# 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.logic import Implies, NotEquals
from proveit.numbers import Abs, Exp, Mod, four, frac, greater, pi, two, zero
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _b_round, _delta_b_round, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = Implies(NotEquals(_delta_b_round, zero), greater(Exp(Abs(SubIndexed(_alpha, [Mod(_b_round, _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(\delta_{b_{\textit{r}}} \neq 0\right) \Rightarrow \left(\left|\alpha_{b_{\textit{r}} ~\textup{mod}~ 2^{t}}\right|^{2} > \frac{4}{\pi^{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',)
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
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12
9Operationoperator: 13
operand: 31
10Literal
11Operationoperator: 15
operands: 16
12Operationoperator: 33
operands: 17
13Literal
14ExprTuple31
15Literal
16ExprTuple18, 19
17ExprTuple20, 35
18Literal
19Operationoperator: 33
operands: 21
20Operationoperator: 22
operand: 25
21ExprTuple24, 35
22Literal
23ExprTuple25
24Literal
25Operationoperator: 26
operand: 28
26Literal
27ExprTuple28
28Operationoperator: 29
operands: 30
29Literal
30ExprTuple31, 32
31Literal
32Operationoperator: 33
operands: 34
33Literal
34ExprTuple35, 36
35Literal
36Literal