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Non-stabilizerness of Sachdev-Ye-Kitaev model

Surajit Bera, Marco Schirò

SciPost Phys. 19, 159 (2025) · published 18 December 2025 | · pdf

We study the non-stabilizerness or quantum magic of the Sachdev-Ye-Kitaev ($\mathrm{SYK}$) model, a prototype example of maximally chaotic quantum matter. We show that the Majorana spectrum of its ground state, encoding the spreading of the state in the Majorana basis, displays a Gaussian distribution as expected for chaotic quantum many-body systems. We compare our results with the case of the $\mathrm{SYK_2}$ model, describing non-chaotic random free fermions, and show that the Majorana spectrum is qualitatively different in the two cases, featuring an exponential Laplace distribution for the $\mathrm{SYK_2}$ model rather than a Gaussian. From the spectrum we extract the Stabilizer Renyi Entropy (SRE) and show that for both models it displays a linear scaling with system size, with a prefactor that is larger for the SYK model, which has therefore higher magic. Finally, we discuss the spreading of quantun magic under unitary dynamics, as described by the evolution of the Majorana spectrum and the Stabilizer Renyi Entropy starting from a stabilizer state. We show that the SRE for the $\mathrm{SYK_2}$ model equilibrates rapidly, but that in the steady-state the interacting chaotic SYK model has more magic than the simple $\mathrm{SYK_2}$. Our results suggest that the Majorana spectrum is qualitatively distinct in chaotic and non-chaotic many-body systems.
Quantifying the effects of noise in a quantum convolutional neural network

Zeyu Fan, Jonathan Wei Zhong Lau, Leong-Chuan Kwek

SciPost Phys. Core 8, 093 (2025) · published 18 December 2025 | · pdf

This study quantifies the effects of quantum noise on the performance of a quantum convolutional neural network (QCNN), building on parallels with classical convolutional neural networks (CNNs), where added Gaussian noise can improve training speed, accuracy, and generalizability. While such benefits are established for classical CNNs, the influence of noise on quantum counterparts remains insufficiently characterized. We specifically examine three types of quantum noise: decoherence, Gaussian noise arising from imperfect quantum gates and experimental error, and systematic noise introduced during input state preparation. Our analysis provides a detailed assessment of how these distinct noise sources affect QCNN operation and outlines considerations for mitigating their impact. Though a QCNN is used as an example in this work, the methods used here can be applied to other quantum machine learning models as well.
A correspondence between the Rabi model and an Ising model with long-range interactions

Bruno Scheihing-Hitschfeld, Néstor Sepúlveda

SciPost Phys. 19, 153 (2025) · published 15 December 2025 | · pdf

By means of Trotter's formula, we show that transition amplitudes between a class of generalized coherent states in the Rabi model can be understood in terms of a certain Ising model featuring long-range interactions beyond nearest neighbors in its thermodynamic limit. Specifically, we relate the transition amplitudes in the Rabi model to a sum over binary variables of the form of a partition function of an Ising model with a number of spin sites equal to the number of steps in Trotter's formula applied to the real-time evolution of the Rabi model. From this, we show that a perturbative expansion in the energy splitting of the two-level subsystem in the Rabi model is equivalent to an expansion in the number of spin domains in the Ising model. We conclude by discussing how calculations in one model give nontrivial information about the other model, and vice versa, as well as applications and generalizations this correspondence may find.
Algebraic law of local correlations in a driven Rydberg atomic system

Xin Wang, XiaoFeng Wu, Bo Yang, Bo Zhang, Bo Xiong

SciPost Phys. 19, 152 (2025) · published 11 December 2025 | · pdf

Understanding the mechanism behind the buildup of inner correlations is crucial for studying nonequilibrium dynamics in complex, strongly interacting many-body systems. Here we investigate both analytically and numerically the buildup of antiferromagnetic (AF) correlations in a dynamically tuned Ising model with various geometries, realized in a Rydberg atomic system. Through second-order Magnus expansion (ME), we demonstrate quantitative agreement with numerical simulations for diverse configurations including $2 × n$ lattice and cyclic lattice with a star. We find that the AF correlation magnitude at fixed Manhattan distance obeys a universal superposition principle: It corresponds to the algebraic sum of contributions from all shortest paths. This superposition law remains robust against variations in path equivalence, lattice geometries, and quench protocols, establishing a new paradigm for correlation propagation in quantum simulators.
Learning the non-Markovian features of subsystem dynamics

Michele Coppola, Mari Carmen Bañuls, Zala Lenarčič

SciPost Phys. 19, 149 (2025) · published 8 December 2025 | · pdf

The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.
On the difference between thermalization in open and isolated quantum systems: A case study

