Expression of type Conditional

from the theory of proveit.physics.quantum.QPE

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, m
from proveit.logic import InSet
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _t

# build up the expression from sub-expressions
expr = Conditional(Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _t)), InSet(k, _m_domain))

expr:

# 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

# 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} \thinspace \lvert k \rangle_{t} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8, 9
5	Literal
6	ExprTuple	20, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operand: 32
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	Literal
12	ExprTuple	19, 32
13	Literal
14	ExprTuple	32
15	Literal
16	ExprTuple	20, 32
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Variable
21	Literal
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operand: 33
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33
31	Literal
32	Literal
33	Literal