# 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, ExprTuple, Lambda, 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 = ExprTuple(Lambda(l, 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(l \mapsto \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 1\}\right..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 30
body: 3
2ExprTuple30
3Conditionalvalue: 4
condition: 5
4Operationoperator: 33
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 35
7Literal
8ExprTuple30, 10
9Operationoperator: 11
operand: 15
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15
13Literal
14ExprTuple16, 17
15Operationoperator: 18
operand: 22
16Operationoperator: 37
operands: 20
17Operationoperator: 37
operands: 21
18Literal
19ExprTuple22
20ExprTuple23, 43
21ExprTuple24, 40
22Operationoperator: 25
operands: 26
23Operationoperator: 41
operand: 31
24Operationoperator: 41
operand: 32
25Literal
26ExprTuple29, 30
27ExprTuple31
28ExprTuple32
29Literal
30Variable
31Operationoperator: 33
operands: 34
32Variable
33Literal
34ExprTuple35, 36
35Literal
36Operationoperator: 37
operands: 38
37Literal
38ExprTuple39, 40
39Literal
40Operationoperator: 41
operand: 43
41Literal
42ExprTuple43
43Literal