How to use grep for multiple strings in perl

Using perl I need to ssh to a remote host and grep a file for strings.  For example, if I want to search just 'string1'  I would do the line of code below and it works.

$my result = qx{ssh $host grep string1 $log_file};

however I want to search 2 or 3 strings in the file. I tried
$my result = qx{ssh $host grep 'string1\|string2' $log_file};

but that does not work.  
The grep command is right because if execute from the shell prompt I get the lines containing either string1 or string2.