Two ways:

1. make a copy of the string and weed out the space characters

   my $string='i am using perl';
   (my $str = $string) =~ s/\s+//g;
   [download]

   then match $pattern against $str
2. insert \s* after (or before) every character in the pattern.

   my $pattern = 'iamusingper';
   $pattern =~ s/(.)/.\\s*$1/g;
   [download]

   then match $pattern against $string

Update: contrary to the title, you apparently don't want to ignore spaces in the regular expression (that's what the /x modifier is for), but in the string you are matching against.

2009-11-14
Original title: 'ignoring spaces in the (was: Regular expressions) string'

An alternate to option 2, slightly faster:

use strict;
use Benchmark qw/cmpthese/;
my $p = 'stringwithnospacesinit';
my ($a,$b);
cmpthese(
  -5,
  {
    a => sub{
      $a = $p;
      $a =~ s/(.)/$1\\s*/g;
    },
    b => sub{
      $b = $p;
      $b = join('\s*',split(//,$b));
    },
  }
);
__END__
     Rate    a    b
a 62530/s   -- -20%
b 78403/s  25%   --
[download]

update - typo fix

... and add a leading and/or trailing \s* ;-)

(update: only needed if the pattern is anchored)

1. Change your pattern as follows:

$pattern = qr/i\s*am\s*using\s*per/;
[download]

2. Make a copy of your string with the spaces removed.

my $pattern = qr(i[ ]*am[ ]*using[ ]*per);

And, when you post code, you'll help yourself by first checking that code by:

use strict;
use warnings
[download]

The apparent failure to do the above; the apparent failure to take several pieces of advice in previous replies; and the missing semi-colons suggest that you don't care so much about learning from the wisdom of the Monks as about using them to write your code.

I do not want generalise $pattern.I want my search of the $pattern which is without spaces ignore the spaces in the $string

If you want to ignore whitespace, you will have to create a new pattern.