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, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import QubitSpace, ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), QubitSpace), InSet(sub_expr1, Interval(Add(Neg(t), one), zero)))

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\{\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2} \textrm{ if } {_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	57, 8
6	Operation	operator: 29 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 15
10	Literal
11	ExprTuple	16, 53
12	Literal
13	ExprTuple	17, 33
14	Operation	operator: 37 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Operation	operator: 21 operands: 22
18	ExprTuple	44, 23
19	Literal
20	ExprTuple	24, 25
21	Literal
22	ExprTuple	26, 44
23	Operation	operator: 51 operands: 27
24	Operation	operator: 40 operand: 33
25	Operation	operator: 29 operands: 30
26	Operation	operator: 55 operand: 36
27	ExprTuple	53, 32
28	ExprTuple	33
29	Literal
30	ExprTuple	34, 35
31	ExprTuple	36
32	Operation	operator: 37 operands: 38
33	Literal
34	Operation	operator: 51 operands: 39
35	Operation	operator: 40 operand: 44
36	Variable
37	Literal
38	ExprTuple	44, 53
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44
42	Literal
43	Operation	operator: 45 operands: 46
44	Literal
45	Literal
46	ExprTuple	53, 47, 48, 49, 50
47	Literal
48	Literal
49	Operation	operator: 51 operands: 52
50	Literal
51	Literal
52	ExprTuple	53, 54
53	Literal
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Variable