1. IBM Research Division, T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
2. Department of Chemistry,
3. Department of Physics,
4. Department of Mathematics, University of California, Berkeley, California 94720, USA
5. École Nationale Superieure des Télécommunications, 46 rue Barrault, 75634 Paris Cedex 13, France
6. Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Correspondence to: D. P. DiVincenzo¹ Correspondence and requests for materials should be addressed to D.P.D. (e-mail: Email: divince@watson.ibm.com).

Abstract

Various physical implementations of quantum computers are being investigated, although the requirements¹ that must be met to make such devices a reality in the laboratory at present involve capabilities well beyond the state of the art. Recent solid-state approaches have used quantum dots², donor-atom nuclear spins³ or electron spins⁴; in these architectures, the basic two-qubit quantum gate is generated by a tunable exchange interaction between spins (a Heisenberg interaction), whereas the one-qubit gates require control over a local magnetic field. Compared to the Heisenberg operation, the one-qubit operations are significantly slower, requiring substantially greater materials and device complexity—potentially contributing to a detrimental increase in the decoherence rate. Here we introduced an explicit scheme in which the Heisenberg interaction alone suffices to implement exactly any quantum computer circuit. This capability comes at a price of a factor 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 complexity of one-qubit operations should accelerate progress towards solid-state implementations of quantum computation¹.