Quantum complexity phase transitions in monitored random circuits
Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a property of a state of $n$ qubits, such as its entanglement...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-02-10-1627/pdf/ |
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| author | Ryotaro Suzuki Jonas Haferkamp Jens Eisert Philippe Faist |
| author_facet | Ryotaro Suzuki Jonas Haferkamp Jens Eisert Philippe Faist |
| author_sort | Ryotaro Suzuki |
| collection | DOAJ |
| description | Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a property of a state of $n$ qubits, such as its entanglement entropy, depending on the rate at which individual qubits are measured. At the same time, quantum complexity emerged as a key quantity for the identification of complex behaviour in quantum many-body dynamics. In this work, we investigate the dynamics of the quantum state complexity in monitored random circuits, where $n$ qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We find that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows at least linearly in time until saturating to a value $e^{\Omega(n)}$. Above, the complexity does not exceed $\operatorname{poly}(n)$. In our proof, we make use of percolation theory to find paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. We lower bound the exact state complexity in the former regime using recently developed techniques from algebraic geometry. Our results combine quantum complexity growth, phase transitions, and computation with measurements to help understand the behavior of monitored random circuits and to make progress towards determining the computational power of measurements in many-body systems. |
| format | Article |
| id | doaj-art-55fd4c53a7be43efbe194cc1470cb2e5 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-55fd4c53a7be43efbe194cc1470cb2e52025-02-10T15:25:12ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-02-019162710.22331/q-2025-02-10-162710.22331/q-2025-02-10-1627Quantum complexity phase transitions in monitored random circuitsRyotaro SuzukiJonas HaferkampJens EisertPhilippe FaistRecently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. The latter refers to a sudden change in a property of a state of $n$ qubits, such as its entanglement entropy, depending on the rate at which individual qubits are measured. At the same time, quantum complexity emerged as a key quantity for the identification of complex behaviour in quantum many-body dynamics. In this work, we investigate the dynamics of the quantum state complexity in monitored random circuits, where $n$ qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We find that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows at least linearly in time until saturating to a value $e^{\Omega(n)}$. Above, the complexity does not exceed $\operatorname{poly}(n)$. In our proof, we make use of percolation theory to find paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. We lower bound the exact state complexity in the former regime using recently developed techniques from algebraic geometry. Our results combine quantum complexity growth, phase transitions, and computation with measurements to help understand the behavior of monitored random circuits and to make progress towards determining the computational power of measurements in many-body systems.https://quantum-journal.org/papers/q-2025-02-10-1627/pdf/ |
| spellingShingle | Ryotaro Suzuki Jonas Haferkamp Jens Eisert Philippe Faist Quantum complexity phase transitions in monitored random circuits Quantum |
| title | Quantum complexity phase transitions in monitored random circuits |
| title_full | Quantum complexity phase transitions in monitored random circuits |
| title_fullStr | Quantum complexity phase transitions in monitored random circuits |
| title_full_unstemmed | Quantum complexity phase transitions in monitored random circuits |
| title_short | Quantum complexity phase transitions in monitored random circuits |
| title_sort | quantum complexity phase transitions in monitored random circuits |
| url | https://quantum-journal.org/papers/q-2025-02-10-1627/pdf/ |
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