Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917873808572416 |
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| author | Yosifov, Alexander Iyer, Aditya Ebler, Daniel Vedral, Vlatko |
| author_facet | Yosifov, Alexander Iyer, Aditya Ebler, Daniel Vedral, Vlatko |
| contents | Quantum homogenization is a reservoir-based quantum state approximation protocol, which has been successfully implemented in state transformation on quantum hardware. In this work we move beyond that and propose the homogenization as a novel platform for quantum state stabilization and information protection. Using the Heisenberg exchange interactions formalism, we extend the standard quantum homogenization protocol to the dynamically-equivalent ($\mathtt{SWAP}$)$^α$ formulation. We then demonstrate its applicability on available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of $\mathtt{CNOT}$ and single-qubit gates. In light of this, we employ the Beny-Oreshkov generalization of the Knill-Laflamme (KL) conditions for near-optimal recovery channels to show that our proposed ($\mathtt{SWAP}$)$^α$ quantum homogenization protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable. Therefore, the protocol protects quantum information contained in a subsystem of the reservoir Hilbert space under CPTP dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware Yosifov, Alexander Iyer, Aditya Ebler, Daniel Vedral, Vlatko Quantum Physics Quantum homogenization is a reservoir-based quantum state approximation protocol, which has been successfully implemented in state transformation on quantum hardware. In this work we move beyond that and propose the homogenization as a novel platform for quantum state stabilization and information protection. Using the Heisenberg exchange interactions formalism, we extend the standard quantum homogenization protocol to the dynamically-equivalent ($\mathtt{SWAP}$)$^α$ formulation. We then demonstrate its applicability on available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of $\mathtt{CNOT}$ and single-qubit gates. In light of this, we employ the Beny-Oreshkov generalization of the Knill-Laflamme (KL) conditions for near-optimal recovery channels to show that our proposed ($\mathtt{SWAP}$)$^α$ quantum homogenization protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable. Therefore, the protocol protects quantum information contained in a subsystem of the reservoir Hilbert space under CPTP dynamics. |
| title | Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.14544 |