Measurement-driven navigation in many-body Hilbert space: Active-decision steering
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866914690187132928 |
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| author | Herasymenko, Yaroslav Gornyi, Igor Gefen, Yuval |
| author_facet | Herasymenko, Yaroslav Gornyi, Igor Gefen, Yuval |
| contents | The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on-the-go. This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity. We show the potential of a significant speedup, employing this greedy approach to a broad family of Matrix Product State targets. For system sizes considered here, an average value of the speedup factor $f$ across this family settles about $20$, for some targets even reaching a few thousands. We also identify a subclass of Matrix Product State targets, for which the value of $f$ increases with system size. In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a Quantum State Machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This State Machine-based approach can be applied to a more restricted set of targets, sometimes offering advantages over the cost function-based method. We give an example of a W-state preparation which is accelerated with this method by $f\simeq3.5$, outperforming the greedy protocol for this target. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_09306 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Measurement-driven navigation in many-body Hilbert space: Active-decision steering Herasymenko, Yaroslav Gornyi, Igor Gefen, Yuval Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on-the-go. This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity. We show the potential of a significant speedup, employing this greedy approach to a broad family of Matrix Product State targets. For system sizes considered here, an average value of the speedup factor $f$ across this family settles about $20$, for some targets even reaching a few thousands. We also identify a subclass of Matrix Product State targets, for which the value of $f$ increases with system size. In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a Quantum State Machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This State Machine-based approach can be applied to a more restricted set of targets, sometimes offering advantages over the cost function-based method. We give an example of a W-state preparation which is accelerated with this method by $f\simeq3.5$, outperforming the greedy protocol for this target. |
| title | Measurement-driven navigation in many-body Hilbert space: Active-decision steering |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2111.09306 |