The high complexity of many-body quantum dynamics means that essentially all analytical or numerical approaches either exploit special structure or are approximate in nature. One such approach—the memory function formalism—involves a carefully chosen split into “fast” and “slow” modes. An approximate model for the fast modes can then be used to solve for Green’s functions $G(z)$ of the slow modes, and the success of this approach depends on the accuracy of the fast space approximation. Using a formulation in operator Krylov space known as the recursion method, we prove the emergence of a universal random matrix description of the fast mode dynamics. This is captured by the “level-$n$ Green’s function” $G_n(z)$, which we show approaches universal scaling forms in the “fast limit” $n\to \infty$. Notably, this emergent universality can occur in both chaotic and nonchaotic systems, provided their spectral functions are sufficiently smooth. This universality of $G_n(z)$ turns out to be precisely analogous to the universality of eigenvalue correlations in random matrix theory (RMT), even though there is no explicit randomness present in the Hamiltonian. Concretely, at finite $z$ we show that $G_n(z)$ approaches the Wigner semicircle law, while if $G(z)$ is the Green’s function of certain hydrodynamical variables, we show that at low frequencies $G_n(z)$ is instead governed by the Bessel universality class from RMT. As an application of this universality, we give a new numerical method, the spectral bootstrap, for approximating spectral functions, including hydrodynamic transport data, from a finite number of Lanczos coefficients. Our proof involves a map to a Riemann-Hilbert problem which we solve using a steepest-descent-type method, rigorously controlled in the $n\to \infty$ limit. Via the steepest-descent procedure, we are led to a related Coulomb gas optimization problem, and we discuss how a recent conjecture—the “Operator Growth Hypothesis”—implies that chaotic operator dynamics can generically be identified with the critical point of a confinement transition in this Coulomb gas. These results elevate the recursion method from a useful numerical technique to a theoretically principled framework with universal content.

Over the past decade, autonomous stabilization of bosonic qubits has emerged as a promising approach for hardware-efficient protection of quantum information. However, applying these techniques to more complex encodings than the Schrödinger cat code requires exquisite control of high-order wave mixing processes. The challenge is to enable specific multiphotonic dissipation channels while avoiding unintended nonlinear interactions. In this work, we leverage a genuine six-wave mixing process enabled by a near Kerr-free Josephson element to enforce dissipation of quartets of excitations in a high-impedance superconducting resonator. Owing to residual nonlinearities stemming from stray inductances in our circuit, this dissipation channel is only effective when the resonator holds a specific number of photons. Applying it to the fourth excited state of the resonator, we show an order-of-magnitude enhancement of the state decay rate while only marginally impacting the relaxation and coherence of lower-energy states. Given that stray inductances could be strongly reduced through simple modifications in circuit design and that our methods can be adapted to activate even higher-order dissipation channels, these results pave the way toward the dynamical stabilization of four-component Schrödinger cat qubits and even more complex bosonic qubits.

We investigate quantum transport in micrometer-sized single crystals of ${\mathrm{Bi}}_4{\mathrm{Br}}_4$, a material predicted to be a second-order topological insulator. 1D topological states with long phase coherence times are revealed via the modulation of quantum interference with magnetic field and gate voltage. In particular, we demonstrate the existence of Aharonov-Bohm interference between 1D ballistic states several micrometers long, that we identify as phase-coherent hinge modes on neighboring step edges at the crystal surface. These Aharonov-Bohm oscillations are made possible by a disordered phase-coherent contact region, the existence of which is confirmed by scanning transmission electron microscopy combined with energy-dispersive x-ray spectroscopy (STEM-EDX) of FIB lamellae. Their coherent nature modulates the transmission of the 1D edge states, leading to weak antilocalization and universal conductance fluctuations with surprisingly large characteristic fields and a strongly anisotropic behavior. These complementary experimental results provide a comprehensive, coherent description of quantum transport in ${\mathrm{Bi}}_4{\mathrm{Br}}_4$ and establish the material as a second-order topological insulator with topologically protected 1D ballistic states.

The development of prototype quantum information processors has progressed to a stage where small instances of logical qubit systems perform better than the best of their physical constituents. Advancing toward fault-tolerant quantum computing will require an understanding of the underlying error mechanisms in logical primitives as they relate to the performance of quantum error correction. In this work we demonstrate the novel capability to characterize the physical error properties relevant to fault-tolerant operations via cycle error reconstruction. We illustrate this diagnostic capability for a transversal controlled-not (cnot) gate, a prototypical component of quantum logical operations, in a 16-qubit register of a trapped-ion quantum computer. Our error characterization technique offers three key capabilities: (i) identifying context-dependent physical layer errors, enabling their mitigation, (ii) contextualizing component gates in the environment of logical operators, validating the performance differences in terms of characterized component-level physics, and (iii) providing a scalable method for predicting quantum error correction performance using pertinent error terms, differentiating correctable versus uncorrectable physical layer errors. The methods with which our results are obtained have scalable resource requirements that can be extended with moderate overhead to capture overall logical performance in increasingly large and complex systems.

