Single-Atom Verification of the Noise-Resilient and Fast Characteristics of Universal Nonadiabatic Noncyclic Geometric Quantum Gates.

Quantum gates induced by geometric phases are intrinsically robust against noise due to the global properties of their evolution paths. Compared to conventional nonadiabatic geometric quantum computation, the recently proposed nonadiabatic noncyclic geometric quantum computation (NNGQC) works in a faster fashion while still remaining the robust feature of the geometric operations. Here, we experimentally implement the NNGQC in a single trapped ultracold $^{40}{\mathrm{Ca}}^{+}$ ion to verify the noise-resilient and fast feature. By performing unitary operations under imperfect conditions, we witness the advantages of the NNGQC with measured fidelities by quantum process tomography in comparison to other two quantum gates by conventional nonadiabatic geometric quantum computation and by straightforward dynamical evolution. Our results provide the first evidence confirming the possibility of accelerated quantum information processing with limited systematic errors even in an imperfect situation.