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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
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _m_domain, _phase, _t
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(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(\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()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Operationoperator: 2
operand: 4
2Literal
3ExprTuple4
4Lambdaparameter: 32
body: 6
5ExprTuple32
6Conditionalvalue: 7
condition: 8
7Operationoperator: 9
operands: 10
8Operationoperator: 11
operands: 12
9Literal
10ExprTuple13, 14
11Literal
12ExprTuple32, 15
13Operationoperator: 35
operands: 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16ExprTuple21, 22
17Literal
18ExprTuple32, 40
19Literal
20ExprTuple23, 24
21Literal
22Operationoperator: 25
operands: 26
23Literal
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple39, 29, 30, 31, 32
27Literal
28ExprTuple33, 34
29Literal
30Literal
31Literal
32Variable
33Operationoperator: 35
operands: 36
34Operationoperator: 37
operand: 41
35Literal
36ExprTuple39, 40
37Literal
38ExprTuple41
39Literal
40Literal
41Literal