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arXiv · 2211.04501

Reducing the qubit requirement of Jordan-Wigner encodings of $N$-mode, $K$-fermion systems from $N$ to $\lceil \log_2 {N \choose K} \rceil$

Brent Harrison·Dylan Nelson·Daniel Adamiak·James Whitfield
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Abstract

To simulate a fermionic system on a quantum computer, it is necessary to encode the state of the fermions onto qubits. Fermion-to-qubit mappings such as the Jordan-Wigner and Bravyi-Kitaev transformations do this using $N$ qubits to represent systems of $N$ fermionic modes. In this work, we demonstrate that for particle number conserving systems of $K$ fermions and $N$ modes, the qubit requirement can be reduced to the information theoretic minimum of $\lceil \log_2 {N \choose K} \rceil$. This will improve the feasibility of simulation of molecules and many-body systems on near-term quantum computers with limited qubit number.

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Brent Harrison, Dylan Nelson, Daniel Adamiak, James Whitfield. 2022-11-08. Reducing the qubit requirement of Jordan-Wigner encodings of $N$-mode, $K$-fermion systems from $N$ to $\lceil \log_2 {N \choose K} \rceil$. https://arxiv.org/abs/2211.04501

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