Implementing universal nonadiabatic holonomic quantum gates with transmons. (arXiv:1710.03141v3 [quant-ph] UPDATED)

Geometric phases are well known to be noise-resilient in quantum
evolutions/operations. Holonomic quantum gates provide us with a robust way
towards universal quantum computation, as these quantum gates are actually
induced by nonabelian geometric phases. Here we propose and elaborate how to
efficiently implement universal nonadiabatic holonomic quantum gates on simpler
superconducting circuits, with a single transmon serving as a qubit. In our
proposal, an arbitrary single-qubit holonomic gate can be realized in a
single-loop scenario, by varying the amplitudes and phase difference of two
microwave fields resonantly coupled to a transmon, while nontrivial two-qubit
holonomic gates may be generated with a transmission-line resonator being
simultaneously coupled to the two target transmons in an effective resonant
way. Moreover, our scenario may readily be scaled up to a two-dimensional
lattice configuration, which is able to support large scalable quantum
computation, paving the way for practically implementing universal nonadiabatic
holonomic quantum computation with superconducting circuits.

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