Solving Quantum Dynamics with a Lie-Algebra Decoupling Method
Quantum technologies rely on the control of quantum systems at the level of individual quanta. Mathematically, this control is described by Hamiltonian or Liouvillian evolution, requiring the application of various techniques to solve the resulting dynamic equations. Here, we present a tutorial for...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.6.010201 |
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| author | Sofia Qvarfort Igor Pikovski |
| author_facet | Sofia Qvarfort Igor Pikovski |
| author_sort | Sofia Qvarfort |
| collection | DOAJ |
| description | Quantum technologies rely on the control of quantum systems at the level of individual quanta. Mathematically, this control is described by Hamiltonian or Liouvillian evolution, requiring the application of various techniques to solve the resulting dynamic equations. Here, we present a tutorial for how the quantum dynamics of systems can be solved using a Lie-algebra decoupling method. The approach involves identifying a Lie algebra that governs the dynamics of the system, enabling the derivation of differential equations to solve the Schrödinger equation. As background, we include an overview of Lie groups and Lie algebras aimed at a general-physicist audience. We then prove the Lie-algebra decoupling theorem and apply it to both closed and open dynamics. The results represent a broad methodology to find the dynamics of quantum systems with applications across many fields of modern quantum research. |
| format | Article |
| id | doaj-art-f59341b2dbb340aebec2ade8bb46d09e |
| institution | Kabale University |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-f59341b2dbb340aebec2ade8bb46d09e2025-01-27T15:04:49ZengAmerican Physical SocietyPRX Quantum2691-33992025-01-016101020110.1103/PRXQuantum.6.010201Solving Quantum Dynamics with a Lie-Algebra Decoupling MethodSofia QvarfortIgor PikovskiQuantum technologies rely on the control of quantum systems at the level of individual quanta. Mathematically, this control is described by Hamiltonian or Liouvillian evolution, requiring the application of various techniques to solve the resulting dynamic equations. Here, we present a tutorial for how the quantum dynamics of systems can be solved using a Lie-algebra decoupling method. The approach involves identifying a Lie algebra that governs the dynamics of the system, enabling the derivation of differential equations to solve the Schrödinger equation. As background, we include an overview of Lie groups and Lie algebras aimed at a general-physicist audience. We then prove the Lie-algebra decoupling theorem and apply it to both closed and open dynamics. The results represent a broad methodology to find the dynamics of quantum systems with applications across many fields of modern quantum research.http://doi.org/10.1103/PRXQuantum.6.010201 |
| spellingShingle | Sofia Qvarfort Igor Pikovski Solving Quantum Dynamics with a Lie-Algebra Decoupling Method PRX Quantum |
| title | Solving Quantum Dynamics with a Lie-Algebra Decoupling Method |
| title_full | Solving Quantum Dynamics with a Lie-Algebra Decoupling Method |
| title_fullStr | Solving Quantum Dynamics with a Lie-Algebra Decoupling Method |
| title_full_unstemmed | Solving Quantum Dynamics with a Lie-Algebra Decoupling Method |
| title_short | Solving Quantum Dynamics with a Lie-Algebra Decoupling Method |
| title_sort | solving quantum dynamics with a lie algebra decoupling method |
| url | http://doi.org/10.1103/PRXQuantum.6.010201 |
| work_keys_str_mv | AT sofiaqvarfort solvingquantumdynamicswithaliealgebradecouplingmethod AT igorpikovski solvingquantumdynamicswithaliealgebradecouplingmethod |