Variational quantum computing offers a flexible computational paradigm with
applications in diverse areas. However, a key obstacle to realizing their
potential is the Barren Plateau (BP) phenomenon. When a model exhibits a BP,
its parameter optimization landscape becomes exponentially flat and featureless
as the problem size increases. Importantly, all the moving pieces of an
algorithm -- choices of ansatz, initial state, observable, loss function and
hardware noise -- can lead to BPs when ill-suited. Due to the significant
impact of BPs on trainability, researchers have dedicated considerable effort
to develop theoretical and heuristic methods to understand and mitigate their
effects. As a result, the study of BPs has become a thriving area of research,
influencing and cross-fertilizing other fields such as quantum optimal control,
tensor networks, and learning theory. This article provides a comprehensive
review of the current understanding of the BP phenomenon.

变分量子计算通过在不同领域中应用提供了一种灵活的计算模式。然而，实现其潜力的一个关键障碍是荒漠高原现象。本文提供了对荒漠高原现象的当前理解的全面回顾。

变分量子计算中贫瘠高原的综述

A Review of Barren Plateaus in Variational Quantum Computing

We develop a framework of "semi-automatic differentiation" that combines
existing gradient-based methods of quantum optimal control with automatic
differentiation. The approach allows to optimize practically any computable
functional and is implemented in two open source Julia packages, GRAPE.jl and
Krotov.jl, part of the QuantumControl.jl framework. Our method is based on
formally rewriting the optimization functional in terms of propagated states,
overlaps with target states, or quantum gates. An analytical application of the
chain rule then allows to separate the time propagation and the evaluation of
the functional when calculating the gradient. The former can be evaluated with
great efficiency via a modified GRAPE scheme. The latter is evaluated with
automatic differentiation, but with a profoundly reduced complexity compared to
the time propagation. Thus, our approach eliminates the prohibitive memory and
runtime overhead normally associated with automatic differentiation and
facilitates further advancement in quantum control by enabling the direct
optimization of non-analytic functionals for quantum information and quantum
metrology, especially in open quantum systems. We illustrate and benchmark the
use of semi-automatic differentiation for the optimization of perfectly
entangling quantum gates on superconducting qubits coupled via a shared
transmission line. This includes the first direct optimization of the
non-analytic gate concurrence.

本文采用半自动微分的方法进行量子优化控制，将优化函数按时间传播和功能计算分解计算其梯度，并应用于开放量子系统中量子信息和量子计量的非解析函数优化控制。

半自动微分实现的量子最优控制

Quantum Optimal Control via Semi-Automatic Differentiation

We implement a quantum optimal control algorithm based on automatic
differentiation and harness the acceleration afforded by graphics processing
units (GPUs). Automatic differentiation allows us to specify advanced
optimization criteria and incorporate them in the optimization process with
ease. We show that the use of GPUs can speed up calculations by more than an
order of magnitude. Our strategy facilitates efficient numerical simulations on
affordable desktop computers, and exploration of a host of optimization
constraints and system parameters relevant to real-life experiments. We
demonstrate optimization of quantum evolution based on fine-grained evaluation
of performance at each intermediate time step, thus enabling more intricate
control on the evolution path, suppression of departures from the truncated
model subspace, as well as minimization of the physical time needed to perform
high-fidelity state preparation and unitary gates.

我们实现了一种基于自动差分的量子最优控制算法，并利用图形处理器的加速。我们的策略有助于在经济实惠的台式机上进行高效的数值模拟，包括探索与现实实验有关的各种优化约束和系统参数。我们演示了基于精细评估中间时间步骤的性能优化的量子演化，从而实现对演化路径的更加复杂的控制。