2025/11/13 by Mathias Mikkelsen, Hubert Okadome Valencia, Mikkelsen, Mathias +2
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #quant-ph
paper · pdf · doi:10.48550/arxiv.2511.10124
openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28
We compare the basic resource requirements for first and second quantized bosonic mappings in a system consisting of N particles in M modes. In addition to the standard binary first quantized mapping, we investigate the unary first quantized mapping. Our comparison focuses on the k-body reduced density matrix (k-RDM) and two standard bosonic Hamiltonians. The first quantized mappings use less resources for off-diagonal terms of the k-RDM by a factor of ∼ Nk, compared to the second quantized mappings. The number of gates for the first quantized binary mapping increases faster with M compared to the other mappings. Nevertheless, a detailed numeric analysis reveals that the binary first quantized mapping still requires fewer gates than the binary and unary second quantized ones for realistic combinations of N and M, while requiring exponentially fewer qubits than the unary mappings. Additionally, the number of CNOT and Rz(ϕ) gates necessary to express a single Trotter step of the Hamiltonian in the binary first quantized mapping is comparable to the (most efficient for a single Trotter step) unary first quantized one when M = 2n for both the Bose-Hubbard model and the harmonic trap with short-range interactions. Additionally the binary mapping leads to lower one-norms than the unary mapping making it the overall most efficient choice for qubitization-based quantum phase estimation.