Journal of Chemical Physics, Vol.113, No.24, 10878-10885, 2000
Quantum codes for controlling coherent evolution
Control over spin dynamics has been obtained in nuclear magnetic resonance (NMR) via coherent averaging, which modifies the effective internal Hamiltonian, and via quantum codes, which can protect against decoherent evolution. Here, we discuss the design and implementation of quantum codes that enable modification of the internal Hamiltonian. A detailed example is given of a quantum code for protecting two data spins from evolution under a weak coupling term in the Hamiltonian, using an "isolated" ancilla that does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labeled alanine, and tested for two initial states. It is also shown that with internal interactions and isolated ancillae, codes exist that do not require the ancillae to initially be in a (pseudo-) pure state. Finally, it is shown that even with nonisolated ancillae, quantum codes exist which can protect against evolution under weak coupling. An example is presented for a six-qubit code that protects two data spins to first order.