Our paper: arXiv:2606.09734
Authors: Brian Coyle, Snehal Raj, Virag Umathe, El Amine Cherrat (Quantum Signals), Elham Kashefi
Measurement cost, not qubit count, is often what makes training a quantum model expensive. This paper replaces the fixed cost of the standard gradient rule with a dial that can be tuned, and an optimiser that tunes it automatically.
Why we wrote it
Under the parameter-shift rule, every training step needs circuit runs proportional to the number of parameters. For models with hundreds or thousands of parameters, that dominates the total shot budget. We wanted a gradient estimator that keeps training unbiased but lets us spend far fewer measurements per step.
How it fits our work
This is the companion to our work on hardware-efficient circuit design. One line of our quantum program makes each gradient cheaper through the circuit's structure; this paper makes gradient estimation cheaper for any parameterised circuit, including the orthogonal quantum neural networks we use as quantum layers. Both feed the same goal: quantum versions of our neural networks that can be trained within a realistic hardware budget. The models are tested on ECG5000, a public time-series classification benchmark, as well as MNIST.
What it adds to our approach
- Forward gradients for quantum circuits. An unbiased estimator that averages a tunable number V of random directional derivatives; SPSA, random coordinate descent and parameter-shift are special cases.
- A convergence proof with an explicit expression for how the estimator's variance moves between the SPSA and parameter-shift extremes.
- QUIVER, an adaptive optimiser that chooses the number of directions and shots from the measurement statistics it already collects.
- Hardware-friendly. No ancilla qubits, mid-circuit measurements or extra gates, and the directional derivatives run in parallel across devices.
Key takeaway
At 60 qubits and 1,770 parameters on ECG5000, the best forward estimator used 25 directions per step, about 70x fewer gradient circuits per step than parameter-shift, and reached parameter-shift accuracy at a fraction of the shot cost. The saving grew with model size across all four benchmarks tested, and QUIVER beat the iCANS and gCANS measurement-frugal optimisers at matched shot budgets on VQE and QAOA problems.
Read the full paper on arXiv. For questions about our research or the quantum versions of our signals, contact info[at]quantumsignals.ai.