Classical simulation of a programmable quantum processor is crucial in identifying the threshold of a quantum advantage. We demonstrate the simple update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random quantum circuit states, which center around recent quantum advantage claims. Applied to square lattices of qubits akin to state-of-the-art superconducting processors, the PEPS representation is exact for circuit depths less than ${\mathcal{D}}_{\mathrm{tr}}=\beta {log}_2\chi$, where $\chi$ is the maximum bond dimension and $2\lesssim \beta \lesssim 4$ depends on the choice of two-qubit gates, independent of the qubit number $n$. We find the universal scaling behaviors of the state fidelity by treating large-scale circuits of $n\le {10}^4$, using $\chi \le 128$ on a conventional CPU. Our method has a polynomial scaling of computational costs with $n$ for circuit depth $\mathcal{D}=O(logn)$ and is more advantageous than matrix product state approaches if $n$ is large. This work underscores PEPSs as a scalable tool for benchmarking quantum algorithms with future potential for sampling applications using advanced contraction techniques.

Vanadium-based kagome metal of $\mathrm{Sc}{\mathrm{V}}_6\mathrm{S}{\mathrm{n}}_6$ has been of current interest as it features unique charge density wave (CDW) ordering accompanied by a structural phase transition, indicating the importance of lattice distortion for the onset of CDW order. To unveil the role of each individual atomic site for the phase transition, we employed a local probe through the nuclear magnetic resonance (NMR) measurements in which the NMR signals from ${}^{45}\mathrm{Sc}, {}^{51}\mathrm{V}$, and ${}^{119}\mathrm{Sn}$ nuclei in both normal and CDW states were observed. From the comparison between the quadrupole splitting of ${}^{45}\mathrm{Sc}$ and ${}^{51}\mathrm{V}$ NMR satellite lines, a noticeable increase in the ${}^{45}\mathrm{Sc}$ quadrupole frequency below the transition temperature was identified. The finding can be accounted for by the structural distortion mainly involving the displacement of Sc and Sn atoms along the crystal $c$ axis. From the analysis of the temperature dependences of the NMR shift, we quantitatively obtained the change in the electronic states for each atom associated with the phase transition. In particular, we demonstrated a marked reduction in the V $3d$ density of states at the Femi level, which can be rationalized as a manifestation of the structural transition. Remarkably, we resolved three ${}^{119}\mathrm{Sn}$ NMR resonance lines corresponding to three nonequivalent crystallographic Sn sites and therefore estimated the variation in the $5s$ electronic states of each Sn atom in $\mathrm{Sc}{\mathrm{V}}_6\mathrm{S}{\mathrm{n}}_6$.

We discuss predominant order parameters for structural chirality and demonstrate that time-reversal-even axial quadrupole plays a key role in stabilizing a chiral structure. Using the symmetry-adapted closest Wannier model of the trigonal Te and Se, we quantify the evolution of the spin-independent (spinless) and spin-dependent (spinful) electric toroidal (ET) (axial) multipole moments across the transition from an achiral to a chiral structure. Our results clearly identify that a spin-independent off-diagonal real hopping between $p$ orbitals, which corresponds to the bond-cluster spinless ET quadrupole of $(3z^2-r^2)$ type $G_u$, is the predominant order parameter in stabilizing helical structures. We further elucidate that the above itinerant spinless ET quadrupole induces a monopolelike orbital angular momentum texture in the momentum space, which can be observed via circular dichroism in soft x-ray photoemission spectroscopy measurement. Our findings highlight a critical role of the orbital angular momentum in chiral materials rather than less dominant spin angular momentum arising from the relativistic spin-orbit coupling.

The excitation of bound states in the continuum (BICs) in two- or multiqubit systems lies at the heart of entanglement generation and harnessing in waveguide quantum electrodynamics platforms. However, the generation of qubit pair BICs through single-photon scattering is hindered by the fact that these states are effectively decoupled from propagating photons. We prove that scattering of a parity-invariant single photon on a qubit pair, combined with a properly engineered time variation of the qubit detuning, is not only feasible, but also more effective than strategies based on the relaxation of the excited states of the qubits when the distance between the qubits gives rise to non-negligible photon delays (non-Markovian regime). The use of tensor network methods to simulate the proposed scheme enables us to include such photon delays in collision models, thus opening the possibility to follow the time evolution of the full quantum system, including qubits and field, and to efficiently implement and characterize the dynamics, hence identifying optimal working points for the BIC generation.

Confinement of molecules within a cavity leads to a strong coupling between light and matter degrees of freedom, merging the two into a quasiparticle known as a polariton. Theoretical treatments of molecular polaritons generally utilize either exact diagonalization of the interacting molecule-cavity system Hamiltonian or perturbation theory to analyze intracavity light-matter interactions. The former is constrained in its capacity to account for the open nature of the molecular cavity system, while the treatment of strong interactions within perturbation theory represents a weakness of the latter. Here, we introduce a pseudoparticle nonequilibrium Green's function (PP-NEGF) formulation for molecular polariton spectroscopy. This formulation addresses the limitations of currently available approaches by accounting for all intrasystem interactions exactly and treating system-bath couplings within diagrammatic expansion and extends a recent NEGF-based formulation for nonlinear optical spectroscopy [J. Chem. Phys. 162, 074108 (2025)] to strongly interacting molecular systems. Theoretical derivations are demonstrated through numerical simulations, where we examine the impact of strong light-matter interaction on fluxes and multidimensional optical spectroscopy of cavity polaritons.

