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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 Conditional, k, m
from proveit.logic import Equals, InSet
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _t))
expr = Equals(Conditional(sub_expr1, InSet(k, _m_domain)), sub_expr1)
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 \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \lvert k \rangle_{t} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right.. = \left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \lvert k \rangle_{t}\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
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11, 12
8Literal
9ExprTuple23, 13
10Operationoperator: 14
operands: 15
11Operationoperator: 16
operand: 35
12Operationoperator: 18
operands: 19
13Operationoperator: 20
operands: 21
14Literal
15ExprTuple22, 35
16Literal
17ExprTuple35
18Literal
19ExprTuple23, 35
20Literal
21ExprTuple24, 25
22Variable
23Variable
24Literal
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Operationoperator: 30
operands: 31
29Operationoperator: 32
operand: 36
30Literal
31ExprTuple34, 35
32Literal
33ExprTuple36
34Literal
35Literal
36Literal