A Simple Derivation of the Spin-Exchange Operator

Sebastian Mehl, David Peter Divincenzo

Efficient operation sequences to couple and interchange quantum information between quantum dot spin qubits of different kinds are derived using exchange interactions. In the qubit encoding of a single-spin qubit, a singlet-triplet qubit, and an exchange-only (triple-dot) qubit, some of the single-qubit interactions remain on during the entangling operation; this greatly simplifies the operation sequences that construct entangling operations. In the ideal setup, the gate operations use the intraqubit exchange interactions only once, and entangling operations with gate times similar to typical single-qubit operations are constructed. The limitations of the entangling sequences are discussed, and it is shown how quantum information can be converted between different kinds of quantum dot spin qubits. These gate sequences are useful for large-scale quantum computation because they show that different kinds of coded spin qubits can be combined easily, permitting the favorable physical properties of each to be employed.

F Berencz

Ruben Pauncz

R. H. Lambert

The equation of motion for the electronic polarization of a ground-state alkali atom undergoing spin-exchange collisions is derived. It is shown that the equation of motion for the electronic polarization is unaffected by the inclusion of nuclear spin. A simple interpretation of the spin-exchange frequency shift is also given.

H. J. Hilhorst

Daniel Klein, David C. Foyt

A new variational derivation scheme for the Heisenberg exchange Hamiltonian is presented. A many-body variational Ansatz for the multistate ket appearing in the derivation is described and is applied to a simple model problem containing the qualitatively important different types of exchange contributions. Advantages of the present derivation over others are briefly indicated.