论文标题
量子张量网络优化中的贫瘠高原
Barren plateaus in quantum tensor network optimization
论文作者
论文摘要
我们分析了受基质产品状态（QMPS），树张量网络（QTTN）和多尺度纠缠重态化ANSATZ（QMERA）启发的量子电路的变化优化中的贫瘠高原现象。我们认为是成本函数，即哈密顿量的期望值，这是本地术语的总和。对于随机选择的变分参数，我们表明，成本函数梯度的方差随着量子张量网络中的汉密尔顿术语与规范中心的距离呈指数下降。因此，作为QMPS的函数，对于QMP，最梯度方差呈指数降低，而对于QTTN以及QMERA，它们以多项式减少。我们还表明，这些梯度的计算在古典计算机上比在量子计算机上更有效。
We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer.
