Exact solutions for universal holonomic quantum gates (5 pages)

Paolo Facchi A, Giuseppe Florio

Guo Jiang Yang

Shogo Tanimura, Daisuke Hayashi, Mikio Nakahara

Vahid Karimipour, N. Majd

We find exact solutions for a universal set of holonomic quantum gates on a scalable candidate for quantum computers, namely an array of two level systems. Previously these gates have been constructed mostly on non-scalable systems and by numerical searches in the space of loops in the space of control parameters of the Hamiltonian.

Vahid Karimipour, N. Majd

We show how one can implement any local quantum gate on specific qubits in an array of qubits by carrying adiabatically a Hamiltonian around a closed loop. We find the exact form of the loop and the Hamiltonian for implementing general one and two qubits gates. Our method is analytical and is not based on numerical search in the space of all loops.

Yan Liang, Tao Chen, Zheng‐Yuan Xue

Nonadiabatic holonomic quantum computation provides a promising approach toward fault-tolerant quantum control, due to its simple requirements for energy level structure and intrinsic robustness stemming from non-Abelian geometric phases. However, conventional nonadiabatic holonomic quantum computation relies on segmented evolution along a specific trajectory, which not only complicates experimental control but also exacerbates decoherence effects. Meanwhile, minor deviations in systematic parameters can directly disrupt the cyclic evolution process necessary to construct holonomic gates, leading to degraded gate robustness. To address these disadvantages, we here propose a general strategy to incorporate cyclic evolution protection into the holonomic gate construction. The aim is to design on-demand trajectories by modulating pulse shapes, thereby circumventing the detrimental impact of systematic errors on cyclic evolution. Consequently, universal holonomic gates implemented through a stable cyclic evolution process can maintain lower error sensitivity. Meanwhile, in our scheme, compressing the state population in the ancillary state ensures less energy consumption, resulting in higher gate fidelity. Therefore, our work serves as a practical solution for achieving high-fidelity and robust universal quantum gates, paving the way for large-scale quantum computation.