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

• URL: http://arxiv.org/abs/2211.04501v4
• Date: Tue, 15 Aug 2023 18:32:20 GMT
• Title: Reducing the qubit requirement of Jordan-Wigner encodings of $N$-mode, $K$-fermion systems from $N$ to $\lceil \log_2 {N \choose K} \rceil$
• Authors: Brent Harrison, Dylan Nelson, Daniel Adamiak and James Whitfield
• Abstract summary: We show that for particle number conserving systems of $K$ fermions and $N$ modes, the qubit requirement can be reduced to theoretic minimum. This will improve the feasibility of simulation of molecules and many-body systems on near-term quantum computers with limited qubit number.
• Score: 1.0884863227198973
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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