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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.19187 |
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| _version_ | 1866917510030295040 |
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| author | Jemcov, Aleksandar Morris, Scott C. |
| author_facet | Jemcov, Aleksandar Morris, Scott C. |
| contents | The Koopman--von Neumann (KvN) formulation of spectrally truncated fluid and plasma dynamics is considered as a potential approach for quantum computation. The KvN framework embeds the Liouville equation into a Hilbert space with norm-preserving, unitary evolution. Here, we propose a Weyl-ordered KvN generator along with a summation-by-parts discretization, which ensures that the resulting operators are exactly unitary as required for quantum computers. The Weyl-ordered KvN generator is derived as the unique anti-Hermitian operator symmetrization for real velocity fields. The formulation operates directly in the physical amplitude space without phase-space doubling, so the Heisenberg uncertainty principle does not constrain the grid resolution during evolution. This limitation re-enters only at the measurement stage on a quantum computer. Exact discrete unitarity is proved as a purely algebraic identity that holds regardless of grid resolution or stencil order. To manage boundaries, a split-step Kraus absorbing layer is introduced via a Stinespring dilation requiring only one ancilla qubit. Validation on three test cases spanning dissipative and Hamiltonian regimes (a viscous Navier--Stokes triad, an incompressible Euler triad, and a Hasegawa--Mima drift-wave triad) confirms fourth-order convergence and machine-precision unitarity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics Jemcov, Aleksandar Morris, Scott C. Fluid Dynamics Quantum Physics The Koopman--von Neumann (KvN) formulation of spectrally truncated fluid and plasma dynamics is considered as a potential approach for quantum computation. The KvN framework embeds the Liouville equation into a Hilbert space with norm-preserving, unitary evolution. Here, we propose a Weyl-ordered KvN generator along with a summation-by-parts discretization, which ensures that the resulting operators are exactly unitary as required for quantum computers. The Weyl-ordered KvN generator is derived as the unique anti-Hermitian operator symmetrization for real velocity fields. The formulation operates directly in the physical amplitude space without phase-space doubling, so the Heisenberg uncertainty principle does not constrain the grid resolution during evolution. This limitation re-enters only at the measurement stage on a quantum computer. Exact discrete unitarity is proved as a purely algebraic identity that holds regardless of grid resolution or stencil order. To manage boundaries, a split-step Kraus absorbing layer is introduced via a Stinespring dilation requiring only one ancilla qubit. Validation on three test cases spanning dissipative and Hamiltonian regimes (a viscous Navier--Stokes triad, an incompressible Euler triad, and a Hasegawa--Mima drift-wave triad) confirms fourth-order convergence and machine-precision unitarity. |
| title | Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics |
| topic | Fluid Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2605.19187 |