2024/02/22 by Sophia Simon, Simon, Sophia, Matthias Degroote +9 · 3 citations
Computer Science · Decision Sciences · Engineering · #FOS: Physical sciences #Fault Detection and Control Systems #Forecasting Techniques and Applications #Quantum Physics (quant-ph) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2402.14791
openalex publication_date 2024/02/22 · openalex created_date 2024/02/24 · openalex updated_date 2026/07/28
We provide a method for estimating the expectation value of an operator that can utilize prior knowledge to accelerate the learning process on a quantum computer. Specifically, suppose we have an operator that can be expressed as a concise sum of projectors whose expectation values we know a priori to be O(ε). In that case, we can estimate the expectation value of the entire operator within error ε using a number of quantum operations that scales as O(1/√ε). We then show how this can be used to reduce the cost of learning a potential energy surface in quantum chemistry applications by exploiting information gained from the energy at nearby points. Furthermore, we show, using Newton-Cotes methods, how these ideas can be exploited to learn the energy via integration of derivatives that we can estimate using a priori knowledge. This allows us to reduce the cost of energy estimation if the block-encodings of directional derivative operators have a smaller normalization constant than the Hamiltonian of the system.