Besides inherent resilience in non-Abelian geometric phases 8, HQC has an appealing advantage 9, 10, 11 in utilizing the state-of-art experimental setups due to its close relationship to the circuit model 12, 13, 14. Consequently, a geometric strategy for implementation of quantum gates permits fault-tolerant and robust quantum information processing. The geometric phase is exclusively determined by the trajectory of the system in its parameter space and robust against local fluctuation 6, 7. The theorem asserts that at any instant a quantum system remains nearby in its instantaneous eigenstate of a slow-varying Hamiltonian, specifically for a cyclic adiabatic process, a geometric phase (the Berry’s phase), is acquired over the course of the cycle 5.

While enormous theoretical strategies for conventional quantum gate implementation have been proposed, there is a revived interest in using geometric phases to perform circuit-based quantum computation, termed as holonomic quantum computation (HQC) 4, which is enabled by the adiabatic quantum theorem. It has been reported experimentally that numbers of pulse-controlled microscopic systems, such as solid-state spins 2 and trapped ions 3, can be hosts for implementation of quantum gates.

As building blocks for quantum computers, the implementation of quantum gates has received considerable research efforts over the recent years 1.

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