Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.03147 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929381737234432 |
|---|---|
| author | Gálvez-Viruet, Juan José Llanes-Estrada, Felipe J. |
| author_facet | Gálvez-Viruet, Juan José Llanes-Estrada, Felipe J. |
| contents | We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second quantization in problems with variable particle number. We establish theorems for the commutation (anticommutation) relations on a finite memory bank and provide the needed symmetrizing and antisymmetrizing operators. Finally, we provide formulae in terms of these operators for unitary evolution under conventional two- and four-body Hamiltonian terms, as well as terms varying the particle number. In this formalism, the number of qubits needed to codify $n$ particles with $N_p$ modes each is of order $n\log_2 N_p$. Such scaling is more efficient than the Jordan-Wigner transformation which requires $O(N_p)$ qubits, whenever there are a modest number of particles with a large number of states available to each (and less advantageous for a large number of particles with few states available to each). And although less efficient, it is also less cumbersome than compact encoding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A dynamical implementation of canonical second quantization on a quantum computer Gálvez-Viruet, Juan José Llanes-Estrada, Felipe J. High Energy Physics - Theory Nuclear Theory Quantum Physics We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second quantization in problems with variable particle number. We establish theorems for the commutation (anticommutation) relations on a finite memory bank and provide the needed symmetrizing and antisymmetrizing operators. Finally, we provide formulae in terms of these operators for unitary evolution under conventional two- and four-body Hamiltonian terms, as well as terms varying the particle number. In this formalism, the number of qubits needed to codify $n$ particles with $N_p$ modes each is of order $n\log_2 N_p$. Such scaling is more efficient than the Jordan-Wigner transformation which requires $O(N_p)$ qubits, whenever there are a modest number of particles with a large number of states available to each (and less advantageous for a large number of particles with few states available to each). And although less efficient, it is also less cumbersome than compact encoding. |
| title | A dynamical implementation of canonical second quantization on a quantum computer |
| topic | High Energy Physics - Theory Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2406.03147 |