41, 42
41Literal
42Operationoperator: 43
operand: 45
43Literal
44ExprTuple45
45Literal