Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.13440 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910066892865536 |
|---|---|
| author | Xue, Yuan Cheng, Zihan Ippoliti, Matteo |
| author_facet | Xue, Yuan Cheng, Zihan Ippoliti, Matteo |
| contents | In the study of open quantum systems it is often useful to treat mixed states as pure states of a fictitious doubled system. In this work we explore the opposite approach: mapping isolated bilayer systems to open monolayer systems. Specifically, we show that arbitrary bilayer Hamiltonians possessing an antiunitary layer exchange symmetry, and subject to a constraint on the sign of interlayer couplings, can be mapped to Lindbladians on a monolayer system with some of the jump operators postselected on a fixed outcome ("monitored"). Low-energy states of the bilayer Hamiltonian then correspond to late-time states of the monolayer dynamics. Simulating the latter by quantum trajectory methods has the potential of substantially reducing the computational cost of estimating low-energy observables in the bilayer Hamiltonian by effectively halving the system size. The overhead due to sampling quantum trajectories can be controlled by a suitable importance sampling scheme. We show that, when the quantum trajectories exhibit free fermion dynamics, our approach reduces to the auxiliary field quantum Monte Carlo (AFQMC) method. This provides a physically transparent interpretation of the AFQMC sign-free criteria in terms of properties of quantum dynamics. Finally, we benchmark our approach on the 1D quantum Ashkin-Teller model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulation of bilayer Hamiltonians based on monitored quantum trajectories Xue, Yuan Cheng, Zihan Ippoliti, Matteo Quantum Physics Statistical Mechanics Strongly Correlated Electrons In the study of open quantum systems it is often useful to treat mixed states as pure states of a fictitious doubled system. In this work we explore the opposite approach: mapping isolated bilayer systems to open monolayer systems. Specifically, we show that arbitrary bilayer Hamiltonians possessing an antiunitary layer exchange symmetry, and subject to a constraint on the sign of interlayer couplings, can be mapped to Lindbladians on a monolayer system with some of the jump operators postselected on a fixed outcome ("monitored"). Low-energy states of the bilayer Hamiltonian then correspond to late-time states of the monolayer dynamics. Simulating the latter by quantum trajectory methods has the potential of substantially reducing the computational cost of estimating low-energy observables in the bilayer Hamiltonian by effectively halving the system size. The overhead due to sampling quantum trajectories can be controlled by a suitable importance sampling scheme. We show that, when the quantum trajectories exhibit free fermion dynamics, our approach reduces to the auxiliary field quantum Monte Carlo (AFQMC) method. This provides a physically transparent interpretation of the AFQMC sign-free criteria in terms of properties of quantum dynamics. Finally, we benchmark our approach on the 1D quantum Ashkin-Teller model. |
| title | Simulation of bilayer Hamiltonians based on monitored quantum trajectories |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2509.13440 |