Exact gradient for general cost functions in variational quantum algorithms

2025/09/22 by Jesus Urbaneja, Urbaneja, Jesus, Le Bin Ho +1
Computer Science · #FOS: Physical sciences #Neural Networks and Reservoir Computing #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2509.17822

openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/30

Abstract

We present a unitary-based gradient formulation for variational quantum algorithms (VQAs) that applies to general differentiable cost function defined by a parameterized quantum circuit composed of Pauli-generated rotations. The gradient is obtained directly from the underlying unitary evolution, without assuming a specific expectation-value form of the cost function. The resulting expressions can be accessed on quantum hardware using the Hadamard and Hilbert-Schmidt tests. We demonstrate the method in variational quantum compilation, where it yields stable and accurate gradient estimates. This unitary-based framework therefore provides a broadly applicable and hardware-compatible tool for gradient evaluation in VQAs.

Citations

• A Photonic Parameter-shift Rule: Enabling Gradient Computation for Photonic Quantum Computers
• Variational quantum algorithms
• Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
• Variational Quantum Gate Optimization
• A Quantum Approximate Optimization Algorithm

Related

• Pure Quantum Gradient Descent Algorithm and Full Quantum Variational Eigensolver
• Efficient Estimation and Sequential Optimization of Cost Functions in Variational Quantum Algorithms
• Towards Efficient Ansatz Architecture for Variational Quantum Algorithms
• A Novel Approach to Reduce Derivative Costs in Variational Quantum Algorithms
• Fast gradient estimation for variational quantum algorithms