Random-Matrix Models of Monitored Quantum Circuits
We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born proba...
| Autori principali: | , , |
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| Natura: | Journal article |
| Lingua: | English |
| Pubblicazione: |
Springer
2024
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| _version_ | 1826313081719881728 |
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| author | Bulchandani, VB Sondhi, SL Chalker, JT |
| author_facet | Bulchandani, VB Sondhi, SL Chalker, JT |
| author_sort | Bulchandani, VB |
| collection | OXFORD |
| description | We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally. |
| first_indexed | 2024-09-25T04:07:16Z |
| format | Journal article |
| id | oxford-uuid:8862b16f-92a2-4073-b1cb-1d0dd15bddbb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:07:16Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:8862b16f-92a2-4073-b1cb-1d0dd15bddbb2024-06-01T20:11:54ZRandom-Matrix Models of Monitored Quantum CircuitsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8862b16f-92a2-4073-b1cb-1d0dd15bddbbEnglishJisc Publications RouterSpringer2024Bulchandani, VBSondhi, SLChalker, JTWe study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally. |
| spellingShingle | Bulchandani, VB Sondhi, SL Chalker, JT Random-Matrix Models of Monitored Quantum Circuits |
| title | Random-Matrix Models of Monitored Quantum Circuits |
| title_full | Random-Matrix Models of Monitored Quantum Circuits |
| title_fullStr | Random-Matrix Models of Monitored Quantum Circuits |
| title_full_unstemmed | Random-Matrix Models of Monitored Quantum Circuits |
| title_short | Random-Matrix Models of Monitored Quantum Circuits |
| title_sort | random matrix models of monitored quantum circuits |
| work_keys_str_mv | AT bulchandanivb randommatrixmodelsofmonitoredquantumcircuits AT sondhisl randommatrixmodelsofmonitoredquantumcircuits AT chalkerjt randommatrixmodelsofmonitoredquantumcircuits |