Fault-tolerant quantum simulation of generalized Hubbard models

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• Dr Nick Blunt (Riverlane)
• Wednesday 05 February 2025, 12:00-13:30
• Todd-Hamied Room, Department of Chemistry, Cambridge.

If you have a question about this talk, please contact Chiara Leadbeater.

Simulating quantum systems of interacting electrons is a widely investigated use case for quantum computers. Despite significant optimization efforts, the quantum simulation of challenging systems such as the FeMoco complex and cytochrome P450 have been estimated to require at least millions of physical qubits and billions of Toffoli gates, which is far beyond the capabilities of near-term devices. Recently, it has been shown that fault-tolerant simulation of classically non-trivial Hubbard model instances may be possible with around one million Toffoli gates. Therefore, there is the exciting possibility that such model systems may be relevant in the “early fault-tolerant” regime. However, these previous studies have focused on the square-lattice Hubbard model. In this talk, we will present an efficient method to perform quantum simulation of generalized Hubbard models, for arbitrary lattices and Hamiltonians with long-range interactions, including extended Hubbard models and the PPP model. We will give an introduction to Trotterization for quantum simulation, and present our scheme, which we call Tile Trotterization. We will discuss the use of Tile Trotterization in quantum phase estimation, using hexagonal lattices as an example, and compare our results to qubitisation, which is a current state-of-the-art approach. We show that our scheme has better scaling with system size than qubitisation, and can be performed with low T gate counts. To conclude, we will discuss the potential use of this technique on early fault-tolerant quantum computers, and the considerations that this will involve.

This talk is part of the Quantum Computing for Quantum Chemistry series.

This talk is included in these lists:

• Quantum Computing for Quantum Chemistry
• Todd-Hamied Room, Department of Chemistry, Cambridge

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