# Accelerating geometric quantum gates through non-cyclic evolution and shortcut to adiabaticity

## TL;DR

This paper introduces a fast, robust method for quantum gates using non-cyclic geometric evolution combined with shortcuts to adiabaticity, improving speed and noise resistance for quantum computation.

## Contribution

It proposes a novel non-cyclic geometric quantum gate scheme that is faster and more noise-resistant than cyclic schemes, utilizing shortcuts to adiabaticity and spin-echo techniques.

## Key findings

- Operation time scales with rotation angle, enabling faster gates for small angles.
- The scheme is robust against random noise due to geometric properties.
- Suitable for systems with weak nonlinearity, like superconducting qubits.

## Abstract

Fast and robust quantum gates is the cornerstone of fault-tolerance quantum computation. In this paper, we propose to achieve quantum gates based on non-cyclic geometric evolution. Dynamical phase during the evolution is cancelled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabatic manner. Different from geometric gates based on cyclic evolution, the superiority of non-cyclic scheme is that the operation time is proportional to the rotation angle (but not the geometric phase) of quantum state. Therefore, the non-cyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle which will be more insensitive to the decoherence and leakage to the states outside the computational basis. The proposed scheme is also robust against random noise due to the geometric characteristic of projective Hilbert space. Since the refined proposed scheme is fast and robust, it is an particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconucting systems.