Superstate Quantum Mechanics
Fuente:
arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915638465789952 |
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| author | Belov, Mikhail Gennadievich Dubov, Victor Victorovich Ivanov, Vadim Konstantinovich Maslov, Alexander Yurievich Proshina, Olga Vladimirovna Malyshkin, Vladislav Gennadievich |
| author_facet | Belov, Mikhail Gennadievich Dubov, Victor Victorovich Ivanov, Vadim Konstantinovich Maslov, Alexander Yurievich Proshina, Olga Vladimirovna Malyshkin, Vladislav Gennadievich |
| contents | We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum mechanics corresponds to a single quadratic constraint of wavefunction normalization with energy expressed as a quadratic form involving the Hamiltonian. When SQM represents states as unitary operators, the stationary problem becomes a quantum inverse problem with multiple applications in physics, machine learning, and artificial intelligence. Any stationary SQM problem is equivalent to a new algebraic problem that we address in this paper. The non-stationary SQM problem considers the evolution of the system itself, involving the same ``energy'' operator as in the stationary case. Two possible options for the SQM dynamic equation are considered: (1) within the framework of linear maps from higher-order quantum theory, where 2D-type quantum circuits transform one quantum system into another; and (2) in the form of a Gross-Pitaevskii-type nonlinear map. Although no known physical process currently describes such 2D dynamics, this approach naturally bridges direct and inverse quantum mechanics problems, allowing for the development of a new type of computer algorithms. As an immediately available practical application of the theory, we consider using a quantum channel as a classical computational model; this type of computation can be performed on a classical computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superstate Quantum Mechanics Belov, Mikhail Gennadievich Dubov, Victor Victorovich Ivanov, Vadim Konstantinovich Maslov, Alexander Yurievich Proshina, Olga Vladimirovna Malyshkin, Vladislav Gennadievich Quantum Physics Machine Learning We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum mechanics corresponds to a single quadratic constraint of wavefunction normalization with energy expressed as a quadratic form involving the Hamiltonian. When SQM represents states as unitary operators, the stationary problem becomes a quantum inverse problem with multiple applications in physics, machine learning, and artificial intelligence. Any stationary SQM problem is equivalent to a new algebraic problem that we address in this paper. The non-stationary SQM problem considers the evolution of the system itself, involving the same ``energy'' operator as in the stationary case. Two possible options for the SQM dynamic equation are considered: (1) within the framework of linear maps from higher-order quantum theory, where 2D-type quantum circuits transform one quantum system into another; and (2) in the form of a Gross-Pitaevskii-type nonlinear map. Although no known physical process currently describes such 2D dynamics, this approach naturally bridges direct and inverse quantum mechanics problems, allowing for the development of a new type of computer algorithms. As an immediately available practical application of the theory, we consider using a quantum channel as a classical computational model; this type of computation can be performed on a classical computer. |
| title | Superstate Quantum Mechanics |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2502.00037 |