Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots
Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a line...
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MDPI AG
2024-12-01
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| author | James R. Hamilton Raphael D. Levine Francoise Remacle |
| author_facet | James R. Hamilton Raphael D. Levine Francoise Remacle |
| author_sort | James R. Hamilton |
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| description | Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients. There are possible applications to the dynamics of systems of coupled coherent two-state systems, such as qubits, pumped by optical excitation and other addressing inputs. Thereby, the interaction of the system with the excitation is bilinear in the coherence between the two states and in the strength of the time-dependent excitation. The total Hamiltonian is a sum of such bilinear terms and of terms linear in the populations. The terms in the Hamiltonian form a basis for Lie algebra, which can be represented as coupled individual two-state systems, each using the population and the coherence between two states. Using the factorization approach of Wei and Norman, we construct a unitary quantum mechanical evolution operator that is a factored contribution of individual two-state systems. By that one can accurately propagate both the wave function and the density matrix with special relevance to quantum computing based on qubit architecture. Explicit examples are derived for the electronic dynamics in coupled semi-conducting nanoparticles that can be used as hardware for quantum technologies. |
| format | Article |
| id | doaj-art-afefb90ed0f6445b92cfac825452d8ef |
| institution | Kabale University |
| issn | 2079-4991 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Nanomaterials |
| spelling | doaj-art-afefb90ed0f6445b92cfac825452d8ef2024-12-27T14:43:37ZengMDPI AGNanomaterials2079-49912024-12-011424205610.3390/nano14242056Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum DotsJames R. Hamilton0Raphael D. Levine1Francoise Remacle2Theoretical Physical Chemistry, UR MOLSYS, University of Liege, B4000 Liège, BelgiumInstitute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, IsraelTheoretical Physical Chemistry, UR MOLSYS, University of Liege, B4000 Liège, BelgiumDynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients. There are possible applications to the dynamics of systems of coupled coherent two-state systems, such as qubits, pumped by optical excitation and other addressing inputs. Thereby, the interaction of the system with the excitation is bilinear in the coherence between the two states and in the strength of the time-dependent excitation. The total Hamiltonian is a sum of such bilinear terms and of terms linear in the populations. The terms in the Hamiltonian form a basis for Lie algebra, which can be represented as coupled individual two-state systems, each using the population and the coherence between two states. Using the factorization approach of Wei and Norman, we construct a unitary quantum mechanical evolution operator that is a factored contribution of individual two-state systems. By that one can accurately propagate both the wave function and the density matrix with special relevance to quantum computing based on qubit architecture. Explicit examples are derived for the electronic dynamics in coupled semi-conducting nanoparticles that can be used as hardware for quantum technologies.https://www.mdpi.com/2079-4991/14/24/2056Lie algebracoherent quantum dynamicscomputing by observablesCdSe nanoparticle dimers |
| spellingShingle | James R. Hamilton Raphael D. Levine Francoise Remacle Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots Nanomaterials Lie algebra coherent quantum dynamics computing by observables CdSe nanoparticle dimers |
| title | Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots |
| title_full | Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots |
| title_fullStr | Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots |
| title_full_unstemmed | Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots |
| title_short | Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots |
| title_sort | constructing dynamical symmetries for quantum computing applications to coherent dynamics in coupled quantum dots |
| topic | Lie algebra coherent quantum dynamics computing by observables CdSe nanoparticle dimers |
| url | https://www.mdpi.com/2079-4991/14/24/2056 |
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