• DOI:10.1088/1367-2630/aac54f
• Corpus ID: 53634097

Lowering qubit requirements for quantum simulations of fermionic systems.

@article{Steudtner2017LoweringQR,
  title={Lowering qubit requirements for quantum simulations of fermionic systems.},
  author={Mark Steudtner and Stephanie Wehner},
  journal={arXiv: Quantum Physics},
  year={2017}
}

• M. Steudtner, S. Wehner
• Published 19 December 2017
• Physics
• arXiv: Quantum Physics

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.