Quantum neural networks (QNNs) have been a promising framework in pursuing
near-term quantum advantage in various fields, where many applications can be
viewed as learning a quantum state that encodes useful data. As a quantum
analog of probability distribution learning, quantum state learning is
theoretically and practically essential in quantum machine learning. In this
paper, we develop a no-go theorem for learning an unknown quantum state with
QNNs even starting from a high-fidelity initial state. We prove that when the
loss value is lower than a critical threshold, the probability of avoiding
local minima vanishes exponentially with the qubit count, while only grows
polynomially with the circuit depth. The curvature of local minima is
concentrated to the quantum Fisher information times a loss-dependent constant,
which characterizes the sensibility of the output state with respect to
parameters in QNNs. These results hold for any circuit structures,
initialization strategies, and work for both fixed ansatzes and adaptive
methods. Extensive numerical simulations are performed to validate our
theoretical results. Our findings place generic limits on good initial guesses
and adaptive methods for improving the learnability and scalability of QNNs,
and deepen the understanding of prior information's role in QNNs.

本文开发了一个不可能定理，证明了使用量子神经网络（QNNs）从高保真度的初始状态开始，学习未知量子态的概率随比特数指数级下降，而与电路深度多项式增长，从而对改善 QNNs 的可学习性和可扩展性的好的初始猜测和自适应方法提出了普遍限制，并深化了先验信息在 QNNs 中的作用的理解。

量子神经网络中量子态学习过程的统计分析

Statistical Analysis of Quantum State Learning Process in Quantum Neural  Networks

There had been well known claims of unconditionally secure quantum protocols
for bit commitment. However, we, and independently Mayers, showed that all
proposed quantum bit commitment schemes are, in principle, insecure because the
sender, Alice, can almost always cheat successfully by using an
Einstein-Podolsky-Rosen (EPR) type of attack and delaying her measurements. One
might wonder if secure quantum bit commitment protocols exist at all. We answer
this question by showing that the same type of attack by Alice will, in
principle, break any bit commitment scheme. The cheating strategy generally
requires a quantum computer. We emphasize the generality of this ``no-go
theorem'': Unconditionally secure bit commitment schemes based on quantum
mechanics---fully quantum, classical or quantum but with measurements---are all
ruled out by this result. Since bit commitment is a useful primitive for
building up more sophisticated protocols such as zero-knowledge proofs, our
results cast very serious doubt on the security of quantum cryptography in the
so-called ``post-cold-war'' applications. We also show that ideal quantum coin
tossing is impossible because of the EPR attack. This no-go theorem for ideal
quantum coin tossing may help to shed some lights on the possibility of
non-ideal protocols.

该研究论文指出了量子协议对于比特承诺方案存在不可避免的攻击并且不存在安全的比特承诺协议，这对于量子密码在后冷战应用中的安全性产生非常严重的质疑。