Superconductivity arises from the global phase coherence of Cooper pairs. Modulation of phase coherence leads to quantum phase transitions, serving as an important tool for studying unconventional superconductivity. Here, we demonstrate bosonic phases across the superconductor-insulator transition in infinite-layer nickelate superconducting films by the control of spatially periodic network patterns. Magnetoresistance oscillations with a periodicity of $h/2e$ provide direct evidence of $2e$ Cooper pairing in nickelates. The phase transition is predominantly driven by enhanced superconducting fluctuations, and Cooper pairs are involved in charge transport across the transition. Notably, we observe two types of anomalous metallic phases, emerging, respectively, at finite magnetic fields and down to zero magnetic field. They can be characterized by bosonic excitations, suggesting the dynamic roles of vortices in the ground states. Our work establishes nickelates as a key platform for investigating the rich landscape of bosonic phases controlled via the phase coherence of Cooper pairs.

While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In quantum physics, an arrow of time emerges when a sequence of measurements is performed on a system. We introduce quantum control tools that can yield dynamics more consistent with time flowing backward than forward. The control tools are based on the explicit construction of a Hamiltonian that can replicate the stochastic trajectories of a monitored quantum system. Such a Hamiltonian can reverse the effect of monitoring and, via a feedback process, generate trajectories consistent with a reversed arrow of time. It can also be used to simulate the backward-in-time dynamics of an open quantum system. Finally, we design a feedback-driven continuous measurement engine powered by the energy pumped into the system by the monitoring process. We show that the engine can operate under experimentally realizable conditions with feedback delay and finite-efficiency measurements.

’t Hooft anomalies of global symmetries play a fundamental role in quantum many-body systems and quantum field theory (QFT). In this paper, we make a systematic analysis of lattice anomalies—the analog of ’t Hooft anomalies in lattice systems—for which we give a precise definition. Crucially, a lattice anomaly is not a feature of a specific Hamiltonian but rather is a topological invariant of the symmetry action. The controlled setting of lattice systems allows for a systematic and rigorous treatment of lattice anomalies, shorn of the technical challenges of QFT. We find that lattice anomalies reproduce the expected properties of QFT anomalies in many ways but also have crucial differences. In particular, lattice anomalies and QFT anomalies are not, contrary to a common expectation, in one-to-one correspondence, and there can be nontrivial anomalies on the lattice that are infrared (IR) trivial: They admit symmetric trivial gapped ground states and map to trivial QFT anomalies at low energies. Nevertheless, we show that lattice anomalies (including IR-trivial ones) have a number of interesting consequences in their own right, including connections to commuting projector models, phases of many-body-localized systems, and quantum cellular automata. We make substantial progress on the classification of lattice anomalies and develop several theoretical tools to characterize their consequences on symmetric Hamiltonians. Our work places symmetries of quantum many-body lattice systems into a unified theoretical framework and may also suggest new perspectives on symmetries in QFT.

Chiral superconductors have long been theorized to break time-reversal symmetry and support exotic topological features such as Majorana modes and spontaneous edge currents, promising ingredients for quantum technologies. Although several unconventional superconductors may exhibit time-reversal symmetry breaking, clear microscopic evidence of chiral pairing has remained out of reach. In this work, we demonstrate direct real-space signatures of chiral superconductivity in a single atomic layer of tin on Si(111). Using quasiparticle interference imaging, we detected symmetry-locked nodal and antinodal points in the Bogoliubov quasiparticle wave function, tightly bound to atomic point defects in the tin lattice. These nodal features, along with their surrounding texture, form a distinct real-space pattern exhibiting a clear and exclusive hallmark of chiral superconductivity. Our findings, reinforced by analytical theory and numerical simulations, offer unambiguous evidence of chiral pairing in a two-dimensional material.

