Bosonic continuous-variable Variational quantum circuits (VQCs) are crucial
for information processing in cavity quantum electrodynamics and optical
systems, widely applicable in quantum communication, sensing and error
correction. The trainability of such VQCs is less understood, hindered by the
lack of theoretical tools such as $t$-design due to the infinite dimension of
the physical systems involved. We overcome this difficulty to reveal an
energy-dependent barren plateau in such VQCs. The variance of the gradient
decays as $1/E^{M\nu}$, exponential in the number of modes $M$ but polynomial
in the (per-mode) circuit energy $E$. The exponent $\nu=1$ for shallow circuits
and $\nu=2$ for deep circuits. We prove these results for state preparation of
general Gaussian states and number states. We also provide numerical evidence
that the results extend to general state preparation tasks. As circuit energy
is a controllable parameter, we provide a strategy to mitigate the barren
plateau in continuous-variable VQCs.

文中提出，针对光学系统中的信息处理，分析了连续变量 Bosonic 量子变分电路（VQCs）中的训练问题，发现其学习难度受到电路能量的影响，提出了一种能够减轻训练难度的方法。

玻色变分量子电路中的能量依赖性贫瘠高原

Energy-dependent barren plateau in bosonic variational quantum circuits

A major roadblock for large-scale photonic quantum technologies is the lack
of practical reliable certification tools. We introduce an experimentally
friendly - yet mathematically rigorous - certification test for experimental
preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states
generated by linear-optical circuits with n-boson Fock-basis states as inputs,
and states of these two classes subsequently post-selected with local
measurements on ancillary modes. The protocol is efficient in m and the inverse
post-selection success probability for all Gaussian states and all mentioned
non-Gaussian states with constant n. We follow the mindset of an untrusted
prover, who prepares the state, and a skeptic certifier, with classical
computing and single-mode homodyne-detection capabilities only. No assumptions
are made on the type of noise or capabilities of the prover. Our technique
exploits an extremality-based fidelity bound whose estimation relies on
non-Gaussian state nullifiers, which we introduce on the way as a byproduct
result. The certification of many-mode photonic networks, as those used for
photonic quantum simulations, boson samplers, and quantum metrology, is now
within reach.

该研究提出了一种可靠的认证测试方法以证实实验制备的任意 m 模式纯高斯态、纯非高斯态和经过局部测量筛选的这两类状态，且无需对噪声类型或制备者的能力做出任何假设，该技术的应用于光子量子仿真、玻色取样器和量子计量学等多模光子网络的认证现在已经接近实现。

光子量子技术的可靠量子认证

Reliable quantum certification for photonic quantum technologies

The concept of steering was introduced by Schrodinger in 1935 as a
generalization of the EPR paradox for arbitrary pure bipartite entangled states
and arbitrary measurements by one party. Until now, it has never been
rigorously defined, so it has not been known (for example) what mixed states
are steerable (that is, can be used to exhibit steering). We provide an
operational definition, from which we prove (by considering Werner states and
Isotropic states) that steerable states are a strict subset of the entangled
states, and a strict superset of the states that can exhibit Bell-nonlocality.
For arbitrary bipartite Gaussian states we derive a linear matrix inequality
that decides the question of steerability via Gaussian measurements, and we
relate this to the original EPR paradox.

提出了操作性定义，在 Werner 状态和 Isotropic 状态上证明了可操纵状态是纠缠态的一个严格子集和能够展示 Bell - 本地性的状态的一个严格超集。对于任意双部分高斯态，我们推导出一个线性矩阵不等式，通过高斯测量来决定是否可操作，并将其与 EPR 佯谬联系起来。