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 TensorProd
from proveit.numbers import Add, Interval, Neg, one, two, zero
from proveit.physics.quantum.QPE import _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = TensorProd(_psi_t_ket, _ket_u)
sub_expr3 = Interval(one, Add(t, _s))
expr = Len(operands = [MultiQubitElem(element = Output(state = sub_expr2, part = one), targets = sub_expr3), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr2, part = Add(sub_expr1, t)), targets = sub_expr3), Add(Neg(t), two), zero)])

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{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 2\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 3\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \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: 14 operands: 5
4	ExprRange	lambda_map: 6 start_index: 7 end_index: 8
5	NamedExprs	element: 9 targets: 19
6	Lambda	parameter: 36 body: 11
7	Operation	operator: 32 operands: 12
8	Literal
9	Operation	operator: 21 operands: 13
10	ExprTuple	36
11	Operation	operator: 14 operands: 15
12	ExprTuple	16, 17
13	NamedExprs	state: 25 part: 27
14	Literal
15	NamedExprs	element: 18 targets: 19
16	Operation	operator: 20 operand: 40
17	Literal
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	NamedExprs	state: 25 part: 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 32 operands: 31
27	Literal
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	34, 35
31	ExprTuple	36, 40
32	Literal
33	ExprTuple	40, 37
34	Operation	operator: 38 operand: 40
35	Literal
36	Variable
37	Literal
38	Literal
39	ExprTuple	40
40	Variable