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Expression of type Sum

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 k, m
from proveit.numbers import Exp, Mult, Sum, 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 = Sum(index_or_indices = [k], summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _t))), domain = _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())
\sum_{k = 0}^{2^{t} - 1} \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)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 40
body: 5
4ExprTuple40
5Conditionalvalue: 6
condition: 7
6Operationoperator: 26
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple40, 13
11Operationoperator: 43
operands: 14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14ExprTuple19, 20
15Literal
16ExprTuple21, 22, 23
17Literal
18ExprTuple24, 25
19Literal
20Operationoperator: 26
operands: 27
21Operationoperator: 28
operands: 29
22Operationoperator: 30
operand: 48
23Operationoperator: 32
operands: 33
24Literal
25Operationoperator: 34
operands: 35
26Literal
27ExprTuple47, 36, 37, 38, 40
28Literal
29ExprTuple39, 48
30Literal
31ExprTuple48
32Literal
33ExprTuple40, 48
34Literal
35ExprTuple41, 42
36Literal
37Literal
38Literal
39Variable
40Variable
41Operationoperator: 43
operands: 44
42Operationoperator: 45
operand: 49
43Literal
44ExprTuple47, 48
45Literal
46ExprTuple49
47Literal
48Literal
49Literal