The barren plateau (BP) phenomenon is one of the main obstacles to implementing variational quantum algorithms in the current generation of quantum processors. Here, we introduce a method capable of avoiding the BP phenomenon in the variational determination of the geometric measure of entanglement for a large number of qubits. The method is based on measuring compatible two-qubit local functions whose optimization allows for achieving a well-suited initial condition from which a global function can be further optimized without encountering a BP. We analytically demonstrate that the local functions can be efficiently estimated and optimized. Numerical simulations up to 18 qubit GHZ and W states demonstrate that the method converges to the exact value. In particular, the method allows for escaping from BPs induced by hardware noise or global functions defined on high-dimensional systems. Numerical simulations with noise agree with experiments carried out on IBM’s quantum processors for seven qubits.

中文翻译：

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避免几何纠缠变分测定中的贫瘠平台

贫瘠高原（BP）现象是在当前一代量子处理器中实现变分量子算法的主要障碍之一。在这里，我们介绍了一种能够避免在大量量子比特的纠缠几何测度的变分确定中出现BP现象的方法。该方法基于测量兼容的两个量子位局部函数，其优化允许实现非常合适的初始条件，从该初始条件可以进一步优化全局函数而不会遇到BP。我们分析证明可以有效地估计和优化局部函数。高达 18 个量子位 GHZ 和 W 状态的数值模拟表明该方法收敛到精确值。特别是，该方法允许逃避由硬件噪声或高维系统上定义的全局函数引起的BP。带有噪声的数值模拟与在 IBM 七个量子位的量子处理器上进行的实验一致。