One of the principal challenges in simulating fermions on a quantum computer is that qubits lack the anti-symmetry of fermions. The simplest solution, the Jordan-Wigner transformation, converts local interactions into non-local ones. I will describe a method based on Majorana fermions that preserves locality, and propose some improvements to it that reduce the CNOT gate cost and make the algorithm more suited to simulating nuclear matter. I will also suggest how a perturbation theory-based approach can be useful for studies in nuclear physics. Finally, I will discuss contributions I have made involving time fractals and quantum algorithms such as the rodeo algorithm, an eigenvalue estimation algorithm that can obtain precise results even on noisy quantum computers.
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