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 I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _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, _t)
sub_expr4 = Lambda(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)))
expr = Len(operands = [sub_expr4, sub_expr4, Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr3)), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation()), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr3)), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2)))])

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 \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 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, 3, 4, 5, 6, 7
3	Lambda	parameter: 42 body: 8
4	Lambda	parameter: 42 body: 9
5	Lambda	parameter: 42 body: 10
6	Lambda	parameter: 42 body: 11
7	Lambda	parameter: 42 body: 13
8	Operation	operator: 18 operands: 14
9	Operation	operator: 18 operands: 15
10	Operation	operator: 31 operands: 16
11	Operation	operator: 18 operands: 17
12	ExprTuple	42
13	Operation	operator: 18 operands: 19
14	NamedExprs	element: 20 targets: 21
15	NamedExprs	element: 22 targets: 25
16	NamedExprs	operation: 23
17	NamedExprs	element: 24 targets: 25
18	Literal
19	NamedExprs	element: 26 targets: 27
20	Operation	operator: 28 operands: 29
21	Operation	operator: 37 operands: 30
22	Operation	operator: 31 operands: 32
23	Literal
24	Operation	operator: 35 operands: 33
25	Operation	operator: 37 operands: 34
26	Operation	operator: 35 operands: 36
27	Operation	operator: 37 operands: 38
28	Literal
29	NamedExprs	state: 39 part: 42
30	ExprTuple	53, 44
31	Literal
32	NamedExprs	operation: 40 part: 42
33	NamedExprs	state: 41 part: 42
34	ExprTuple	53, 57
35	Literal
36	NamedExprs	state: 52 part: 42
37	Literal
38	ExprTuple	43, 44
39	Operation	operator: 45 operands: 46
40	Operation	operator: 47 operand: 57
41	Literal
42	Variable
43	Operation	operator: 49 operands: 48
44	Operation	operator: 49 operands: 50
45	Literal
46	ExprTuple	51, 52
47	Literal
48	ExprTuple	57, 53
49	Literal
50	ExprTuple	57, 54
51	Operation	operator: 55 operand: 57
52	Literal
53	Literal
54	Literal
55	Literal
56	ExprTuple	57
57	Literal