Archak Purkayastha, Giacomo Guarnieri, Janet Anders, Marco Merkli

SciPost Phys. 19, 136 (2025) · published 25 November 2025 | · pdf

Thermalization of isolated and open quantum systems has been studied extensively. However, being the subject of investigation by different scientific communities and being analysed using different mathematical tools, the connection between the isolated (IQS) and open (OQS) approaches to thermalization has remained opaque. Here we demonstrate that the fundamental difference between the two paradigms is the order in which the long time and the thermodynamic limits are taken. This difference implies that they describe physics on widely different time and length scales. Our analysis is carried out numerically for the case of a double quantum dot (DQD) coupled to a fermionic lead, also known as the interacting resonant level model in quantum impurity physics. We show how both OQS and IQS thermalization can be explored in this model on equal footing, allowing a fair comparison between the two. We find that while the quadratically coupled (free) DQD experiences no isolated thermalization, it of course does experience open thermalization. For the non-linearly interacting DQD coupled to a fermionic lead, the many-body interaction in the DQD breaks the integrability of the whole system. We find that this system shows strong evidence of both OQS and IQS thermalization in the same dynamics, but at widely different time scales, consistent with reversing the order of the long time and the thermodynamic limits.
Digital quantum simulation of bosonic systems and quantum complementarity

Victor P. Brasil, Diego S. Starke, Jonas Maziero

SciPost Phys. Core 8, 086 (2025) · published 24 November 2025 | · pdf

Digital quantum simulation (DQS) has emerged as a powerful approach to investigate complex quantum systems using digital quantum computers. Such systems, like many-particle bosonic systems and intricate optical experimental setups, pose significant challenges for classical simulation methods. In this paper, we utilize a general formalism for the DQS of bosonic systems, which consists of mapping bosonic operators to Pauli operators using the Gray code, in order to simulate interferometric variants of Afshar's experiment—an intricate optical experiment—on IBM's quantum computers. We investigated experiments analogous to Afshar's double-slit experiment performed by Unruh and Pessoa Júnior, exploring discussions on the apparent violation of Bohr's complementarity principle when considering the entire experimental setup. Based on the aforementioned experiments, we construct a variation of a delayed-choice setup. We also explore another experiment starting with a two-photon initial state. Finally, we analyze these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations and remains consistent with the foundational principles of Quantum Mechanics.
Quench dynamics of entanglement from crosscap states

Konstantinos Chalas, Pasquale Calabrese, Colin Rylands

SciPost Phys. 19, 132 (2025) · published 19 November 2025 | · pdf

The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics. It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments. The entanglement dynamics emerging from long-range correlated states is far less studied, although no less viable using modern quantum simulation experiments. In this work, we investigate the dynamics of the bipartite entanglement entropy and mutual information from initial states which have long-range entanglement with correlation between antipodal points of a finite and periodic system. Starting from these crosscap states, we study both brickwork quantum circuits and Hamiltonian dynamics and find distinct patterns of behaviour depending on the type of dynamics and whether the system is integrable or chaotic. Specifically, we study both dual unitary and random unitary quantum circuits as well as free and interacting fermion Hamiltonians. For integrable systems, we find that after a time delay the entanglement experiences a linear in time decrease followed by a series of revivals, while, in contrast, chaotic systems exhibit constant entanglement entropy. On the other hand, both types of systems experience an immediate linear decrease of the mutual information in time. In chaotic systems this then vanishes, whereas integrable systems instead experience a series of revivals. We show how the quasiparticle and membrane pictures of entanglement dynamics can be modified to describe this behaviour, and derive explicitly the quasiparticle picture in the case of free fermion models which we then extend to all integrable systems.

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Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers

Daniel González-Cuadra, Alejandro Bermudez

SciPost Phys. 19, 130 (2025) · published 18 November 2025 | · pdf

We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange ($\Gamma$-couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.
A Fermi surface descriptor quantifying the correlations between anomalous Hall effect and Fermi surface geometry

Elena Derunova, Jacob Gayles, Yan Sun, Michael W. Gaultois, Mazhar N. Ali

SciPost Phys. Core 8, 085 (2025) · published 18 November 2025 | · pdf

In the last few decades, basic ideas of topology have completely transformed the prediction of quantum transport phenomena. Following this trend, we go deeper into the incorporation of modern mathematics into quantum material science focusing on geometry. Here we investigate the relation between the geometrical type of the Fermi surface and Anomalous and Spin Hall Effects. An index, $\mathbb{H}_F$, quantifying the hyperbolic geometry of the Fermi surface, shows a universal correlation (R$^2$ = 0.97) with the experimentally measured intrinsic anomalous Hall conductivity, of 16 different compounds spanning a wide variety of crystal, chemical, and electronic structure families, including those where topological methods give R$^2$ = 0.52. This raises a question about the predictive limits of topological physics and its transformation into a wider study of bandstructures' and Fermi surfaces' geometries and relating them to the quantum geometry theory of a more general metric of eigenstates, opening horizon for the prediction of phenomena beyond topological understanding.

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Publications

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