Coherence-Limited Quantum Speed Limit Unifying Margolus–Levitin and Lloyd Bounds
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2025
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| _version_ | 1866902190706130944 |
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| author | Arrabal, humberto |
| author_facet | Arrabal, humberto |
| contents | <p>This work clarifies the relationship between two foundational principles in quantum<br>information theory: the Margolus-Levitin (M-L) theorem on the maximum speed<br>of state evolution and the Lloyd limit on computational rate. We demonstrate that<br>the energy E in these bounds refers to the quantum transition energy of the<br>system, not its bulk kinetic energy. By imposing the physical constraint that any<br>quantum operation must be completed within the system’s coherence time (τc), we<br>derive a minimum energy threshold, Emin = πℏ/(2τc), required to achieve a single<br>observable state change (an orthogonalization). Applying this minimum energy to<br>the Lloyd limit correctly shows that the maximum operational rate is 1/τc, meaning<br>exactly one operation is possible within the coherence window at this energy floor.<br>This reframes the limits not as a function of motion, but as a direct trade-off<br>between the system’s coherence and the energy required for computation, offering<br>a physically grounded perspective for designing quantum processors.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16867468 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Coherence-Limited Quantum Speed Limit Unifying Margolus–Levitin and Lloyd Bounds Arrabal, humberto margolus-levitin Lloyd limit quantum information theory minimum energy quantum operation quantum computation orthogonalization humberto arrabal coherence time the speed of the quantum microprocessor microprocessor quantum computing <p>This work clarifies the relationship between two foundational principles in quantum<br>information theory: the Margolus-Levitin (M-L) theorem on the maximum speed<br>of state evolution and the Lloyd limit on computational rate. We demonstrate that<br>the energy E in these bounds refers to the quantum transition energy of the<br>system, not its bulk kinetic energy. By imposing the physical constraint that any<br>quantum operation must be completed within the system’s coherence time (τc), we<br>derive a minimum energy threshold, Emin = πℏ/(2τc), required to achieve a single<br>observable state change (an orthogonalization). Applying this minimum energy to<br>the Lloyd limit correctly shows that the maximum operational rate is 1/τc, meaning<br>exactly one operation is possible within the coherence window at this energy floor.<br>This reframes the limits not as a function of motion, but as a direct trade-off<br>between the system’s coherence and the energy required for computation, offering<br>a physically grounded perspective for designing quantum processors.</p> |
| title | Coherence-Limited Quantum Speed Limit Unifying Margolus–Levitin and Lloyd Bounds |
| topic | margolus-levitin Lloyd limit quantum information theory minimum energy quantum operation quantum computation orthogonalization humberto arrabal coherence time the speed of the quantum microprocessor microprocessor quantum computing |
| url | https://doi.org/10.5281/zenodo.16867468 |