Measurement-induced topological entanglement transitions in symmetric random quantum circuits

By A. Lavasani, Yahya Alavirad, Maissam Barkeshli. Nature Physics, 2020

278 citations recorded by the source corpus.

Random quantum circuits, in which an array of qubits is subjected to a series of randomly chosen unitary operations, have provided key insights into the dynamics of many-body quantum entanglement. Recent work has shown that interleaving the unitary operations with single-qubit measurements can drive a transition between high- and low-entanglement phases. Here we study a class of symmetric random quantum circuits with two competing types of measurement in addition to unitary dynamics. We find a rich phase diagram involving robust symmetry-protected topological, trivial and volume law entangled phases, where the transitions are hidden to expectation values of any operator and are only apparent by averaging the entanglement entropy over quantum trajectories. In the absence of unitary dynamics, we find a purely measurement-induced critical point, which maps exactly to two copies of a classical two-dimensional percolation problem. Numerical simulations indicate that this transition is a tricritical point that splits into two critical lines in the presence of arbitrarily sparse unitary dynamics with an intervening volume law entangled phase. Our results show that measurements alone are sufficient to induce criticality and logarithmic entanglement scaling, and arbitrarily sparse unitary dynamics can be sufficient to stabilize volume law entangled phases in the presence of rapid, yet competing, measurements. Repeatedly measuring an array of qubits can create topologically distinct phases depending on which measurements are applied. Lavasani et al. show that critical behaviour can arise from the competition between different choices of measurements.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3c0c26eb6a962137785721208add336030960bfd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. B. Skinner
5. J. Ruhman
6. Yaodong Li
7. S. Vijay
8. Sthitadhi Roy

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. Yaodong Li
5. B. Skinner
6. J. Ruhman
7. S. Vijay
8. S. Gopalakrishnan

Citations in the corpus

• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “An alternative profitable direction is to study circuits made from Clifford unitaries [7, 12, 15, 17, 22, 36–40].”
• Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, background): “Extensions of the paradigmatic random hybrid circuit model presently studied can harbor more intricate behavior, such as an interplay of topological and entanglement phase transitions [22, 27], that become accessible with ∼ 10(2) mid-circuit measurements and ∼ 0.”
• Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, background): “[31] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, “Measurement-induced topological entanglement transitions in symmetric random quantum circuits,” Nature Physics 17, 342–347 (2021), arXiv:2004.”
• Random Quantum Circuits (2022, background): “Monitored many-body systems have been the subject of much recent progress (58, 59, 60, 61, 62, 54, 55, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 57, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84).”
• Statistical mechanics of quantum error correcting codes (2020, background): “[68] Ali Lavasani, Yahya Alavirad, and Maissam Barkeshli, “Measurement-induced topological entanglement transitions in symmetric random quantum circuits,” arXiv e-prints , arXiv:2004.”