Quantum low-density parity-check (qLDPC) codes with high-performance and nonlocal stabilizers are an attractive alternative to the surface code because of their relatively high code rate and distance. However, unlike the surface code that has simple, geometrically local, stabilizer checks, qLDPC codes with nonlocal stabilizers are challenging to measure. Recent advances have shown how to deterministically perform high-fidelity, cavity-mediated many-body gates, enabling the encoding and decoding of nonlocal GHZ states. We show how to use this resource for constant-depth fault-tolerant stabilizer measurements in hypergraph product and lifted product codes. Using circuit-level noise simulations, including leakage and collective error from the noise-optimized cavity-mediated gate, we find promising thresholds of $0.84\%–0.60\%$ for the hypergraph product code and pseudothreshold of $0.3\%–0.4\%$ for the lifted product codes, with cavity cooperativities in the range $C\sim {10}^4–{10}^6$. We propose a trilayer architecture, compatible with neutral atom platforms, which enhances circuit parallelizability.

The advent of non-Hermitian physics has enriched the plethora of topological phases to include phenomena without Hermitian counterparts. Despite being among the most well-studied uniquely non-Hermitian features, the topological properties of multifold exceptional points, $n$-fold spectral degeneracies ($\mathrm{EP}n\mathrm{s}$) at which also the corresponding eigenvectors coalesce, were only recently revealed in terms of topological resultant winding numbers and concomitant Abelian doubling theorems. Nevertheless, a more mathematically fundamental description of $\mathrm{EP}n\mathrm{s}$ and their topological nature has remained an open question. To fill this void, in this article, we revisit the topological classification of $\mathrm{EP}n\mathrm{s}$ in generic systems and systems with local symmetries, generalize it in terms of more mathematically tractable (local) similarity relations, and extend it to include all such similarities as well as nonlocal symmetries. Through the resultant vector, whose components are given in terms of the resultants between the corresponding characteristic polynomial and its derivatives, the topological nature of the resultant winding number is understood in several ways: in terms of (1) the tenfold classification of (Hermitian) topological matter, (2) the framework of Mayer-Vietoris sequence, and (3) the classification of vector bundles. The classification scheme further predicts the existence of topological bulk Fermi arcs protected by a ${\mathbb{Z}}_2$-invariant, induced by nonlocal symmetries, dubbed ${\mathbb{Z}}_2$-protected Fermi arcs. Our work reveals the mathematical foundations on which the topological nature of $\mathrm{EP}n\mathrm{s}$ resides, enriches the theoretical understanding of non-Hermitian spectral features, and will therefore find great use in modern experiments within both classical and quantum physics.

Determining the closeness of two quantum states with minimal error probability is a central problem in quantum information theory. The optimal exponents characterizing the error probability in the symmetric and asymmetric settings are given by the quantum Chernoff bound (QCB) and the quantum Hoeffding bound (QHB), respectively. In this work, we introduce the first algorithms for estimating the QCB and QHB of two unknown states. We propose a unitary encoding for diagonal density matrix based on the copy matrix, which enables unbiased estimation of nonlinear matrix functions via quantum singular value transformation (QSVT). For general density matrices, we combine QSVT with the Hadamard test to estimate both QCB and QHB. Numerical simulations demonstrate that the algorithm converges to the optimal value within a limited number of iterations. Furthermore, we establish the first integration of QSVT with convex optimization, yielding a hybrid quantum-classical framework for quantum estimation.

A theoretical approach to estimating stable drainage front widths in three-dimensional (3D) random porous media under gravitational and capillary effects is presented here. Based on the frontier of the infinite cluster in gradient percolation, we propose an expression for the 3D front width dependent on the pore-network topology, the distribution of capillary-pressure thresholds for the pore throats, the stabilizing capillary-pressure gradient, the average pore size, and the correlation length critical exponent from percolation in three dimensions. Theoretical predictions are successfully compared to numerical results obtained with a bond invasion-percolation model for a wide range of drainage flow parameters.

We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, 5, 6, and 8 using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the standard Potts models are used, cyclic changes in the $q$ homogeneous phases and $q$-state coexisting wave mode appear at low and high flipping energies, respectively, for all values of $q$. However, for a factorizable $q$ value, dynamic modes with skipping states emerge, depending on the contact energies. For $q=6$, a spiral wave mode with three domain types (one state dominant or two states mixed) and cyclic changes in three homogeneous phases are found. Although three states can coexist spatially under thermal equilibrium, the scaling exponents of the transitions to the wave modes are modified from the equilibrium values.

