# 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 Variable, l
from proveit.numbers import Abs, Add, Exp, Sum, two
from proveit.physics.quantum.QPE import _pos_domain, _rel_indexed_alpha

In [2]:
# build up the expression from sub-expressions
expr = Add(Variable("_a", latex_format = r"{_{-}a}"), Sum(index_or_indices = [l], summand = Exp(Abs(_rel_indexed_alpha), two), 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())

{_{-}a} + \left(\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
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 34
operands: 1
1ExprTuple2, 3
2Variable
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameter: 37
body: 8
7ExprTuple37
8Conditionalvalue: 9
condition: 10
9Operationoperator: 26
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 30
12Literal
13ExprTuple37, 15
14Operationoperator: 16
operand: 20
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20
18Literal
19ExprTuple21, 22
20Operationoperator: 23
operand: 28
21Operationoperator: 34
operands: 25
22Operationoperator: 26
operands: 27
23Literal
24ExprTuple28
25ExprTuple29, 42
26Literal
27ExprTuple30, 31
28Operationoperator: 32
operands: 33
29Variable
30Literal
31Operationoperator: 34
operands: 35
32Literal
33ExprTuple36, 37
34Literal
35ExprTuple38, 39
36Literal
37Variable
38Literal
39Operationoperator: 40
operand: 42
40Literal
41ExprTuple42
42Literal