Overshifted Parameter-Shift Rules: Optimizing Complex Quantum Systems with Few Measurements

• URL: http://arxiv.org/abs/2510.05289v1
• Date: Mon, 06 Oct 2025 18:56:57 GMT
• Title: Overshifted Parameter-Shift Rules: Optimizing Complex Quantum Systems with Few Measurements
• Authors: Leonardo Banchi, Dominic Branford, Chetan Waghela,
• Abstract summary: A key ingredient of variational quantum algorithms, gradient-based optimization is a key ingredient of variational quantum algorithms.<n>We present a generalized framework that extends parameter shift rules beyond this restrictive setting to encompass basically arbitrary gate generators.<n>Our generalization enables the use of more expressive quantum circuits in variational quantum optimization and enlarges its scope by harnessing all the available hardware degrees of freedom.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for evaluating gradients of expectation values with respect to circuit parameters, but its applicability is limited to circuits whose gate generators have a particular spectral structure. In this work, we present a generalized framework that, with optimal minimum measurement overhead, extends parameter shift rules beyond this restrictive setting to encompass basically arbitrary gate generator, possibly made of complex multi-qubit interactions with unknown spectrum and, in some settings, even infinite dimensional systems such as those describing photonic devices or qubit-oscillator systems. Our generalization enables the use of more expressive quantum circuits in variational quantum optimization and enlarges its scope by harnessing all the available hardware degrees of freedom.

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