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, ket0
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Conditional(InSet(TensorProd(ket0, 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 0 \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	51, 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	28, 18
14	Operation	operator: 19 operand: 28
15	Operation	operator: 21 operands: 22
16	Operation	operator: 24 operands: 23
17	Operation	operator: 24 operands: 25
18	Operation	operator: 26 operands: 27
19	Literal
20	ExprTuple	28
21	Literal
22	ExprTuple	29, 30
23	ExprTuple	31, 47
24	Literal
25	ExprTuple	31, 32
26	Literal
27	ExprTuple	32, 33
28	Literal
29	Operation	operator: 37 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	Operation	operator: 37 operands: 38
33	Operation	operator: 39 operand: 44
34	ExprTuple	41, 42
35	Literal
36	ExprTuple	51, 43
37	Literal
38	ExprTuple	47, 43
39	Literal
40	ExprTuple	44
41	Literal
42	Operation	operator: 45 operands: 46
43	Variable
44	Literal
45	Literal
46	ExprTuple	47, 48, 49, 50, 51
47	Literal
48	Literal
49	Literal
50	Literal
51	Variable