# 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 _pos_domain, _rel_indexed_alpha, _two_pow__t_minus_one

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 = Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))), 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}^{-e - 1} \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: 51
operands: 1
1ExprTuple2, 3
2Operationoperator: 5
operand: 7
3Operationoperator: 5
operand: 8
4ExprTuple7
5Literal
6ExprTuple8
7Lambdaparameter: 46
body: 9
8Lambdaparameter: 46
body: 11
9Conditionalvalue: 13
condition: 12
10ExprTuple46
11Conditionalvalue: 13
condition: 14
12Operationoperator: 17
operands: 15
13Operationoperator: 47
operands: 16
14Operationoperator: 17
operands: 18
15ExprTuple46, 19
16ExprTuple20, 49
17Literal
18ExprTuple46, 21
19Operationoperator: 25
operands: 22
20Operationoperator: 23
operand: 29
21Operationoperator: 25
operands: 26
22ExprTuple27, 28
23Literal
24ExprTuple29
25Literal
26ExprTuple30, 43
27Operationoperator: 51
operands: 31
28Operationoperator: 51
operands: 32
29Operationoperator: 33
operand: 38
30Operationoperator: 51
operands: 35
31ExprTuple36, 57
32ExprTuple37, 54
33Literal
34ExprTuple38
35ExprTuple44, 57
36Operationoperator: 55
operand: 43
37Operationoperator: 55
operand: 44
38Operationoperator: 41
operands: 42
39ExprTuple43
40ExprTuple44
41Literal
42ExprTuple45, 46
43Operationoperator: 47
operands: 48
44Variable
45Literal
46Variable
47Literal
48ExprTuple49, 50
49Literal
50Operationoperator: 51
operands: 52
51Literal
52ExprTuple53, 54
53Literal
54Operationoperator: 55
operand: 57
55Literal
56ExprTuple57
57Literal