Topological Fermionic Quantum Simulation

bell curve graph on a green background
2018-2021
  Funded Projects
  James D. Whitfield
  National Science Foundation

National Science Foundation Grant PHYS-1820747
PI
$407k/3 years

Abstract
Quantum physics has the potential to expand computer power in industrially and economically significant ways. Just as computers have become an integral part of people’s lives, quantum computation is likely to become equally impactful in the long term. The path to this grandiose goal needs achievable milestones along the way, and quantum simulation provides many such stepping stones. However, to take advantage of quantum computation for simulating matter, new tools and methods must be developed to map model systems of fermions (e.g. electrons and certain nuclei) onto quantum computers. This project will develop models that incorporate topological ideas that aid qubit-based quantum computers to simulate the fermion systems found throughout chemistry, physics, and materials science. The nature of topologically inspired fermion-to-qubit mappings opens new possibilities for simulating electronic structure on the qubits of a quantum computer. This allows local addressing of information that is stored non-locally which helps to simplify the algorithms for quantum simulation. The goals of this project include designing and implementing new algorithms that can be tested on early quantum hardware and incorporated into open-source code collections. The outcomes of this project will serve the broader scientific community by introducing tools that will be incorporated into rapidly developing quantum technology on the path to outpacing traditional computers. This project also include efforts to increase the inclusion of underrepresented groups in science and technology by inviting female freshmen and sophomore interns in conjunction with the Women In Science Project.

As part of the long-term goal to understand how best to utilize a quantum computer, the Topological Fermionic Quantum Simulation project aims to flesh out topological quantum simulation algorithms. The central hypothesis of this work is that topological approaches can enhance the efficiency of quantum simulations. This hypothesis has been formulated based on this team’s preliminary findings demonstrating benefits for fermionic encodings based on locality of the encoded spin operator. The proposed work has three major directions. The first delves into automation and implementation of the Bravyi-Kitaev Super-Fast model and explores its close connections to the toric code. The second area is to consider auxiliary fermion methods where additional modes are included to reduce the locality of the spin operators. Third, group theoretic approaches to black box simulation are ripe to explore and integrate with this growing area of quantum simulation. There are two cross-cutting themes that overlap with all branches of the project: local basis set design and benchmarking with numerical tools and with existing quantum hardware. The basis sets play a vital role in determining the efficiency and accuracy of any simulation while actual implementations provide metrics for success. Extension of quantum simulation algorithms based on topology has the potential for an immediate impact on the use of quantum computers. Additionally, this project opens questions about the nature of fermions, provides insights into the limitations of simulating them, and informs the requirements for the quantum simulation path to quantum supremacy.

This project is jointly funded by the Atomic, Molecular, and Optical Physics Experiment program in the Division of Physics and the Chemical Theory, Models and Computational Methods program in the Division of Chemistry (both Divisions are in the NSF Directorate for Mathematical and Physical Sciences) as well as the Established Program to Stimulate Competitive Research (NSF EPSCoR program).

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