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
from proveit.physics.quantum.circuits import Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(t)
sub_expr3 = frac(one, sqrt(two))
expr = Len(operands = [Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1)))), ExprRange(sub_expr1, Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(sub_expr2, two), 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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\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)} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 3} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\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)} 
} \end{array}\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: 12 operands: 5
4	ExprRange	lambda_map: 6 start_index: 7 end_index: 36
5	NamedExprs	state: 8
6	Lambda	parameter: 67 body: 9
7	Operation	operator: 62 operands: 10
8	Operation	operator: 32 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	65, 60
11	ExprTuple	19, 14
12	Literal
13	NamedExprs	state: 15
14	Operation	operator: 23 operands: 16
15	Operation	operator: 32 operands: 17
16	ExprTuple	27, 18
17	ExprTuple	19, 20
18	Operation	operator: 32 operands: 21
19	Operation	operator: 40 operands: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	25, 38
22	ExprTuple	66, 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 57 operands: 29
26	Operation	operator: 57 operands: 30
27	Operation	operator: 43 operand: 36
28	Operation	operator: 32 operands: 33
29	ExprTuple	46, 34
30	ExprTuple	60, 35
31	ExprTuple	36
32	Literal
33	ExprTuple	37, 38
34	Operation	operator: 49 operands: 39
35	Operation	operator: 40 operands: 41
36	Literal
37	Operation	operator: 57 operands: 42
38	Operation	operator: 43 operand: 66
39	ExprTuple	60, 52, 53, 45, 55
40	Literal
41	ExprTuple	66, 60
42	ExprTuple	46, 47
43	Literal
44	ExprTuple	66
45	Operation	operator: 57 operands: 48
46	Literal
47	Operation	operator: 49 operands: 50
48	ExprTuple	60, 51
49	Literal
50	ExprTuple	60, 52, 53, 54, 55
51	Operation	operator: 68 operand: 59
52	Literal
53	Literal
54	Operation	operator: 57 operands: 58
55	Literal
56	ExprTuple	59
57	Literal
58	ExprTuple	60, 61
59	Operation	operator: 62 operands: 63
60	Literal
61	Operation	operator: 68 operand: 67
62	Literal
63	ExprTuple	65, 66
64	ExprTuple	67
65	Operation	operator: 68 operand: 70
66	Literal
67	Variable
68	Literal
69	ExprTuple	70
70	Variable