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

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

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\{\lvert \psi_{t} \rangle = \left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes}  \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes}  \ldots {\otimes}  \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right)\right) \textrm{ if } t \in \mathbb{N}^+\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
5	Literal
6	ExprTuple	27, 9
7	Operation	operator: 10 operand: 27
8	Operation	operator: 11 operands: 12
9	Literal
10	Literal
11	Literal
12	ExprTuple	13
13	ExprRange	lambda_map: 14 start_index: 15 end_index: 36
14	Lambda	parameter: 59 body: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 33 operands: 19
17	Literal
18	ExprTuple	20, 46
19	ExprTuple	21, 22
20	Operation	operator: 57 operand: 27
21	Operation	operator: 39 operands: 24
22	Operation	operator: 25 operands: 26
23	ExprTuple	27
24	ExprTuple	46, 28
25	Literal
26	ExprTuple	29, 30
27	Variable
28	Operation	operator: 53 operands: 31
29	Operation	operator: 42 operand: 36
30	Operation	operator: 33 operands: 34
31	ExprTuple	55, 35
32	ExprTuple	36
33	Literal
34	ExprTuple	37, 38
35	Operation	operator: 39 operands: 40
36	Literal
37	Operation	operator: 53 operands: 41
38	Operation	operator: 42 operand: 46
39	Literal
40	ExprTuple	46, 55
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	46
44	Literal
45	Operation	operator: 47 operands: 48
46	Literal
47	Literal
48	ExprTuple	55, 49, 50, 51, 52
49	Literal
50	Literal
51	Operation	operator: 53 operands: 54
52	Literal
53	Literal
54	ExprTuple	55, 56
55	Literal
56	Operation	operator: 57 operand: 59
57	Literal
58	ExprTuple	59
59	Variable