量子机器学习团队终于有了一个能大幅降低测量成本的梯度估计框架——QUIVER在60量子比特规模上效率提升数个数量级，做量子电路优化的研究者可以直接用。
训练参数化量子电路（PQC）时，梯度估计的测量成本是主要瓶颈，传统参数平移规则的成本随参数数量线性增长。本文提出基于前向自动微分的梯度估计框架，通过平均可调数量的随机方向导数获得无偏梯度，并统一了SPSA、随机坐标下降和参数平移规则。在此框架下，作者推导出QUIVER（量子迭代V自适应估计规则）优化器，实现最小测量成本分配。数值实验表明，前向梯度在训练含60量子比特、1770参数的量子神经网络时，效率比参数平移规则高出数个数量级。QUIVER在量子近似优化算法和变分量子本征求解器任务上，也优于iCANS和gCANS等测量节俭优化器。
Adaptive directional gradients for parameterised quantum circuits
Training parameterised quantum circuits (PQCs) on quantum hardware is bottlenecked by the measurement cost of gradient estimation, which under the parameter-shift rule scales linearly in the number of trainable parameters and dominates the total shot budget of training at scale. In this work, we propose a framework of forward gradient estimators for PQCs, based on the forward mode of automatic differentiation, that yields an unbiased estimator of the gradient by averaging a freely tunable number of random directional derivatives and recovers SPSA, random coordinate descent, and the parameter-shift rule as limiting cases, with no ancilla qubits or controlled-gate overhead. We prove that stochastic quantum forward gradient descent converges under standard assumptions, with an explicit second-moment expansion that interpolates between the single-direction extreme of SPSA and the full-gradient extreme of parameter-shift. Within this framework we derive QUIVER (Quantum Iterative V-adaptive Estimator Rule), an adaptive optimiser for parameterised circuits whose update rule follows from a closed-form minimum measurement-cost allocation. We show numerically that forward gradients train Hamming-weight-preserving orthogonal quantum neural networks with up to 60 qubits and 1770 parameters on the ECG5000 and MNIST datasets orders of magnitude more efficiently than the parameter-shift rule. We also demonstrate that our proposed QUIVER optimiser can outperform iCANS and gCANS measurement-frugal optimisers on optimisation problems using the quantum approximate optimisation algorithm and quantum simulation with the variational quantum eigensolver.