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Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.
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This content will become publicly available on November 25, 2025
Advances in Simulating Fermions on a Quantum Computer
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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- Award ID(s):
- 2310620
- PAR ID:
- 10599344
- Publisher / Repository:
- Michigan State University
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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