Problems using a map with a bitset as a key

Just use your own comparator class:

struct Comparer {
    bool operator() (const bitset<8> &b1, const bitset<8> &b2) const {
        return b1.to_ulong() < b2.to_ulong();
    }
};
/* ... */
map <bitset<8> , int, Comparer> mymap;

Note that you can extend this solution to support arbitrary length bitsets, as long as they are small enough to be converted to an unsigned long:

template<size_t sz> struct bitset_comparer {
    bool operator() (const bitset<sz> &b1, const bitset<sz> &b2) const {
        return b1.to_ulong() < b2.to_ulong();
    }
};
map <bitset<8> , int, bitset_comparer<8> > mymap;
map <bitset<16> , int, bitset_comparer<16> > mymap16;

An alternative solution would be to simply use an unordered_map, if this still meets your requirements.

This could be std::unordered_map<bitset<N>, T> or boost::unordered_map<bitset<N>, T>, depending on C++ version or performance considerations.

This avoids the need for comparison and may prove faster, depending on requirements.