  Quantum error correcting codes have been developed to protect a quantum
computer from decoherence due to a noisy environment. In this paper, we present
two methods for optimizing the physical implementation of such error correction
schemes. First, we discuss an optimal quantum circuit implementation of the
smallest error-correcting code (the three bit code). Quantum circuits are
physically implemented by serial pulses, i.e. by switching on and off external
parameters in the Hamiltonian one after another. In contrast to this, we
introduce a new parallel switching method that allows faster gate operation by
switching all external parameters simultaneously. These two methods are applied
to electron spins in coupled quantum dots subject to a Heisenberg coupling
H=J(t) S_1*S_2 which can generate the universal quantum gate
`square-root-of-swap'. Using parallel pulses, the encoding for three-bit
quantum error correction in a Heisenberg system can be accelerated by a factor
of about two. We point out that parallel switching has potential applications
for arbitrary quantum computer architectures.
