A Geometric Characterization of Quantum Gates

Ralph Kenneth Colmenar, Utkan Güngördü, J. P. Kestner

Geometric quantum gates are often expected to be more resilient than dynamical gates against certain types of error, which would make them ideal for robust quantum computing.However, this is still up for debate due to seemingly conflicting results in the literature.Here we use dynamical invariant theory in conjunction with filter functions in order to analytically characterize the noise sensitivity of an arbitrary quantum gate.For any control Hamiltonian that produces a geometric gate, we find that, under certain common conditions, one can construct another control Hamiltonian that produces an equivalent dynamical gate with identical noise sensitivity (as characterized by the filter function).Our result holds for a Hilbert space of arbitrary dimensions, but we illustrate our result by examining experimentally relevant singlequbit scenarios and providing explicit examples of equivalent geometric and dynamical gates.

Zakaria Giunashvili

Klaus Mølmer, Anders Søndberg Sørensen, Xiaoguang Wang

Ralph Kenneth Colmenar, Utkan Güngördü, J. P. Kestner

Geometric quantum gates are conjectured to be more resilient than dynamical gates against certain types of error, which makes them ideal for robust quantum computing. However, there are conflicting claims within the literature about the validity of that robustness conjecture. Here we use dynamical invariant theory in conjunction with filter functions in order to analytically characterize the noise sensitivity of an arbitrary quantum gate. Under certain conditions, we find that there exists a transformation of the Hamiltonian that leaves invariant the final gate and noise sensitivity (as characterized by the filter function) while changing the phase from geometric to dynamical. Our result holds for a Hilbert space of arbitrary dimensions, but we illustrate our result by examining experimentally relevant single-qubit scenarios and providing explicit constructions of such a transformation.

Yuan Xu, Ziyue Hua, Tao Chen +9 more

Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.