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, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, QubitSpace, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Conditional(InSet(TensorProd(ket1, ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t))), TensorProd(QubitSpace, CartExp(Complex, two_pow_t))), InSet(k, Interval(zero, subtract(two_pow_t, one))))

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(\lvert 1 \rangle {\otimes} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right) \in \left(\mathbb{C}^{2} {\otimes} \mathbb{C}^{2^{t}}\right) \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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	50, 8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 15
10	Literal
11	ExprTuple	16, 17
12	Literal
13	ExprTuple	18, 19
14	Operation	operator: 20 operand: 43
15	Operation	operator: 21 operands: 22
16	Operation	operator: 24 operands: 23
17	Operation	operator: 24 operands: 25
18	Literal
19	Operation	operator: 26 operands: 27
20	Literal
21	Literal
22	ExprTuple	28, 29
23	ExprTuple	30, 46
24	Literal
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	31, 32
28	Operation	operator: 36 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	Operation	operator: 36 operands: 37
32	Operation	operator: 38 operand: 43
33	ExprTuple	40, 41
34	Literal
35	ExprTuple	50, 42
36	Literal
37	ExprTuple	46, 42
38	Literal
39	ExprTuple	43
40	Literal
41	Operation	operator: 44 operands: 45
42	Variable
43	Literal
44	Literal
45	ExprTuple	46, 47, 48, 49, 50
46	Literal
47	Literal
48	Literal
49	Literal
50	Variable