Pulse sequences for exchange-based quantum computation

A CNOT-gate is one of the possible fundamental two-qubit gates for universal quantum computation. We consider a system where two qubits are encoded in any three spins of value 1/2 (arranged in a row), where each pair of neighboring spins can interact via the Heisenberg interaction. This could be realized by six quantum dots, each occupied by one excess electron. Electrons can virtually tunnel from one quantum dot to a neighboring dot, which switches on the interaction. Numerically a composition of 19 spin-interactions has been found leading to a quantum gate locally equivalent to a CNOT. This has shown that universal quantum computation in such an exchange-only scheme is feasible if the experimental requirements can be met. Here we present a different sequence that consists of a larger number of pulses, but is less restrictive on the preparation of the qubits. One assumption of the former sequence is that the total spin of the system was set to be 1, for which reason one can turn on a magnetic field aligning certain spins during initialization. The new solution works for a total spin of 0 and 1 thus making the magnetic field unnecessary. The new sequence consists of approximately 40 pulses. It was found analytically, which will be the main focus of the talk.