Variational Time Evolution Compression for Solving Impurity Models on Quantum Hardware
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914423631773696 |
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| author | Wolf, Stefan Eckstein, Martin Hartmann, Michael J. |
| author_facet | Wolf, Stefan Eckstein, Martin Hartmann, Michael J. |
| contents | Dynamical mean-field theory (DMFT) is a useful tool to analyze models of strongly correlated fermions like the Hubbard model. In DMFT, the lattice of the model is replaced by a single impurity site embedded in an effective bath. The resulting single impurity Anderson model (SIAM) can then be solved self-consistently with a quantum-classical hybrid algorithm. This procedure involves repeatedly preparing the ground state on a quantum computer and evolving it in time to measure the Greens function. We here develop an approximation of the time evolution operator for this setting by training a Hamiltonian variational ansatz. The parameters of the ansatz are obtained via a variational quantum algorithm that utilizes a small number of time steps, given by the Suzuki-Trotter expansion of the time evolution operator, to guide the evolution of the parameters. The resulting circuit has a fixed depth for the time evolution depending on the size of the bath and is significantly shallower than a comparable Suzuki-Trotter expansion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Time Evolution Compression for Solving Impurity Models on Quantum Hardware Wolf, Stefan Eckstein, Martin Hartmann, Michael J. Quantum Physics Strongly Correlated Electrons Dynamical mean-field theory (DMFT) is a useful tool to analyze models of strongly correlated fermions like the Hubbard model. In DMFT, the lattice of the model is replaced by a single impurity site embedded in an effective bath. The resulting single impurity Anderson model (SIAM) can then be solved self-consistently with a quantum-classical hybrid algorithm. This procedure involves repeatedly preparing the ground state on a quantum computer and evolving it in time to measure the Greens function. We here develop an approximation of the time evolution operator for this setting by training a Hamiltonian variational ansatz. The parameters of the ansatz are obtained via a variational quantum algorithm that utilizes a small number of time steps, given by the Suzuki-Trotter expansion of the time evolution operator, to guide the evolution of the parameters. The resulting circuit has a fixed depth for the time evolution depending on the size of the bath and is significantly shallower than a comparable Suzuki-Trotter expansion. |
| title | Variational Time Evolution Compression for Solving Impurity Models on Quantum Hardware |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.10526 |