Physical optimization of quantum error correction circuits

Quantum error-correcting codes have been developed to protect a quantum com puter from decoherence due to a noisy environment. In this paper, we presen t two methods for optimizing the physical implementation of such error corr ection schemes. First, we discuss an optimal quantum circuit implementation of the smallest error-correcting code (the three bit code). Quantum circui ts are physically implemented by serial pulses, i.e., by switching on and o ff external parameters in the Hamiltonian one after another. In contrast to this we introduce a parallel switching method which allows faster gate ope ration by switching all external parameters simultaneously, and which has p otential applications for arbitrary quantum computer architectures. We appl y both serial and parallel switching to electron spins in coupled quantum d ots subject to a Heisenberg coupling H = J(t)S-1.S-2. We provide a list of steps that can be implemented experimentally and used as a test for the fun ctionality of quantum error correction. [S0163-1829(99)03740-6].