We propose a natural quantization of a standard neural network, where the neurons correspond to qubits and the activation functions are implemented via quantum gates and measurements. The simplest quantized neural network corresponds to applying single-qubit rotations, with the rotation angles being dependent on the weights and measurement outcomes of the previous layer. This realization has the advantage of being smoothly tunable from the purely classical limit with no quantum uncertainty (thereby reproducing the classical neural network exactly) to a quantum case, where superpositions introduce an intrinsic uncertainty in the network. We benchmark this architecture on a subset of the standard MNIST dataset and find a regime of "quantum advantage," where the validation error rate in the quantum realization is smaller than that in the classical model. We also consider another approach where quantumness is introduced via weak measurements of ancilla qubits entangled with the neuron qubits. This quantum neural network also allows for smooth tuning of the degree of quantumness by controlling an entanglement angle, $g$, with $g=\frac\pi 2$ replicating the classical regime. We find that validation error is also minimized within the quantum regime in this approach. We also observe a quantum transition, with sharp loss of the quantum network's ability to learn at a critical point $g_c$. The proposed quantum neural networks are readily realizable in present-day quantum computers on commercial datasets.

翻译：我们提出了一种标准神经网络的自然量子化方案，其中神经元对应于量子比特，激活函数通过量子门和测量实现。最简单的量子化神经网络对应应用单量子比特旋转操作，其旋转角度取决于前一层的权重和测量结果。这种实现方式的优势在于能够从无量子不确定性的纯经典极限（从而精确复现经典神经网络）平滑调节至量子情形，其中叠加态会为网络引入内在不确定性。我们在标准MNIST数据集的子集上对该架构进行基准测试，发现了"量子优势"区域——量子实现的验证错误率低于经典模型。我们还研究了另一种通过辅助量子比特弱测量引入量子特性的方法，这些辅助比特与神经元量子比特处于纠缠态。通过控制纠缠角$g$（当$g=\frac\pi 2$时可复现经典情形），这种量子神经网络同样能实现量子化程度的平滑调节。我们发现该方法中验证错误率也在量子区域内达到最小化。同时我们观测到量子相变现象：在临界点$g_c$处，量子网络的学习能力会出现急剧下降。所提出的量子神经网络可在现有量子计算机上针对商业数据集直接实现。