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Expression of type Conditional

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, k
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
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 = Conditional(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), 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\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple26, 9
7Operationoperator: 29
operands: 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operands: 14
10ExprTuple15, 16
11Literal
12ExprTuple26, 34
13Literal
14ExprTuple17, 18
15Literal
16Operationoperator: 19
operands: 20
17Literal
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple33, 23, 24, 25, 26
21Literal
22ExprTuple27, 28
23Literal
24Literal
25Literal
26Variable
27Operationoperator: 29
operands: 30
28Operationoperator: 31
operand: 35
29Literal
30ExprTuple33, 34
31Literal
32ExprTuple35
33Literal
34Literal
35Literal