# 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 Equals, InSet
from proveit.numbers import Abs, Add, Exp, Interval, Neg, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha, _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Exp(Abs(_rel_indexed_alpha), two)
expr = Equals(Conditional(sub_expr1, InSet(l, _neg_domain)), Conditional(sub_expr1, InSet(l, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))))).with_wrapping_at(1)
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())
\begin{array}{c} \begin{array}{l} \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right.. \\  = \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 1\}\right.. \end{array} \end{array}
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.()(1)('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',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Conditionalvalue: 6
condition: 5
4Conditionalvalue: 6
condition: 7
5Operationoperator: 10
operands: 8
6Operationoperator: 42
operands: 9
7Operationoperator: 10
operands: 11
8ExprTuple39, 12
9ExprTuple13, 44
10Literal
11ExprTuple39, 14
12Operationoperator: 18
operands: 15
13Operationoperator: 16
operand: 21
14Operationoperator: 18
operands: 19
15ExprTuple22, 20
16Literal
17ExprTuple21
18Literal
19ExprTuple22, 23
20Operationoperator: 50
operand: 29
21Operationoperator: 25
operand: 30
22Operationoperator: 46
operands: 27
23Operationoperator: 46
operands: 28
24ExprTuple29
25Literal
26ExprTuple30
27ExprTuple31, 52
28ExprTuple32, 49
29Operationoperator: 46
operands: 33
30Operationoperator: 34
operands: 35
31Operationoperator: 50
operand: 40
32Operationoperator: 50
operand: 41
33ExprTuple41, 52
34Literal
35ExprTuple38, 39
36ExprTuple40
37ExprTuple41
38Literal
39Variable
40Operationoperator: 42
operands: 43
41Variable
42Literal
43ExprTuple44, 45
44Literal
45Operationoperator: 46
operands: 47
46Literal
47ExprTuple48, 49
48Literal
49Operationoperator: 50
operand: 52
50Literal
51ExprTuple52
52Literal