Dynamical Purification Phase Transition Induced by Quantum Measurements

By Michael J. Gullans, D. Huse. Physical Review X, 2019

439 citations recorded by the source corpus.

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate, and (ii) a "mixed" phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace where quantum information can be reliably hidden from the measurements. We show that these codes are of potential relevance to fault-tolerant quantum computation as they satisfy optimal tradeoffs between encoded information densities and error thresholds. In spatially local models in 1 + 1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. We numerically explore this transition for random quantum circuits in 1+1 dimensions and all-to-all models. Unlike for pure initial states, the mutual information of an initially completely-mixed state grows at most logarithmically in time. The purification transition studied here naturally generalizes to systems with long-range interactions where conventional notions of entanglement transitions have to be reformulated. Purification dynamics may also be more robust in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of non-equilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.

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

View Paper: https://www.semanticscholar.org/paper/8707999fe236c12b7751ad1d83bdaa5cf1972b97

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. S. Vijay
6. D. Huse
7. J. Ruhman
8. Tianci Zhou

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. D. Huse
5. Tianci Zhou
6. B. Skinner
7. S. Vijay
8. J. Ruhman

Citations in the corpus

• Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, methodology): “In a recent work on a trapped-ion quantum computer, a purification phase transition, expected to occur concurrently with entanglement phase transitions [33, 37], was observed using Clifford circuits and deferred measurements [38].”
• Measurement-induced quantum criticality under continuous monitoring (2020, result): “[19] M.”
• Measurement-induced quantum phases realized in a trapped-ion quantum computer (2021, background): “5, 1) and L = (4, 6, 8), and observe the first experimental evidence of the phases of a dynamical purification phase transition.”
• Random Quantum Circuits (2022, methodology): “Numerical evidence for this transition has by now been found in a wide range of microscopic models (52, 53, 58, 68, 65, 66, 61, 62, 54, 63, 64, 77, 67).”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “In the many-body case this random dynamics admits a “measurement phase transition” (MPT) between two qualitatively different, stable dynamical phases, with distinct entanglement properties [6–27].”
• Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “[71] Michael J Gullans and David A Huse.”