Optimizing digital quantum simulation of open quantum lattice models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911140362059776 |
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| author | Yu, Xie-Hang Li, Hongchao Cirac, J. Ignacio Trivedi, Rahul |
| author_facet | Yu, Xie-Hang Li, Hongchao Cirac, J. Ignacio Trivedi, Rahul |
| contents | Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated. We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment. Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with $N$ spins and evolution time $t$, attain a simulation error $δ$ in the system-state with $\mathcal{O}(Nt(Nt/δ)^{o(1)})$ gates, $\mathcal{O}(t(Nt/δ)^{o(1)})$ parallelized circuit depth and $\tilde{\mathcal{O}}(N(Nt/δ)^{o(1)})$ ancillas. We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size $N$. This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices. Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively. These algorithms reduce the asymptotic gate complexity on $N$ compared to currently available algorithms in terms of the required number of geometrically local gates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing digital quantum simulation of open quantum lattice models Yu, Xie-Hang Li, Hongchao Cirac, J. Ignacio Trivedi, Rahul Quantum Physics Statistical Mechanics Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated. We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment. Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with $N$ spins and evolution time $t$, attain a simulation error $δ$ in the system-state with $\mathcal{O}(Nt(Nt/δ)^{o(1)})$ gates, $\mathcal{O}(t(Nt/δ)^{o(1)})$ parallelized circuit depth and $\tilde{\mathcal{O}}(N(Nt/δ)^{o(1)})$ ancillas. We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size $N$. This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices. Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively. These algorithms reduce the asymptotic gate complexity on $N$ compared to currently available algorithms in terms of the required number of geometrically local gates. |
| title | Optimizing digital quantum simulation of open quantum lattice models |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2509.02268 |