Operator Sampling for Shot-frugal Optimization in Variational Algorithms

Abstract

Quantum chemistry is a near-term application for quantum computers. This application may be facilitated by variational quantum-classical algorithms (VQCAs), although a concern for VQCAs is the large number of measurements needed for convergence, especially for chemical accuracy. Here we introduce a strategy for reducing the number of measurements (i.e., shots) by randomly sampling operators $h_i$ from the overall Hamiltonian $H={\sum }_i{c}_i{h}_i$. In particular, we employ weighted sampling, which is important when the $c_i$'s are highly non-uniform, as is typical in chemistry. We integrate this strategy with an adaptive optimizer developed recently by our group to construct an improved optimizer called Rosalin (Random Operator Sampling for Adaptive Learning with Individual Number of shots). Rosalin implements stochastic gradient descent while adapting the shot noise for each partial derivative and randomly assigning the shots amongst the $h_i$ according to a weighted distribution. We implement this and other optimizers to find the ground states of molecules H${}_2$, LiH, and BeH${}_2$, without and with quantum hardware noise, and Rosalin outperforms other optimizers in most cases.

11 pages, 5 figures

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• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
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• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Fermionic partial tomography via classical shadows
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• Implementation of Measurement Reduction for the Variational Quantum Eigensolver
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• Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction
• Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: application to the $XXZ$ model on the square lattice