The fidelity of operations on a solid-state quantum processor is fundamentally bounded by environmental decoherence. Characterizing environmental fluctuations is challenging because the acquisition time of nonadaptive experimental protocols limits temporal precision and can average out rapid features of the underlying dynamics. Here, we overcome this temporal-resolution limit by 2 orders of magnitude using a field-programmable gate-array powered classical controller that adaptively and continuously tracks the relaxation-time fluctuations of two fixed-frequency superconducting transmon qubits, which exhibit average relaxation times of approximately 0.17 ms and occasionally exceed 0.5 ms. We report events in which the relaxation time switches by nearly an order of magnitude over timescales of just tens of milliseconds, rather than minutes or hours as previously reported. Our real-time Bayesian estimation protocol estimates relaxation times within a few milliseconds, close to the decoherence timescale itself. Our statistical analysis further suggests that some of these fast fluctuations arise from two-level systems switching at rates up to 10 Hz, 4 orders of magnitude faster than earlier reports. These results redefine the timescales relevant for calibration in superconducting quantum processing units, establish a reference for rapid relaxation-rate characterization in device screening, and improve our understanding of fast relaxation dynamics.

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

Triboelectric charging of insulating particles through contact is critical in diverse physical and engineering processes, from dust storms and volcanic eruptions to industrial powder handling. However, many experiments over the years have consistently revealed counterintuitive charging patterns, including variable impact charge under identical conditions, charge sign reversal with repeated impacts, and bipolar charging of differently sized particles. Existing computational models cannot predict these patterns; they either rely on oversimplified heuristics or require inaccessible detailed surface properties. We present a stochastic scaling model (SSM) for particle charging that unifies same-material (particle-particle) and different-material (particle-wall) charging in a single theoretical framework. The model is grounded in a physics-based stochastic closure by the mean, variance, skewness, and minimum impact charge measured in a highly controlled reference experiment. To test the SSM, we implemented it in an open-source Lagrangian-Eulerian computational fluid dynamics solver. When simulating 300 000 insulating particles transported by turbulent wall-bounded flows, the SSM takes less than 0.01% of the CPU time. By scaling the statistical parameters of the reference impact to each collision, the new model reproduces the complex charging patterns observed in experiments without requiring surface-level first-principles inputs. The SSM offers a physically grounded route to large-scale simulations of electrostatic effects across many fields of particle-laden flows.

The Yang-Lee universality class arises when an imaginary magnetic field is tuned to its critical value in the paramagnetic phase of the $d<6$ Ising model. In $d=2$, this nonunitary conformal field theory (CFT) is exactly solvable via the $M(2,5)$ minimal model. As found long ago by von Gehlen using exact diagonalization, the corresponding real-time, quantum critical behavior arises in the periodic Ising spin chain when the imaginary longitudinal magnetic field is tuned to its critical value from below. Even though the Hamiltonian is not Hermitian, the energy levels are real due to the $\mathcal{PT}$ symmetry. In this paper, we explore the analogous quantum critical behavior in higher-dimensional non-Hermitian Hamiltonians on regularized spheres $S^{d-1}$. For $d=3$, we use the recently invented, powerful fuzzy sphere method, as well as discretization by the platonic solids cube, icosahedron, and dodecahedron. The low-lying energy levels and structure constants we find are in agreement with expectations from the conformal symmetry. The energy levels are in good quantitative agreement with the high-temperature expansions and with Padé extrapolations of the $6-\epsilon$ expansions in Fisher’s $i{\varphi }^3$ Euclidean field theory for the Yang-Lee criticality. In the course of this work, we clarify some aspects of matching between operators in this field theory and quasiprimary fields in the $M(2,5)$ minimal model. For $d=4$, we obtain new results by replacing $S^3$ with the self-dual polytope called the 24-cell.

In this work, we demonstrate a remarkable field-induced ferroquadrupolar phase emanating from the magnetoelastic coupling. Using synchrotron x-ray and neutron diffraction, heat capacity measurements, as well as mean-field modeling, we show that above the critical magnetic field, ferroquadrupolar $O_2^{-2}$ order is stabilized as the main order parameter, in competition with the field-induced magnetic polarization. This is revealed by a severe lattice distortion and the suppression of antiferromagnetic ordering of the dipole moments. Even in zero magnetic field, the previously reported antiferromagnetic order is a mixed quadrupolar-dipolar phase, further highlighting the crucial role of spin-lattice interactions. This complete understanding of the magnetoelastic phase diagram establishes ${\mathrm{TbPO}}_4$ as a model system for studying nematic-antiferromagnetic transitions and provides key Hamiltonian parameters for its description.

The quantization of transport and its resilience to backscattering are key features for leveraging topological matter in applications that demand stringent noise mitigation, such as metrology and quantum information processing. Because of the bosonic nature of light, engineering such robust, “one-way” channels in synthetic photonic systems imposes the implementation of topological models with broken time-reversal symmetry; this is challenging, since photons possess neither an electric charge nor a magnetic moment. Here, we propose and demonstrate an approach to realizing photonic Chern insulators—topological insulators with broken time-reversal symmetry—by encoding a Haldane-like model in the synthetic frequency dimension of an optical fiber loop platform. The bands’ topology is assessed by reconstructing the Bloch state geometry across the Brillouin zone. We further highlight its consequences by measuring a driven-dissipative analog of the quantized transverse Hall conductivity. Our results open avenues for harnessing topologically protected light propagation in frequency-multiplexed photonic systems, with applications ranging from precision metrology to photonic quantum processors.

