Extending the Variational Quantum Eigensolver to Finite Temperatures
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866914822202851328 |
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| author | Selisko, Johannes Amsler, Maximilian Hammerschmidt, Thomas Drautz, Ralf Eckl, Thomas |
| author_facet | Selisko, Johannes Amsler, Maximilian Hammerschmidt, Thomas Drautz, Ralf Eckl, Thomas |
| contents | We present a variational quantum thermalizer (VQT), called quantum-VQT (qVQT), which extends the variational quantum eigensolver (VQE) to finite temperatures. The qVQT makes use of an intermediate measurement between two variational circuits to encode a density matrix on a quantum device. A classical optimization provides the thermal state and, simultaneously, all associated excited states of a quantum mechanical system. We demonstrate the capabilities of the qVQT for two different spin systems. First, we analyze the performance of qVQT as a function of the circuit depth and the temperature for a 1-dimensional Heisenberg chain. Second, we use the excited states to map the complete, temperature dependent phase diagram of a 2-dimensional J1-J2 Heisenberg model. The numerical experiments demonstrate the efficiency of our approach, which can be readily applied to study various quantum many-body systems at finite temperatures on currently available NISQ devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_07621 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extending the Variational Quantum Eigensolver to Finite Temperatures Selisko, Johannes Amsler, Maximilian Hammerschmidt, Thomas Drautz, Ralf Eckl, Thomas Quantum Physics Strongly Correlated Electrons We present a variational quantum thermalizer (VQT), called quantum-VQT (qVQT), which extends the variational quantum eigensolver (VQE) to finite temperatures. The qVQT makes use of an intermediate measurement between two variational circuits to encode a density matrix on a quantum device. A classical optimization provides the thermal state and, simultaneously, all associated excited states of a quantum mechanical system. We demonstrate the capabilities of the qVQT for two different spin systems. First, we analyze the performance of qVQT as a function of the circuit depth and the temperature for a 1-dimensional Heisenberg chain. Second, we use the excited states to map the complete, temperature dependent phase diagram of a 2-dimensional J1-J2 Heisenberg model. The numerical experiments demonstrate the efficiency of our approach, which can be readily applied to study various quantum many-body systems at finite temperatures on currently available NISQ devices. |
| title | Extending the Variational Quantum Eigensolver to Finite Temperatures |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2208.07621 |