Entanglement Transitions in Unitary Circuit Games
Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-01-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.5.010309 |
| _version_ | 1797347516153331712 |
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| author | Raúl Morral-Yepes Adam Smith S.L. Sondhi Frank Pollmann |
| author_facet | Raúl Morral-Yepes Adam Smith S.L. Sondhi Frank Pollmann |
| author_sort | Raúl Morral-Yepes |
| collection | DOAJ |
| description | Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: the “entangler” applies a random local unitary gate with the aim of generating extensive (volume-law) entanglement. The “disentangler,” based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area-law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general U(4) unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate, which have similar properties that can be understood through a connection to the stochastic Fredkin chain. In contrast, the entangler always wins when using Haar random unitary gates and we observe extensive, volume-law entanglement for all nonzero rates of entangling. |
| first_indexed | 2024-03-08T11:48:54Z |
| format | Article |
| id | doaj.art-eabd4dc059914325937c2e5fe665e437 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-08T11:48:54Z |
| publishDate | 2024-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-eabd4dc059914325937c2e5fe665e4372024-01-24T15:06:13ZengAmerican Physical SocietyPRX Quantum2691-33992024-01-015101030910.1103/PRXQuantum.5.010309Entanglement Transitions in Unitary Circuit GamesRaúl Morral-YepesAdam SmithS.L. SondhiFrank PollmannRepeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: the “entangler” applies a random local unitary gate with the aim of generating extensive (volume-law) entanglement. The “disentangler,” based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area-law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general U(4) unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate, which have similar properties that can be understood through a connection to the stochastic Fredkin chain. In contrast, the entangler always wins when using Haar random unitary gates and we observe extensive, volume-law entanglement for all nonzero rates of entangling.http://doi.org/10.1103/PRXQuantum.5.010309 |
| spellingShingle | Raúl Morral-Yepes Adam Smith S.L. Sondhi Frank Pollmann Entanglement Transitions in Unitary Circuit Games PRX Quantum |
| title | Entanglement Transitions in Unitary Circuit Games |
| title_full | Entanglement Transitions in Unitary Circuit Games |
| title_fullStr | Entanglement Transitions in Unitary Circuit Games |
| title_full_unstemmed | Entanglement Transitions in Unitary Circuit Games |
| title_short | Entanglement Transitions in Unitary Circuit Games |
| title_sort | entanglement transitions in unitary circuit games |
| url | http://doi.org/10.1103/PRXQuantum.5.010309 |
| work_keys_str_mv | AT raulmorralyepes entanglementtransitionsinunitarycircuitgames AT adamsmith entanglementtransitionsinunitarycircuitgames AT slsondhi entanglementtransitionsinunitarycircuitgames AT frankpollmann entanglementtransitionsinunitarycircuitgames |