Digital Quantum Simulation of Nonadiabatic Geometric Gates via Shortcuts to Adiabaticity.

Yapeng Wang,Yongcheng Ding,Jianan Wang,Xi Chen

doi:10.3390/e22101175

Yapeng Wang, Yongcheng Ding + Show 2 more

Open Access

https://doi.org/10.3390/e22101175

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Abstract

Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.

Highlights

A quantum computer based on a quantum gate and quantum circuits is one of the most promising solutions to the arising demand for computational resources, which is so-called digital quantum computing [1]
One has the universal gate set for geometric quantum computing, realizing quantum error correction physically, which could be an alternative approach to fault-tolerant quantum computation
Derived from the JC model with rotation-wave approximation (RWA), we obtain an effective two-level Hamiltonian describing a qubit driven by controllable pulses in the σx and σy direction

Summary

Introduction

A quantum computer based on a quantum gate and quantum circuits is one of the most promising solutions to the arising demand for computational resources, which is so-called digital quantum computing [1]. The systematic errors induced by inaccurate driving fields harm the performance of geometric gates [26,27], which should be further optimized by quantum control techniques. Both theoretical [28,29,30,31] and experimental researches [32,33] have been devoted to improving the robustness of (non-)Abelian gates against systematic errors. For the construction of a geometric single-qubit gate by time-dependent external field, we choose the two lowest levels, |0i and |1i, as the computational bases, with the dynamics governed by. U ( T ) gives a universal single-qubit gate

STA Design and Digital Simulation

Discussion

Conclusions