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}")
expr = Len(operands = [ExprRange(sub_expr1, Output(state = 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(\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 - 1} \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}, \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
3	ExprRange	lambda_map: 4 start_index: 5 end_index: 29
4	Lambda	parameter: 52 body: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 39
9	Literal
10	NamedExprs	state: 12
11	Operation	operator: 50 operand: 15
12	Operation	operator: 26 operands: 14
13	ExprTuple	15
14	ExprTuple	16, 17
15	Variable
16	Operation	operator: 32 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	39, 21
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 46 operands: 24
22	Operation	operator: 35 operand: 29
23	Operation	operator: 26 operands: 27
24	ExprTuple	48, 28
25	ExprTuple	29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Literal
30	Operation	operator: 46 operands: 34
31	Operation	operator: 35 operand: 39
32	Literal
33	ExprTuple	39, 48
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39
37	Literal
38	Operation	operator: 40 operands: 41
39	Literal
40	Literal
41	ExprTuple	48, 42, 43, 44, 45
42	Literal
43	Literal
44	Operation	operator: 46 operands: 47
45	Literal
46	Literal
47	ExprTuple	48, 49
48	Literal
49	Operation	operator: 50 operand: 52
50	Literal
51	ExprTuple	52
52	Variable