Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10124 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914156281593856 |
|---|---|
| author | Mikkelsen, Mathias Valencia, Hubert Okadome |
| author_facet | Mikkelsen, Mathias Valencia, Hubert Okadome |
| contents | 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, which we show to be the most gate-efficient mapping for bosons in the general case, although less qubit-efficient than binary mappings. Our comparison focuses on the $k$-body reduced density matrix ($k$-RDM) as well as two standard bosonic Hamiltonians. The first quantized mappings use less resources for off-diagonal terms of the $k$-RDM by a factor of $ \sim N^k$, 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 $R_z(ϕ)$ gates necessary to express the exponential of the Hamiltonian in the binary first quantized mapping is comparable to the (overall most efficient) unary first quantized one when $M = 2^n$ for both the Bose-Hubbard model and the harmonic trap with short-range interactions. This suggests that this mapping can be both qubit- and gate-efficient for practical problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First and second quantized digital quantum simulations of bosonic systems Mikkelsen, Mathias Valencia, Hubert Okadome Quantum Physics 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, which we show to be the most gate-efficient mapping for bosons in the general case, although less qubit-efficient than binary mappings. Our comparison focuses on the $k$-body reduced density matrix ($k$-RDM) as well as two standard bosonic Hamiltonians. The first quantized mappings use less resources for off-diagonal terms of the $k$-RDM by a factor of $ \sim N^k$, 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 $R_z(ϕ)$ gates necessary to express the exponential of the Hamiltonian in the binary first quantized mapping is comparable to the (overall most efficient) unary first quantized one when $M = 2^n$ for both the Bose-Hubbard model and the harmonic trap with short-range interactions. This suggests that this mapping can be both qubit- and gate-efficient for practical problems. |
| title | First and second quantized digital quantum simulations of bosonic systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.10124 |