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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 Conditional, ExprTuple, Lambda, k, m
from proveit.logic import InSet
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 _m_domain, _phase, _t
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _t))), InSet(k, _m_domain))))
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(k \mapsto \left\{\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) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 38
body: 3
2ExprTuple38
3Conditionalvalue: 4
condition: 5
4Operationoperator: 24
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple38, 11
9Operationoperator: 41
operands: 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operands: 16
12ExprTuple17, 18
13Literal
14ExprTuple19, 20, 21
15Literal
16ExprTuple22, 23
17Literal
18Operationoperator: 24
operands: 25
19Operationoperator: 26
operands: 27
20Operationoperator: 28
operand: 46
21Operationoperator: 30
operands: 31
22Literal
23Operationoperator: 32
operands: 33
24Literal
25ExprTuple45, 34, 35, 36, 38
26Literal
27ExprTuple37, 46
28Literal
29ExprTuple46
30Literal
31ExprTuple38, 46
32Literal
33ExprTuple39, 40
34Literal
35Literal
36Literal
37Variable
38Variable
39Operationoperator: 41
operands: 42
40Operationoperator: 43
operand: 47
41Literal
42ExprTuple45, 46
43Literal
44ExprTuple47
45Literal
46Literal
47Literal