Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems
The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dyna...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-02-04-1620/pdf/ |
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| _version_ | 1832540651372150784 |
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| author | Sara Santos Xinyu Song Vincenzo Savona |
| author_facet | Sara Santos Xinyu Song Vincenzo Savona |
| author_sort | Sara Santos |
| collection | DOAJ |
| description | The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational ansatze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device. |
| format | Article |
| id | doaj-art-2378736a985745cd8c092590955fe082 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-2378736a985745cd8c092590955fe0822025-02-04T16:32:24ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-02-019162010.22331/q-2025-02-04-162010.22331/q-2025-02-04-1620Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum SystemsSara SantosXinyu SongVincenzo SavonaThe simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational ansatze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device.https://quantum-journal.org/papers/q-2025-02-04-1620/pdf/ |
| spellingShingle | Sara Santos Xinyu Song Vincenzo Savona Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems Quantum |
| title | Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems |
| title_full | Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems |
| title_fullStr | Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems |
| title_full_unstemmed | Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems |
| title_short | Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems |
| title_sort | low rank variational quantum algorithm for the dynamics of open quantum systems |
| url | https://quantum-journal.org/papers/q-2025-02-04-1620/pdf/ |
| work_keys_str_mv | AT sarasantos lowrankvariationalquantumalgorithmforthedynamicsofopenquantumsystems AT xinyusong lowrankvariationalquantumalgorithmforthedynamicsofopenquantumsystems AT vincenzosavona lowrankvariationalquantumalgorithmforthedynamicsofopenquantumsystems |