First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States
We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measur...
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MDPI AG
2024-10-01
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| Series: | Entropy |
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| author | Qingyuan Wang Silin Ren Ruoyu Yin Klaus Ziegler Eli Barkai Sabine Tornow |
| author_facet | Qingyuan Wang Silin Ren Ruoyu Yin Klaus Ziegler Eli Barkai Sabine Tornow |
| author_sort | Qingyuan Wang |
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| description | We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements. |
| format | Article |
| id | doaj-art-5b7e8768fe124997af19e413493c0549 |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-10-01 |
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| series | Entropy |
| spelling | doaj-art-5b7e8768fe124997af19e413493c05492025-08-20T02:11:09ZengMDPI AGEntropy1099-43002024-10-01261086910.3390/e26100869First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark StatesQingyuan Wang0Silin Ren1Ruoyu Yin2Klaus Ziegler3Eli Barkai4Sabine Tornow5Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, IsraelDepartment of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, IsraelDepartment of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, IsraelInstitut für Physik, Universität Augsburg, 86135 Augsburg, GermanyDepartment of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, IsraelResearch Institute CODE, University of the Bundeswehr Munich, 81739 Munich, GermanyWe investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements.https://www.mdpi.com/1099-4300/26/10/869quantum walkquantum computingdark and bright states |
| spellingShingle | Qingyuan Wang Silin Ren Ruoyu Yin Klaus Ziegler Eli Barkai Sabine Tornow First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States Entropy quantum walk quantum computing dark and bright states |
| title | First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States |
| title_full | First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States |
| title_fullStr | First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States |
| title_full_unstemmed | First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States |
| title_short | First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States |
| title_sort | first hitting times on a quantum computer tracking vs local monitoring topological effects and dark states |
| topic | quantum walk quantum computing dark and bright states |
| url | https://www.mdpi.com/1099-4300/26/10/869 |
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