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 Lambda, Variable
from proveit.core_expr_types import Len
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE, _Psi_ket, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
sub_expr3 = Interval(one, sub_expr2)
sub_expr4 = Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr3))
sub_expr5 = Lambda(sub_expr1, MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = sub_expr3))
expr = Len(operands = [Lambda(sub_expr1, Input(state = ket_plus)), Lambda(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2))), sub_expr4, sub_expr4, sub_expr5, sub_expr5])

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({_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert + \rangle} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\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, 5, 5, 6, 6
3	Lambda	parameter: 38 body: 7
4	Lambda	parameter: 38 body: 8
5	Lambda	parameter: 38 body: 9
6	Lambda	parameter: 38 body: 11
7	Operation	operator: 25 operands: 12
8	Operation	operator: 15 operands: 13
9	Operation	operator: 15 operands: 14
10	ExprTuple	38
11	Operation	operator: 15 operands: 16
12	NamedExprs	state: 17
13	NamedExprs	element: 18 targets: 19
14	NamedExprs	element: 20 targets: 22
15	Literal
16	NamedExprs	element: 21 targets: 22
17	Operation	operator: 23 operand: 34
18	Operation	operator: 25 operands: 26
19	Operation	operator: 32 operands: 27
20	Operation	operator: 28 operands: 29
21	Operation	operator: 30 operands: 31
22	Operation	operator: 32 operands: 33
23	Literal
24	ExprTuple	34
25	Literal
26	NamedExprs	state: 50 part: 38
27	ExprTuple	35, 39
28	Literal
29	NamedExprs	operation: 36 part: 38
30	Literal
31	NamedExprs	state: 37 part: 38
32	Literal
33	ExprTuple	47, 39
34	Literal
35	Operation	operator: 45 operands: 40
36	Operation	operator: 41 operands: 42
37	Operation	operator: 43 operands: 44
38	Variable
39	Operation	operator: 45 operands: 46
40	ExprTuple	51, 47
41	Literal
42	ExprTuple	48, 51
43	Literal
44	ExprTuple	49, 50
45	Literal
46	ExprTuple	51, 52
47	Literal
48	Literal
49	Literal
50	Literal
51	Literal
52	Literal