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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, VecSum
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(Qmult(NumBra(m, _t), InverseFourierTransform(_t)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), 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())
\left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t}, \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \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: 3
operands: 4
2Operationoperator: 5
operand: 9
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operand: 50
9Lambdaparameter: 42
body: 15
10Literal
11ExprTuple16, 50
12Literal
13ExprTuple50
14ExprTuple42
15Conditionalvalue: 17
condition: 18
16Variable
17Operationoperator: 19
operands: 20
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple42, 25
23Operationoperator: 45
operands: 26
24Operationoperator: 27
operands: 28
25Operationoperator: 29
operands: 30
26ExprTuple31, 32
27Literal
28ExprTuple42, 50
29Literal
30ExprTuple33, 34
31Literal
32Operationoperator: 35
operands: 36
33Literal
34Operationoperator: 37
operands: 38
35Literal
36ExprTuple49, 39, 40, 41, 42
37Literal
38ExprTuple43, 44
39Literal
40Literal
41Literal
42Variable
43Operationoperator: 45
operands: 46
44Operationoperator: 47
operand: 51
45Literal
46ExprTuple49, 50
47Literal
48ExprTuple51
49Literal
50Literal
51Literal