logo

Expression of type Equals

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 ExprRange, Variable, m
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, frac, one, three, two
from proveit.physics.quantum import NumBra
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [NumBra(m, _t), frac(one, Exp(two, frac(_t, two))), InverseFourierTransform(_t)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))
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({_{t}}\langle m \rvert, \frac{1}{2^{\frac{t}{2}}}, {\mathrm {FT}}^{\dag}_{t}\right)| = |\left(1, 2, \ldots, 3\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9, 10
6Literal
7ExprTuple11
8Operationoperator: 12
operands: 13
9Operationoperator: 27
operands: 14
10Operationoperator: 15
operand: 29
11ExprRangelambda_map: 17
start_index: 20
end_index: 18
12Literal
13ExprTuple19, 29
14ExprTuple20, 21
15Literal
16ExprTuple29
17Lambdaparameter: 25
body: 25
18Literal
19Variable
20Literal
21Operationoperator: 23
operands: 24
22ExprTuple25
23Literal
24ExprTuple30, 26
25Variable
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Literal
30Literal