# 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 e
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Neg(e)
sub_expr2 = Mult(frac(one, Exp(two, one)), _two_pow_t)
sub_expr3 = subtract(sub_expr2, 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(\left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-2^{t - 1} + 1 - e\right)\right) = \left(\left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\right)\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: 30
operands: 5
4Operationoperator: 30
operands: 6
5ExprTuple8, 7
6ExprTuple8, 9
7Operationoperator: 30
operands: 10
8Operationoperator: 30
operands: 11
9Operationoperator: 30
operands: 12
10ExprTuple13, 43, 16
11ExprTuple22, 14
12ExprTuple15, 43, 16
13Operationoperator: 38
operand: 21
14Operationoperator: 38
operand: 42
15Operationoperator: 38
operand: 22
16Operationoperator: 38
operand: 23
17ExprTuple21
18ExprTuple42
19ExprTuple22
20ExprTuple23
21Operationoperator: 40
operands: 24
22Operationoperator: 25
operands: 26
23Variable
24ExprTuple42, 27
25Literal
26ExprTuple28, 29
27Operationoperator: 30
operands: 31
28Operationoperator: 32
operands: 33
29Operationoperator: 40
operands: 34
30Literal
31ExprTuple37, 35
32Literal
33ExprTuple43, 36
34ExprTuple42, 37
35Operationoperator: 38
operand: 43
36Operationoperator: 40
operands: 41
37Literal
38Literal
39ExprTuple43
40Literal
41ExprTuple42, 43
42Literal
43Literal