Non-Hermitian systems have been at the center of intense research for over a decade, partly due to their nontrivial energy topology formed by intersecting Riemann manifolds with branch points known as exceptional points (EPs). This spectral property can be exploited, e.g., to achieve topologically controlled state permutations that are necessary for implementing a wide class of classical and quantum information protocols. However, the complex-valued spectra of typical non-Hermitian systems lead to instabilities, losses, and breakdown of adiabaticity, which impedes the practical use of EP-induced energy topologies in quantum information protocols based on state permutation symmetries. Indeed, in a given non-Hermitian multiqubit system, the dynamical winding around EPs always results in a predetermined set of attenuated final eigenstates, due to the interplay of decoherence and nonadiabatic transitions, irrespective of the initial conditions. In this work, we address this long-standing problem by introducing a model of interacting qubits governed by an effective non-Hermitian Hamiltonian that hosts a special type of EPs while maintaining a completely real energy spectrum, ensuring the absence of losses in the system’s dynamics. We demonstrate that such non-Hermitian Hamiltonians enable the realization of genuine, in general, non-Abelian permutation groups in the multiqubit system’s eigenspace while dynamically encircling these EPs. Our findings indicate that, contrary to previous beliefs, non-Hermiticity can be utilized to achieve controlled topological state permutations in time-modulated multiqubit systems, thus paving the way for the advancement and development of quantum information protocols in real-world non-Hermitian quantum systems.

There is a growing interest in methods for detecting and interpreting changes in experimental time-evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at $q=1$ in the order-$q$ dynamical Rényi entropy, we measure the derivative of its spectrum given by the variance of the logarithmic probability of trajectories. To overcome the difficulties inherent in trajectory-space descriptions of finite-length time series, we derive—within the general framework of Markov processes—a computationally efficient closed-form expression for this measure, while maintaining control over the trade-off between statistical and truncation errors. We investigate the properties of the measure and assess the efficacy of the associated method in estimating characteristic quantities of well-known dynamical systems. Furthermore, we examine its scope and limitations, including its potential utility in predicting dynamical phase transitions from time series and in characterizing the complexity of the underlying behavior. Grounded in the thermodynamic formalism of chaotic systems, the developed framework bridges dynamical systems theory, network theory, and time-series analysis, extending classical concepts such as bit-number variance or varentropy in phase-space statistics, permutation entropy in time-series analysis, and path-length statistics in network science.

We investigate the spin-1 Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L=19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension as the temperature decreases below the tricritical point. Finally, we validate our tricritical point estimate through precise agreement with conformal field theory predictions for the tricritical Ising universality class. Our results underscore the continued utility of the transfer-matrix approach for studying phase transitions in complex lattice models.

We present a theoretical study of a mesoscopic two-dimensional electron gas confined in a double quantum well that is coupled to a uniform quasistatic cavity mode via fluctuations of the dipole moment. We focus on the regime of large number of electrons participating in the virtual intersubband transitions. In this regime, the effective photonic potential is no longer quadratic but, instead, it contains large number of minima. Each minimum represents a nearly harmonic oscillator with the renormalized cavity frequency that is much greater than its bare value. The energy offset of a minimum scales quadratically with respect to the photon coordinate corresponding to this minimum. These energy offsets determine the statistical weight of each minimum, and altogether they result in the additive correction to the heat capacity of the system. This correction exhibits a Schottky anomaly and a $0.5k_{\text{B}}$ plateau at low temperatures. This behavior can be associated with the emergence of a new degree of freedom. This degree of freedom does not manifest in the optical conductivity and can only be observed via the heat capacity measurement.

For planar architectures, surface code-based quantum error correction is one of the most promising approaches to fault-tolerant quantum computation. This is partially due to the variety of fault-tolerant logical protocols that can be implemented in two dimensions using local operations. One such protocol is the lattice surgery-based logical state teleportation, which transfers a logical quantum state from an initial location on a quantum chip to a target location through a linking region of qubits. This protocol serves as a basis for higher-level routines, such as the entangling cnot gate or magic state injection. In this work, we investigate the correctability phase diagram of this protocol for distinct error rates inside the surface code patches and within the linking region. We adopt techniques from statistical physics to describe the numerically observed crossover regime between correctable and uncorrectable quantum error correction phases, where the correctability depends on the separation between the initial and target locations. We find that inside the crossover regime the correctability-threshold lines decay as a power law with increasing separation, which we explain accurately using a finite-size scaling analysis. Our results indicate that the logical state teleportation protocol can tolerate much higher noise rates in the linking region compared to the bulk of the surface code patches, provided the separation between the positions is relatively small.

Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semidefinite programming to derive certified bounds on the expectation value of an arbitrary observable in the steady state of Lindbladian dynamics. We illustrate our method on a series of many-body systems, including paradigmatic spin-1/2 chains and two-dimensional ladders, considering both equilibrium and nonequilibrium steady states. We benchmark our method with state-of-the-art tensor-network approaches that, unlike our method, are only able to provide estimates, with no guarantee, on steady-state quantities. For the tested models, only modest computational effort is needed to obtain certified nontrivial bounds for system sizes intractable by exact methods. Our method introduces the first general numerical tool for bounding steady-state properties of open quantum dynamics, opening an avenue in the understanding of stable configurations in many-body systems.