Holonomic quantum computation

Ognyan Oreshkov

We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.

Deep Bhattacharjee

Ognyan Oreshkov, Todd A. Brun, Daniel A. Lidar

We explain how to combine holonomic quantum computation (HQC) with fault-tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of computation, while retaining the inherent robustness the method derives from its geometric nature.

Jiang Zhang, Thi Ha Kyaw, Stefan Filipp +3 more

Demosthenes Ellinas, Jiannis K. Pachos

Holonomic quantum computation (HQC) is materialized here with quantum optics components. Holonomies are the generalization of the Berry phases to unitary matrices. In a nonlinear Kerr medium the degenerate states of a laser beams are interpreted as qubits. Control manipulations with displacers, squeezers and two-mode interfering devices in a cyclic, adiabatic fashion produces holonomies. Hence, they are employed as logical gates for our HQC proposal. The effects of errors from imperfect control of classical parameters, the looping variation of which builds up holonomic gates, are also investigated. Additionally, the influence of quantum decoherence on holonomic tele-portation used as a computational primitive is studied, and particular features of control error resilience are discussed.

Jiang Zhang, Thi Ha Kyaw, Stefan Filipp +3 more