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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 m
from proveit.logic import Equals
from proveit.numbers import Exp, frac, one, two
from proveit.physics.quantum import NumBra, Qmult
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 = NumBra(m, _t)
sub_expr2 = InverseFourierTransform(_t)
sub_expr3 = frac(one, Exp(two, frac(_t, two)))
expr = Equals(Qmult(sub_expr1, sub_expr3, sub_expr2), Qmult(Qmult(sub_expr1, sub_expr3), sub_expr2)).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left({_{t}}\langle m \rvert \thinspace \frac{1}{2^{\frac{t}{2}}} \thinspace {\mathrm {FT}}^{\dag}_{t}\right) =  \\ \left(\left({_{t}}\langle m \rvert \thinspace \frac{1}{2^{\frac{t}{2}}}\right) \thinspace {\mathrm {FT}}^{\dag}_{t}\right) \end{array} \end{array}
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.()(2)('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: 9
operands: 5
4Operationoperator: 9
operands: 6
5ExprTuple13, 14, 8
6ExprTuple7, 8
7Operationoperator: 9
operands: 10
8Operationoperator: 11
operand: 26
9Literal
10ExprTuple13, 14
11Literal
12ExprTuple26
13Operationoperator: 15
operands: 16
14Operationoperator: 24
operands: 17
15Literal
16ExprTuple18, 26
17ExprTuple19, 20
18Variable
19Literal
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple27, 23
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Literal
27Literal