Simulating the Fermi-Hubbard Model on near term quantum devices

Lead Research Organisation: University College London
Department Name: Physics and Astronomy

Abstract

In this project I will investigate fermion to spin encodings in the context of the Fermi-Hubbard Hamiltonian, a simplified model of superconducting systems, and attempt to find optimal fermion to spin encodings for this system for different simulation methods on existing or near-term quantum devices. In the case of analogue simulation, this includes determining which encoding most faithfully reproduces the noise found in real fermionic systems. This research could be an important first step in eventually using quantum computers to simulate superconductivity, leading to greater understanding of the phenomenon.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/P510270/1 31/03/2016 30/08/2022
1917123 Studentship EP/P510270/1 24/09/2017 29/09/2021 Charles Nicholas Derby
 
Description A new encoding for fermions onto qubits has been found with uniquely low weight interaction operators. This would allow physical systems involving many particles like electrons (e.g. superconductors) to be more efficiently simulated on a quantum computer or similar device.

The way that qubit errors map onto the simulated fermion system has been shown to be local to first order. This means that if an error occurs on the quantum computer that is simulating a fermionic system via the new encoding mentioned above, then the effect on the simulated system will be that of a local error that could feasibly occur on that system in real life. How faithfully the errors map to the real life behaviour of such a system is still being investigated but it seems favourable.

An explicit connection between the new fermionic encoding and the toric code (a well known quantum error correction protocol) has been found. There exist many fermion to qubit encodings but a general theory linking them together has not been found. Others have noticed that other fermion encodings are seemingly related to the toric code but have not explored this connection in any great detail, establishing a strong connection between this new encoding and the toric code could open the door to finding how other codes are linked to it and perhaps lead to a general theory of fermionic encodings.

The first two findings are to be published soon, the third is still to be worked on.
Exploitation Route The new fermion encoding could be used by experimental groups to carry out simulations of fermionic systems.

If a general theory of fermionic encodings is found then theorists could perhaps use it to find the most appropriate encoding for a particular system and a particular simulation device.
Sectors Other