Project Description

In this postdoctoral project proposal, we propose to conduct a comprehensive study of the loss landscapes associated with Variational Quantum Eigensolvers (VQE) through large-scale simulations. Our approach is two-fold: First, we will systematically increase the complexity of quantum systems under study, starting from hydrogen chains and extending to more intricate chemical models. Second, we will leverage the latest advancements in quantum circuit simulations to test these systems on a scale of up to 64 qubits and tens of thousands of variational parameters.

Our research aims to address several critical questions for the first time. We will investigate the quality of the ansatz that can be practically implemented on existing quantum hardware. This will provide insights into the accuracy levels achievable as the problem sizes approach the limits of classical computation. Additionally, we will identify which quantum systems are most amenable to quantum hardware, thereby guiding future experimental designs. We will also delve into the hardware requirements for maintaining high accuracy levels, focusing on how to mitigate the loss of accuracy due to coherent errors. Finally, we will characterize the behavior of various optimization algorithms in navigating the VQE loss landscapes, with particular attention to issues such as local minima and barren plateaus.

Through this research, we aim to bridge the gap between theory and practical implementation, providing actionable insights for the development of more efficient and accurate quantum algorithms.
Close collaboration with the Purdue Quantum Science and Engineering Institute will ensure access to cutting-edge quantum computing resources and interdisciplinary collaborations, enriching the understanding of quantum-classical hybrid methodologies.

Start Date

Spring 2025

Postdoc Qualifications

Previous experience in high-performance computing is required.
Previous experience in computational chemistry and/or material science is recommended.

Co-advisors

David E. Bernal Neira. dbernaln@purdue.edu, Davidson School of Chemical Engineering, https://engineering.purdue.edu/ChE/people/ptProfile?resource_id=286478
Sabre Kais, kais@purdue.edu, Chemistry Department, https://www.chem.purdue.edu/kais/

Bibliography

- Jules Tilly, et al., “The variational quantum eigensolver: A review of methods and best practices,” Physics Reports 986, 1–128 (2022), the Variational Quantum Eigensolver: A review of methods and best practices

- J. Wayne Mullinax and Norm M. Tubman, “Large-scale sparse wavefunction circuit simulator for applications with the variational quantum eigensolver,” (2023), arXiv:2301.05726.

- Samson Wang, et al., “Noise-induced barren plateaus in variational quantum algorithms,” Nature Communications 12, 1–11 (2021).

- Manuel S. Rudolph, et al., “Orqviz: Visualizing high-dimensional landscapes in variational quantum algorithms,” (2021)

- Joonho Kim, et al., “Universal effectiveness of high-depth circuits in variational eigenproblems,” Physical Review Research 3 (2021), 10.1103/physrevresearch.3.023203.