AI summaryⓘ
The authors address a major challenge in training quantum circuits, which is the high measurement cost needed to estimate gradients using the traditional parameter-shift rule. They introduce a new method called forward gradient estimators that uses random directional derivatives to estimate gradients more efficiently without extra quantum resources. Their approach generalizes existing methods and includes a new optimizer named QUIVER that smartly allocates measurement effort to speed up training. They show that their framework works well on large quantum neural networks and outperforms other optimizers in various quantum tasks. Overall, their work aims to make training large parameterized quantum circuits more practical by reducing measurement overhead.
parameterised quantum circuitsparameter-shift rulegradient estimationautomatic differentiationforward gradientSPSAquantum neural networksQUIVER optimizervariational quantum eigensolverquantum approximate optimisation algorithm
Authors
Brian Coyle, Snehal Raj, Virag Umathe, El Amine Cherrat, Elham Kashefi
Abstract
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.