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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13078 |
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| _version_ | 1866911061428404224 |
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| author | Gonzalez, Mario Sim, Karin Chitra, R. |
| author_facet | Gonzalez, Mario Sim, Karin Chitra, R. |
| contents | Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism, provides a rigorous formulation of non-Hermitian quantum mechanics wherein norms and probabilities are conserved. The key feature is that the Hilbert space is endowed with a non-trivial dynamical metric. Beyond theoretical considerations, the physical implementation of the metric formalism remains unaddressed. In this work, we propose novel operator dilation schemes, which show that the self-consistent non-Hermitian quantum mechanics can be accessed in physical platforms via an embedding in closed Hermitian systems. Using digital quantum simulators, we present a proof of principle and the first experimental evidence for the dynamical metric engendered by non-Hermiticity in a qubit. Our work ushers in a new paradigm in the quantum simulation of non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emulation of Self-Consistent Non-Hermitian Quantum Formalisms Gonzalez, Mario Sim, Karin Chitra, R. Quantum Physics Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism, provides a rigorous formulation of non-Hermitian quantum mechanics wherein norms and probabilities are conserved. The key feature is that the Hilbert space is endowed with a non-trivial dynamical metric. Beyond theoretical considerations, the physical implementation of the metric formalism remains unaddressed. In this work, we propose novel operator dilation schemes, which show that the self-consistent non-Hermitian quantum mechanics can be accessed in physical platforms via an embedding in closed Hermitian systems. Using digital quantum simulators, we present a proof of principle and the first experimental evidence for the dynamical metric engendered by non-Hermiticity in a qubit. Our work ushers in a new paradigm in the quantum simulation of non-Hermitian systems. |
| title | Emulation of Self-Consistent Non-Hermitian Quantum Formalisms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.13078 |