Youre getting these errors because your while loop loops 468 times. Each time it iterates it increases both $X and $Y, which in turn will cause the loop to search for an array value that indeed is not initialized. Either add 466 more items to each array, or decrease the amount of loops.

I would use a different approach myself. Soemthing like:

use strict;
use warnings;

my @GI = (  "gi|Q384722390|emb|WP_938420210.1|Gene name",
            "gi|342546780|emb|WP_934203412.1|Gene name"
        );
my @Accession = qw( WP_938420210.1
                    WP_934203412.1
                    );

my $i = 0;

for my $A(@Accession) {
    for my $G(@GI) {
        if ( $A =~ $G ) {
            print "$G\n";
        }
    }
}
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