A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic.
Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1⁄2 particle. It can be surprisingly difficult to achieve certain gate operations — most notably, those of arbitrary one-qubit gates — in spintronic hardware according to this model. However, ironically, certain twoqubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware.
Therefore, it would be fortunate if it were possible to implement any one-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any one-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report that the derivation provides explicit constructions for finding the exchange couplings in the physical basis needed to implement any arbitrary one-qubit gate. These constructions lead to spintronic encodings of quantum logic that are more efficient than those of a previously published scheme that utilizes a universal but fixed set of gates.
Given this mapping, universal quantum computation could be achieved in the encoded basis if, in addition, it were also possible to implement a controlled-NOT (CNOT) gate in the encoded basis. It had been demonstrated in prior research that such encoded construction of a CNOT gate is possible. Hence, in the present scheme, the mapping of arbitrary one-qubit gates is augmented with the encoded construction of CNOT gates, making it theoretically possible to perform universal quantum computation in the encoded basis.
This work was done by Colin Williams and Farrokh Vatan of Caltech for NASA’s Jet Propulsion Laboratory. The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (818) 393-2827. Refer to NPO-42996.