Universal quantum computation with the exchange interaction

Various physical implementations of quantum computers are being investigate d, although the requirements(1) that must be met to make such devices a rea lity in the laboratory at present involve capabilities well beyond the stat e of the art. Recent solid-state approaches have used quantum dots(2), dono r-atom nuclear spins(3) or electron spins(4); in these architectures, the b asic two-qubit quantum gate is generated by a tunable exchange interaction between spins (a Heisenberg interaction), whereas the one-qubit gates requi re control over a local magnetic field. Compared to the Heisenberg operatio n, the one-qubit operations are significantly slower, requiring substantial ly greater materials and device complexity-potentially contributing to a de trimental increase in the decoherence rate. Here we introduced an explicit scheme in which the Heisenberg interaction alone suffices to implement exac tly any quantum computer circuit. This capability comes at a price of a fac tor of three in additional qubits, and about a factor of ten in additional two-qubit operations. Even at this cost, the ability to eliminate the compl exity of one-qubit operations should accelerate progress towards solid-stat e implementations of quantum computation(1).