Universal quantum computation with the exchange interaction

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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.

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Figure 1: Possible layouts of spin-1/2 devices.
Figure 2: Circuits for implementing single-qubit and two-qubit rotations using serial operations.

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Acknowledgements

We thank P. O. Boykin and B. M. Terhal for discussions. D.P.D., D.B., J.K. and K.B.W. were supported by the National Security Agency and the Advanced Research and Development Activity. D.P.D. also thanks the UCLA DARPA program on spin-resonance transistors for support, and is also grateful for the hospitality of D. Loss at the University of Basel, where much of this work was completed. J.K. also acknowledges support from the US National Science Foundation. G.B. is supported in part by the Swiss National Science Foundation.

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Correspondence to D. P. DiVincenzo.

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