Operator Sampling for Shot-frugal Optimization in Variational Algorithms

2020/04/14 by Andrew Arrasmith, Łukasz Cincio, Arrasmith, Andrew +5 · 6 citations
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2004.06252

openalex publication_date 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 = ∑_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 H₂, LiH, and BeH₂, without and with quantum hardware noise, and Rosalin outperforms other optimizers in most cases.

Citations

• A Quantum Approximate Optimization Algorithm
• Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families
• Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes

Cited by

• SPARTA: χ²-calibrated, risk-controlled exploration-exploitation for variational quantum algorithms
• Adaptive Measurement Allocation for Learning Kernelized SVMs Under Noisy Observations
• Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation
• A Noise-Aware Scalable Subspace Classical Optimizer for the Quantum Approximate Optimization Algorithm
• Gate Freezing Method for Gradient-Free Variational Quantum Algorithms in Circuit Optimization

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