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Expression of type ExprTuple

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 ExprTuple, k, m
from proveit.linear_algebra import ScalarMult
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _phase, _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = NumBra(m, _t)
sub_expr2 = InverseFourierTransform(_t)
sub_expr3 = NumKet(k, _t)
sub_expr4 = Exp(e, Mult(two, pi, i, _phase, k))
expr = ExprTuple(Qmult(sub_expr1, sub_expr2, ScalarMult(sub_expr4, sub_expr3)), Mult(sub_expr4, Qmult(sub_expr1, sub_expr2, sub_expr3)))
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 \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right), \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \lvert k \rangle_{t}\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 9
operands: 3
2Operationoperator: 27
operands: 4
3ExprTuple12, 13, 5
4ExprTuple11, 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 14
9Literal
10ExprTuple12, 13, 14
11Operationoperator: 15
operands: 16
12Operationoperator: 17
operands: 18
13Operationoperator: 19
operand: 26
14Operationoperator: 21
operands: 22
15Literal
16ExprTuple23, 24
17Literal
18ExprTuple25, 26
19Literal
20ExprTuple26
21Literal
22ExprTuple33, 26
23Literal
24Operationoperator: 27
operands: 28
25Variable
26Literal
27Literal
28ExprTuple29, 30, 31, 32, 33
29Literal
30Literal
31Literal
32Literal
33Variable