Thermal State Preparation via Rounding Promises
A promising avenue for the preparation of Gibbs states on a quantum computer is to simulate the physical thermalization process. The Davies generator describes the dynamics of an open quantum system that is in contact with a heat bath. Crucially, it does not require simulation of the heat bath itsel...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-10-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-10-10-1132/pdf/ |
| _version_ | 1797662266133315584 |
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| author | Patrick Rall Chunhao Wang Pawel Wocjan |
| author_facet | Patrick Rall Chunhao Wang Pawel Wocjan |
| author_sort | Patrick Rall |
| collection | DOAJ |
| description | A promising avenue for the preparation of Gibbs states on a quantum computer is to simulate the physical thermalization process. The Davies generator describes the dynamics of an open quantum system that is in contact with a heat bath. Crucially, it does not require simulation of the heat bath itself, only the system we hope to thermalize. Using the state-of-the-art techniques for quantum simulation of the Lindblad equation, we devise a technique for the preparation of Gibbs states via thermalization as specified by the Davies generator.
In doing so, we encounter a severe technical challenge: implementation of the Davies generator demands the ability to estimate the energy of the system unambiguously. That is, each energy of the system must be deterministically mapped to a unique estimate. Previous work showed that this is only possible if the system satisfies an unphysical 'rounding promise' assumption. We solve this problem by engineering a random ensemble of rounding promises that simultaneously solves three problems: First, each rounding promise admits preparation of a 'promised' thermal state via a Davies generator. Second, these Davies generators have a similar mixing time as the ideal Davies generator. Third, the average of these promised thermal states approximates the ideal thermal state. |
| first_indexed | 2024-03-11T18:57:41Z |
| format | Article |
| id | doaj.art-8684662a4b644eeaa835bdfafcc55161 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-11T18:57:41Z |
| publishDate | 2023-10-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-8684662a4b644eeaa835bdfafcc551612023-10-10T15:39:06ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-10-017113210.22331/q-2023-10-10-113210.22331/q-2023-10-10-1132Thermal State Preparation via Rounding PromisesPatrick RallChunhao WangPawel WocjanA promising avenue for the preparation of Gibbs states on a quantum computer is to simulate the physical thermalization process. The Davies generator describes the dynamics of an open quantum system that is in contact with a heat bath. Crucially, it does not require simulation of the heat bath itself, only the system we hope to thermalize. Using the state-of-the-art techniques for quantum simulation of the Lindblad equation, we devise a technique for the preparation of Gibbs states via thermalization as specified by the Davies generator. In doing so, we encounter a severe technical challenge: implementation of the Davies generator demands the ability to estimate the energy of the system unambiguously. That is, each energy of the system must be deterministically mapped to a unique estimate. Previous work showed that this is only possible if the system satisfies an unphysical 'rounding promise' assumption. We solve this problem by engineering a random ensemble of rounding promises that simultaneously solves three problems: First, each rounding promise admits preparation of a 'promised' thermal state via a Davies generator. Second, these Davies generators have a similar mixing time as the ideal Davies generator. Third, the average of these promised thermal states approximates the ideal thermal state.https://quantum-journal.org/papers/q-2023-10-10-1132/pdf/ |
| spellingShingle | Patrick Rall Chunhao Wang Pawel Wocjan Thermal State Preparation via Rounding Promises Quantum |
| title | Thermal State Preparation via Rounding Promises |
| title_full | Thermal State Preparation via Rounding Promises |
| title_fullStr | Thermal State Preparation via Rounding Promises |
| title_full_unstemmed | Thermal State Preparation via Rounding Promises |
| title_short | Thermal State Preparation via Rounding Promises |
| title_sort | thermal state preparation via rounding promises |
| url | https://quantum-journal.org/papers/q-2023-10-10-1132/pdf/ |
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