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
from proveit.core_expr_types import Len
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, one)
sub_expr3 = Add(_t, _s)
sub_expr4 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Len(operands = [[ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s)], [ExprRange(sub_expr1, sub_expr4, one, _t), ExprRange(sub_expr1, sub_expr4, sub_expr2, sub_expr3)]])

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(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\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	ExprTuple	5, 6
4	ExprTuple	7, 8
5	ExprRange	lambda_map: 9 start_index: 45 end_index: 47
6	ExprRange	lambda_map: 10 start_index: 45 end_index: 48
7	ExprRange	lambda_map: 11 start_index: 45 end_index: 47
8	ExprRange	lambda_map: 11 start_index: 36 end_index: 39
9	Lambda	parameter: 38 body: 12
10	Lambda	parameter: 38 body: 13
11	Lambda	parameter: 38 body: 15
12	Operation	operator: 27 operands: 16
13	Operation	operator: 18 operands: 17
14	ExprTuple	38
15	Operation	operator: 18 operands: 19
16	NamedExprs	state: 20
17	NamedExprs	element: 21 targets: 22
18	Literal
19	NamedExprs	element: 23 targets: 24
20	Operation	operator: 25 operand: 34
21	Operation	operator: 27 operands: 28
22	Operation	operator: 32 operands: 29
23	Operation	operator: 30 operands: 31
24	Operation	operator: 32 operands: 33
25	Literal
26	ExprTuple	34
27	Literal
28	NamedExprs	state: 35 part: 38
29	ExprTuple	36, 39
30	Literal
31	NamedExprs	operation: 37 part: 38
32	Literal
33	ExprTuple	45, 39
34	Literal
35	Literal
36	Operation	operator: 43 operands: 40
37	Operation	operator: 41 operands: 42
38	Variable
39	Operation	operator: 43 operands: 44
40	ExprTuple	47, 45
41	Literal
42	ExprTuple	46, 47
43	Literal
44	ExprTuple	47, 48
45	Literal
46	Literal
47	Literal
48	Literal