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, m
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, NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
expr = Len(operands = [Lambda(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))), Lambda(sub_expr1, Measure(basis = Z)), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation()), Lambda(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t))), 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 \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{
& & \meter 
} \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 m \rangle_{t}~\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, 4, 5, 6, 7
3	Lambda	parameter: 41 body: 8
4	Lambda	parameter: 41 body: 9
5	Lambda	parameter: 41 body: 10
6	Lambda	parameter: 41 body: 11
7	Lambda	parameter: 41 body: 13
8	Operation	operator: 20 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	Operation	operator: 20 operands: 19
12	ExprTuple	41
13	Operation	operator: 20 operands: 21
14	NamedExprs	element: 22 targets: 23
15	Literal
16	NamedExprs	basis: 24
17	Literal
18	NamedExprs	operation: 25
19	NamedExprs	element: 26 targets: 27
20	Literal
21	NamedExprs	element: 28 targets: 29
22	Operation	operator: 30 operands: 31
23	Operation	operator: 37 operands: 32
24	Literal
25	Literal
26	Operation	operator: 35 operands: 33
27	Operation	operator: 37 operands: 34
28	Operation	operator: 35 operands: 36
29	Operation	operator: 37 operands: 38
30	Literal
31	NamedExprs	state: 39 part: 41
32	ExprTuple	54, 43
33	NamedExprs	state: 40 part: 41
34	ExprTuple	54, 55
35	Literal
36	NamedExprs	state: 52 part: 41
37	Literal
38	ExprTuple	42, 43
39	Operation	operator: 44 operands: 45
40	Operation	operator: 46 operands: 47
41	Variable
42	Operation	operator: 49 operands: 48
43	Operation	operator: 49 operands: 50
44	Literal
45	ExprTuple	51, 52
46	Literal
47	ExprTuple	53, 55
48	ExprTuple	55, 54
49	Literal
50	ExprTuple	55, 56
51	Literal
52	Literal
53	Variable
54	Literal
55	Literal
56	Literal