  We consider a model of two interacting always-on, exchange-only qubits for
which controlled phase ($CPHASE$), controlled NOT ($CNOT$), quantum Fourier
transform ($QFT$) and $SWAP$ operations can be implemented only in a few
electrical pulses in a nanosecond time scale. Each qubit is built of three
quantum dots (TQD) in a triangular geometry with three electron spins which are
always kept coupled by exchange interactions only. The qubit states are encoded
in a doublet subspace and are fully electrically controlled by a voltage
applied to gate electrodes. The two qubit quantum gates are realized by short
electrical pulses which change the triangular symmetry of TQD and switch on
exchange interaction between the qubits. We found an optimal configuration to
implement the $CPHASE$ gate by a single pulse of the order 2.3 ns. Using this
gate, in combination with single qubit operations, we searched for optimal
conditions to perform the other gates: $CNOT$, $QFT$ and $SWAP$. Our studies
take into account environment effects and leakage processes as well. The
results suggest that the system can be implemented for fault tolerant quantum
computations.
