量子光学神经网络中线性光学模块的有效可训练性
Efficient trainability of linear optical modules in quantum optical neural networks
摘要：
由于连续变量状态的强度的可调谐性和具有指数较小维度的相关酉群，在量子光学神经网络中的通用线性光学模块的情况下，通用离散变量量子神经网络的“贫瘠高原景观”的存在将是令人惊讶的，这阻碍了由全局测量定义的成本函数的有效的基于梯度的优化。我们表明，相干光在$m$模式可以被有效地编译，如果总强度的规模与$m$次线性，并将这一结果的成本函数的基础上零差，外差，或光子检测测量统计，和噪声成本函数中存在的衰减。我们进一步证明了$m$模式的线性光量子线路的变分平均场能量估计的正二次哈密顿输入状态，不具有能量指数消失与$m$。
英文摘要：
The existence of "barren plateau landscapes" for generic discrete variable quantum neural networks, which obstructs efficient gradient-based optimization of cost functions defined by global measurements, would be surprising in the case of generic linear optical modules in quantum optical neural networks due to the tunability of the intensity of continuous variable states and the relevant unitary group having exponentially smaller dimension. We demonstrate that coherent light in $m$ modes can be generically compiled efficiently if the total intensity scales sublinearly with $m$, and extend this result to cost functions based on homodyne, heterodyne, or photon detection measurement statistics, and to noisy cost functions in the presence of attenuation. We further demonstrate efficient trainability of $m$ mode linear optical quantum circuits for variational mean field energy estimation of positive quadratic Hamiltonians for input states that do not have energy exponentially vanishing with $m$.
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