Controlling qubit arrays with anisotropic Heisenberg interaction (Vol. 42, No. 5)

Quantum-control methods are employed to manipulate physical and chemical processes using time-dependent fields. In particular they can be used to develop quantum logic gates thus helping us achieve a major goal of modern physics, the realization of scalable quantum computation.

A large body of work in quantum control has been devoted to the study of interacting spin-1/2 chains since these are effective models of qubit arrays. While interactions between qubits are necessary for realizing entangling two-qubit gates, standard approaches for controlling such arrays by acting on each qubit do not make an explicit use of these interactions. However for some particular types of interaction it suffices to control only a small subsystem of a given system, the idea underpinning the local-control approach.

In this paper we have explored anisotropic Heisenberg interactions, relevant for the use of Josephson junction based superconducting charge-qubit arrays. This example is particularly interesting as the concept of local control can be taken to the extreme -- controlling just one end qubit in an  array. We investigated how time-dependent control fields acting on the first qubit in an array can be selected in order to realize relevant quantum logic operations (e.g. controlled-NOT, square-root-of-SWAP) in the shortest possible times.

Further extending the idea of local control, we showed that in building some quantum gates the degree of control over the chosen end qubit can be further reduced by acting with a control field in only one direction (say, x direction). Most remarkably, we demonstrated that in the parameter regime of interest for superconducting charge qubits this reduced  control can lead to a more time-efficient realization of relevant   gates than the approach involving alternate x and y control fields. We anticipate that our findings will facilitate implementations of quantum  computation in superconducting qubit arrays.

Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit
R. Heule, C. Bruder, D. Burgarth, and V.M. Stojanovic, Eur. Phys. J. D 63, 41 (2011)