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, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, 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}")
sub_expr2 = frac(one, sqrt(two))
expr = Len(operands = [ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, two_pow_t, _phase)), ket1))), ExprRange(sub_expr1, ScalarMult(sub_expr2, 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}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right),\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), \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), \ldots, \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: 30 operands: 5
4	ExprRange	lambda_map: 6 start_index: 7 end_index: 34
5	ExprTuple	16, 8
6	Lambda	parameter: 61 body: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 21 operands: 12
9	Operation	operator: 30 operands: 13
10	Literal
11	ExprTuple	14, 46
12	ExprTuple	25, 15
13	ExprTuple	16, 17
14	Operation	operator: 59 operand: 50
15	Operation	operator: 30 operands: 19
16	Operation	operator: 38 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	50
19	ExprTuple	23, 36
20	ExprTuple	46, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 55 operands: 27
24	Operation	operator: 55 operands: 28
25	Operation	operator: 41 operand: 34
26	Operation	operator: 30 operands: 31
27	ExprTuple	44, 32
28	ExprTuple	57, 33
29	ExprTuple	34
30	Literal
31	ExprTuple	35, 36
32	Operation	operator: 48 operands: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	Operation	operator: 55 operands: 40
36	Operation	operator: 41 operand: 46
37	ExprTuple	57, 51, 52, 43, 54
38	Literal
39	ExprTuple	46, 57
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	46
43	Operation	operator: 55 operands: 47
44	Literal
45	Operation	operator: 48 operands: 49
46	Literal
47	ExprTuple	57, 50
48	Literal
49	ExprTuple	57, 51, 52, 53, 54
50	Variable
51	Literal
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	57, 58
57	Literal
58	Operation	operator: 59 operand: 61
59	Literal
60	ExprTuple	61
61	Variable