# 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 l
from proveit.numbers import Abs, Add, 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 = Add(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}\right) + \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: 49
operands: 1
1ExprTuple2, 3
2Operationoperator: 5
operand: 7
3Operationoperator: 5
operand: 8
4ExprTuple7
5Literal
6ExprTuple8
7Lambdaparameter: 44
body: 9
8Lambdaparameter: 44
body: 11
9Conditionalvalue: 13
condition: 12
10ExprTuple44
11Conditionalvalue: 13
condition: 14
12Operationoperator: 17
operands: 15
13Operationoperator: 45
operands: 16
14Operationoperator: 17
operands: 18
15ExprTuple44, 19
16ExprTuple20, 47
17Literal
18ExprTuple44, 21
19Operationoperator: 25
operands: 22
20Operationoperator: 23
operand: 29
21Operationoperator: 25
operands: 26
22ExprTuple27, 28
23Literal
24ExprTuple29
25Literal
26ExprTuple35, 41
27Operationoperator: 49
operands: 30
28Operationoperator: 53
operand: 35
29Operationoperator: 32
operand: 36
30ExprTuple34, 55
31ExprTuple35
32Literal
33ExprTuple36
34Operationoperator: 53
operand: 41
35Operationoperator: 49
operands: 38
36Operationoperator: 39
operands: 40
37ExprTuple41
38ExprTuple42, 55
39Literal
40ExprTuple43, 44
41Operationoperator: 45
operands: 46
42Variable
43Literal
44Variable
45Literal
46ExprTuple47, 48
47Literal
48Operationoperator: 49
operands: 50
49Literal
50ExprTuple51, 52
51Literal
52Operationoperator: 53
operand: 55
53Literal
54ExprTuple55
55Literal