# 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.numbers import Abs, Exp, Mod, Mult, Round, four, frac, greater, pi, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _phase, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = greater(Exp(Abs(SubIndexed(_alpha, [Mod(Round(Mult(_two_pow_t, _phase)), _two_pow_t)])), two), frac(four, Exp(pi, two)))

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|\alpha_{round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t}}\right|^{2} > \frac{4}{\pi^{2}}

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',)
directionDirection of the relation (normal or reversed)normalreversed('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
3Operationoperator: 5
operands: 6
4Operationoperator: 29
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple10, 31
8Literal
9Operationoperator: 29
operands: 11
10Operationoperator: 12
operand: 15
11ExprTuple14, 31
12Literal
13ExprTuple15
14Literal
15Operationoperator: 16
operand: 18
16Literal
17ExprTuple18
18Operationoperator: 19
operands: 20
19Literal
20ExprTuple21, 27
21Operationoperator: 22
operand: 24
22Literal
23ExprTuple24
24Operationoperator: 25
operands: 26
25Literal
26ExprTuple27, 28
27Operationoperator: 29
operands: 30
28Literal
29Literal
30ExprTuple31, 32
31Literal
32Literal