\(H_H\left(t\right)\ =\ H_s\left(\hat p_H\left(t\right),\text{\hat x}_H\left(t\right),t\right)\)
2. operator is time dependent (\(\bigcirc=\bigcirc\left(t\right)\))
\(H_H\left(t\right)=H_s\left(\hat p_H\left(t\right),\hat x_H\left(t\right),t\right)\)
which is contrasting to the Schrödinger picture where operators are constant and state vectors are time dependent . 
In the Heisenberg picture , the basis does not change with time . This is accomplished by adding a term to the  Schrödinger states to eliminate the time - dependence .
                        \(\left|\psi_H>=e^{\frac{iH_st}{\hbar}}\left|\psi_S\left(t\right)=\right|\psi_s\left(0\right)>\right|\)
The quantum operators , however do change with time .
                                \(O\ =O\left(t\right)\)
Heisenberg Operators
Let consider a Schrödinger operator \(A_s\)(subscript s is for Schrödinger). This operator may or may not have time dependence. Now ,we will examine \(A_s\) in between time dependent states |a,t> and |b,t> and  use the time-evolution operator to convert the states to time zero:
                                    \(<a,t\left|A_s\right|b,t>\ =\ <a,0\left|U^+\left(t,0\right)A_sU\left(t,0\right)\right|b,0>\)