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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, frac, i, one, 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(frac(one, Exp(two, frac(_t, two))), 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(\frac{1}{2^{\frac{t}{2}}}, \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: 14
operands: 3
2Operationoperator: 4
operand: 7
3ExprTuple48, 6
4Literal
5ExprTuple7
6Operationoperator: 42
operands: 8
7Lambdaparameter: 39
body: 10
8ExprTuple46, 11
9ExprTuple39
10Conditionalvalue: 12
condition: 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13Operationoperator: 18
operands: 19
14Literal
15ExprTuple47, 46
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple39, 22
20Operationoperator: 42
operands: 23
21Operationoperator: 24
operands: 25
22Operationoperator: 26
operands: 27
23ExprTuple28, 29
24Literal
25ExprTuple39, 47
26Literal
27ExprTuple30, 31
28Literal
29Operationoperator: 32
operands: 33
30Literal
31Operationoperator: 34
operands: 35
32Literal
33ExprTuple46, 36, 37, 38, 39
34Literal
35ExprTuple40, 41
36Literal
37Literal
38Literal
39Variable
40Operationoperator: 42
operands: 43
41Operationoperator: 44
operand: 48
42Literal
43ExprTuple46, 47
44Literal
45ExprTuple48
46Literal
47Literal
48Literal