Optimized nonadiabatic holonomic quantum computation via reverse engineering

TL;DR

This work addresses the speed and robustness of nonadiabatic holonomic quantum computation by blending unconventional geometric quantum computation with NHQC+ through a general reverse-engineering method (UNHQC+). The authors derive a Hamiltonian that enforces UNHQC+ constraints along arbitrarily chosen evolution paths, enabling faster holonomic gates. They demonstrate a faster T-gate in a three-level system and extend the approach to a nontrivial two-qubit gate, showing reduced evolution time (e.g., $57.6$ ns vs ~$100$ ns for OSSP) and high fidelities (e.g., $\sim99.94\%$ under decoherence) while maintaining robustness against control errors. The results suggest that UNHQC+ offers a flexible, scalable route to high-fidelity, fault-tolerant holonomic quantum computation.

Abstract

The challenge in building high-fidelity quantum gates lies in overcoming control errors and decoherence effects caused by the coupling between the quantum system and the external environment. Nonadiabatic holonomic quantum computation uses the topological protection of the cyclic evolution of the computational subspace to make holonomic gates highly robust to control errors. Therefore, our main goal is to accelerate this evolution. Here we propose a general reverse engineering approach to combine the unconventional geometric quantum computation with optimized holonomic quantum computation [Bao-Jie Liu et al. Phys.Rev.Lett.123,100501 (2019)]. Our approach allows us to select evolution paths that require less time. Consequently, the proposed scheme is highly flexible and promising for achieving robust quantum computation in the future.

Figures (4)

• Figure 1: Evolution paths of the first and second strategy. (a) shows the conventional OSSP loop, where the quantum state evolves from the North Pole to the South Pole along the red geodesic, $\xi(t)=0$, and then returns from the South Pole to the North Pole along the black geodesic, $\xi(t)=\pi/4$. (b) shows the evolution path of the UNHQC+ strategy.
• Figure 2: The Rabi frequency and detuning of our UNHQC+ scheme. Here, (a) shows the pulse shape of Rabi frequency $\Omega(t)$ and (b) is the shape of detunning $\Delta(t)$.
• Figure 3: (a)T-gate fidelity for OSSP (dashed line) and UNHQC+ (solid line) as function of decoherence rate. (b)Dynamics of the gate fidelity and states population for UHNQC+ T-gate, with the fidelity reaching $99.94\%$.
• Figure 4: Gate fidelities of (a)OSSP and (b)UNHQC+ T-gates as functions of control errors $\delta$ and $\epsilon$. Here the black dashed line represents the fidelity $99\%$.