Entanglement Criticality in Random Gaussian Quantum Circuits

Po-Yao Chang, Xiao Chen, Sarang Gopalakrishnan +1 more

Chao‐Ming Jian, Bela Bauer, Anna Keselman +1 more

Entanglement dynamics in nonunitary quantum systems have been found to exhibit novel nonequilibrium quantum phase transitions and have attracted tremendous attention with connections to various aspects of quantum information theory. This work establishes, for systems of noninteracting fermions, an exact three-way correspondence between (i) nonunitary (as well as unitary) quantum circuits dynamics in $d$ spatial dimensions; (ii) ($d$+1)-dimensional Gaussian tensor networks, and (iii) fermion systems in ($d$+1) spatial dimensions subject to unitary evolution with static Hamiltonians. Through this correspondence, $d$-dimensional random quantum circuits are connected with the classic subject area of Anderson localization in ($d$+1) spatial dimensions and consequently follow the ``tenfold way'' Altland-Zirnbauer classification. Selected examples of quantum circuits exhibiting entanglement phases and criticalities are used to illustrate these general principles.

Jincheng Zhang

Reservoir computing (RC) has demonstrated significant promise in time series forecasting, particularly for chaotic systems. However, a critical limitation of traditional RC approaches is their vulnerability to non-Gaussian noise, a common characteristic of real-world time series data. This paper proposes a novel framework, Quantum Reservoir Computing (QRC), designed to address this challenge. QRC utilizes a quantum reservoir – a randomly initialized quantum circuit – to leverage the inherent noise robustness of quantum mechanics, specifically quantum entanglement and superposition. The quantum reservoir is coupled with a variational quantum circuit for output mapping. We demonstrate that this approach significantly improves forecasting accuracy when dealing with non-Gaussian noise, offering a pathway to more reliable RC implementations. The core claim of this work is that reservoir computing struggles with non-Gaussian noise, which is prevalent in many time series datasets. The core mechanism involves extending reservoir computing using a quantum reservoir – a randomly initialized quantum circuit – that is inherently robust to non-Gaussian noise due to quantum entanglement and superposition, combined with a variational quantum circuit for output mapping. The methodology incorporates a mapping function to translate quantum states into time series predictions, and the variational quantum circuit is trained to minimize the error between predicted and actual time series values. We explore the theoretical underpinnings of this method and discuss its potential for various time series forecasting applications.

Mario Collura, Benjamin Béri, Emanuele Tirrito

Nonlocal magic quantifies the irreducible nonstabilizerness of a bipartite quantum state after optimizing over local basis changes. We study nonlocal magic for pure fermionic Gaussian states, and derive a simple closed-form entanglement spectrum bound in terms of the singular values of the subsystem-restricted covariance matrix. We benchmark our result against simulated annealing over local Gaussian unitary transformations, which supports optimality along the full local Gaussian orbit. For states drawn from the Gaussian Haar ensemble, we show that the average nonlocal magic is extensive and determine its thermodynamic limit using random matrix theory for the appropriate circular unitary ensemble. We also study Gaussian ground states, focusing on the Kitaev chain, and find that nonlocal magic is suppressed deep in both trivial and topological phases and peaks near the critical points. Finally, we investigate Gaussian evolution via random circuits and in quenches with the XY chain. For random circuits, we find that nonlocal magic grows diffusively, while in the XY chain the XX limit reveals a striking separation between nonlocal magic and entanglement.

Salvatore F. E. Oliviero, Lorenzo Leone, Alioscia Hamma

Bastien Lapierre, Mo, Liang-Hong, Shinsei Ryu

We study measurement-induced phase transitions in quantum circuits consisting of kicked Ising models with postselected weak measurements, whose dynamics can be mapped onto a classical dynamical system. For a periodic (Floquet) non-unitary evolution, such circuits are exactly tractable and admit volume-to-area law transitions. We show that breaking time-translation symmetry down to a quasiperiodic (Fibonacci) time evolution leads to the emergence of a critical phase with tunable effective central charge and with a fractal origin. Furthermore, for some classes of random non-unitary circuits, we demonstrate the robustness of the volume-to-area law phase transition for arbitrary random realizations, thanks to the emergent compactness of the classical map encoding the circuit's dynamics.