Building on AnonyMonk's approach above (and this actually works):

c:\@Work\Perl>perl -wMstrict -MData::Dump -le
"use constant OPS => qw{ ( (  ) )  ! !  | ||  & && };
 ;;
 sub compile {
   my ($expr, $hr_vars) = @_;
   ;;
   my %xlate = (OPS, %$hr_vars);
   ;;
   $expr =~ s{ (.) }
             { exists $xlate{$1}
                 or die qq{bad: '$1' at offset $-[1] in '$expr'};
               $xlate{$1};
             }xmsge;
   ;;
   return $expr;
   }
 ;;
 my %vars = qw(Q 0  T 1  C 0);
 dd \%vars;
 ;;
 my $expr = '(!(C)&T)&!Q';
 print qq{initial expr: '$expr'};
 ;;
 my $final_expr = compile($expr, \%vars);
 print qq{  final expr: '$final_expr'};
 ;;
 my $result = eval $final_expr;
 if ($@) {
   print qq{eval of '$final_expr' failed: $@}
   }
 else {
   print qq{'$final_expr' -> '$result'};
   }
"
{ C => 0, Q => 0, T => 1 }

initial expr: '(!(C)&T)&!Q'
  final expr: '(!(0)&&1)&&!0'
'(!(0)&&1)&&!0' -> '1'
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Some thoughts:

• Caution: Because it uses string eval, this code is not guaranteed to be safe, whatever your definition of "safe" may be. Caveat programmor.
• Play with this. E.g., are the outputs of  '(x!(C)&T)&!Q' or  '(!(C(&T)&!Q' acceptable?
• The expression  !1 evaluates to  '' (the empty string), which can propagate through subsequent logical expressions to produce an empty string as output, so after all you may want the bitwise  | & operators, which can produce  0 1 outputs.
• This code works under ActiveState 5.8.9 and should work, but has not been tested, under any higher Perl version.