Expression of type Len

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 ExprRange, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, subtract, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Len(operands = [frac(one, Exp(two, subtract(frac(Add(t, one), two), frac(t, two)))), TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), 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())])

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(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}}, \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\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 - 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)|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 55 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	63, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 70 operands: 11
9	Operation	operator: 33 operands: 12
10	ExprRange	lambda_map: 13 start_index: 14 end_index: 51
11	ExprTuple	72, 15
12	ExprTuple	39, 16
13	Lambda	parameter: 76 body: 17
14	Operation	operator: 41 operands: 18
15	Operation	operator: 41 operands: 19
16	Operation	operator: 47 operands: 20
17	Operation	operator: 47 operands: 21
18	ExprTuple	22, 63
19	ExprTuple	23, 24
20	ExprTuple	25, 53
21	ExprTuple	26, 27
22	Operation	operator: 74 operand: 60
23	Operation	operator: 55 operands: 29
24	Operation	operator: 74 operand: 36
25	Operation	operator: 70 operands: 31
26	Operation	operator: 55 operands: 32
27	Operation	operator: 33 operands: 34
28	ExprTuple	60
29	ExprTuple	35, 72
30	ExprTuple	36
31	ExprTuple	61, 37
32	ExprTuple	63, 38
33	Literal
34	ExprTuple	39, 40
35	Operation	operator: 41 operands: 42
36	Operation	operator: 55 operands: 43
37	Operation	operator: 64 operands: 44
38	Operation	operator: 70 operands: 45
39	Operation	operator: 58 operand: 51
40	Operation	operator: 47 operands: 48
41	Literal
42	ExprTuple	60, 63
43	ExprTuple	60, 72
44	ExprTuple	72, 66, 67, 69, 49
45	ExprTuple	72, 50
46	ExprTuple	51
47	Literal
48	ExprTuple	52, 53
49	Operation	operator: 70 operands: 54
50	Operation	operator: 55 operands: 56
51	Literal
52	Operation	operator: 70 operands: 57
53	Operation	operator: 58 operand: 63
54	ExprTuple	72, 60
55	Literal
56	ExprTuple	63, 72
57	ExprTuple	61, 62
58	Literal
59	ExprTuple	63
60	Variable
61	Literal
62	Operation	operator: 64 operands: 65
63	Literal
64	Literal
65	ExprTuple	72, 66, 67, 68, 69
66	Literal
67	Literal
68	Operation	operator: 70 operands: 71
69	Literal
70	Literal
71	ExprTuple	72, 73
72	Literal
73	Operation	operator: 74 operand: 76
74	Literal
75	ExprTuple	76
76	Variable