# 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 Conditional, e, l
from proveit.logic import InSet
from proveit.numbers import Abs, Add, Exp, Interval, Neg, 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 = Conditional(Exp(Abs(_rel_indexed_alpha), two), InSet(l, 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())

\left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 1\}\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 30
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 32
4Literal
5ExprTuple27, 7
6Operationoperator: 8
operand: 12
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12
10Literal
11ExprTuple13, 14
12Operationoperator: 15
operand: 19
13Operationoperator: 34
operands: 17
14Operationoperator: 34
operands: 18
15Literal
16ExprTuple19
17ExprTuple20, 40
18ExprTuple21, 37
19Operationoperator: 22
operands: 23
20Operationoperator: 38
operand: 28
21Operationoperator: 38
operand: 29
22Literal
23ExprTuple26, 27
24ExprTuple28
25ExprTuple29
26Literal
27Variable
28Operationoperator: 30
operands: 31
29Variable
30Literal
31ExprTuple32, 33
32Literal
33Operationoperator: 34
operands: 35
34Literal
35ExprTuple36, 37
36Literal
37Operationoperator: 38
operand: 40
38Literal
39ExprTuple40
40Literal