The interplay between symmetry and topological properties plays a very important role in modern physics. In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been systematically studied for bosonic systems. Very recently, the concept of SET phases has been generalized into fermionic systems and their corresponding classification schemes are also proposed. Nevertheless, how to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem. In this paper, we first construct exactly solvable models for nonanomalous nonchiral $2+1\mathrm{D}$ fSET phases, namely, the symmetry-enriched fermionic string-net models, which are described by commuting-projector Hamiltonians whose ground states are the fixed-point wave functions of each fSET phase. Mathematically, we provide a partial definition to $G$-graded super fusion category (when the total symmetry $G^f$ is a direct product of physical symmetry $G$ and fermion-parity symmetry ${\mathbb{Z}}_2^f$), which is the input data of a symmetry-enriched fermionic string-net model. Next, we construct exactly solvable models for nonchiral $2+1\mathrm{D}$ fSET phases with ’t Hooft anomaly, especially the $H^3(G,{\mathbb{Z}}_2)$ fermionic ’t Hooft anomaly which is different from the well-known bosonic $H^4[G,U(1{)}_T]$ anomaly. In our construction, this $H^3(G,{\mathbb{Z}}_2)$ fermionic ’t Hooft anomaly is characterized by a violation of fermion-parity conservation in some of the surface $\mathcal{F}$ moves (a type of renormalization moves for the ground state wave functions of surface fSET phases), and also by a new fermionic obstruction $\mathrm{\Theta }$ in the surface pentagon equation. We demonstrate this construction in a concrete example that the surface topological order is a ${\mathbb{Z}}_4$ gauge theory embedded into a fermion system and the total symmetry $G^f={\mathbb{Z}}_2^f\times {\mathbb{Z}}_2\times {\mathbb{Z}}_4$. We further conjecture that the $H^2(G,{\mathbb{Z}}_2)$ fermionic ’t Hooft anomaly is characterized by a possible violation of nonterminating $q$-type (called $\sigma$-type) string in the fusion rules of surface models.

Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies: one, quasiparticle interference (QPI) measured by scanning-tunneling microscopy, and the other, angle-resolved photoemission spectroscopy (ARPES). We combine these two sets of data in a unified theoretical analysis. Through explicit calculations of experimentally measurable quantities, we show that a simple two-component fermion model (TCFM) representing electron fractionalization succeeds in reproducing various detailed features of these experimental data: ARPES and QPI data are concomitantly reproduced by the TCFM in full energy and momentum spaces. The measured QPI pattern reveals a signature characteristic of the TCFM, distinct from the conventional single-component prediction, supporting the validity of the electron fractionalization in the cuprates. The integrated analysis also solves the puzzles of ARPES and QPI data that are seemingly inconsistent with each other. The overall success of the TCFM offers a comprehensive understanding of the electronic structure of the cuprates, in particular, the unoccupied side of the spectra, of which momentum-resolved structure has long been unexplored experimentally. We further predict that a characteristic QPI pattern should appear in the unoccupied high-energy part if the fractionalization is at work. We propose that integrated-spectroscopy analyses offer a promising way to explore challenging issues of strongly correlated electron systems.

What happens when fermions hop on a lattice with crystalline defects? The answer depends on topological quantum numbers that specify the action of lattice rotations and translations in the low energy theory. One can understand the topological quantum numbers as a twist of continuum gauge fields in terms of crystalline gauge fields. We find that disclinations and dislocations—defects of crystalline symmetries—generally lead to a certain “emanant” quantized magnetic flux in the continuum. To demonstrate these facts, we study in detail tight-binding models whose low-energy descriptions are $(2+1)\mathrm{D}$ Dirac cones. Our map from lattice to continuum defects explains the crystalline topological response to disclinations and dislocations, and motivates the fermion crystalline equivalence principle used in the classification of crystalline topological phases. When the gap closes, the presence of emanant flux leads to pair creation from the vacuum with the particles and antiparticles swirling around the defect. We compute the associated currents and energy density using the tools of defect conformal field theory. There is a rich set of renormalization group fixed points, depending on how particles scatter from the defect. At half flux, there is a defect conformal manifold leading to a continuum of possible low-energy theories. We present extensive numerical evidence supporting the emanant magnetic flux at lattice defects, and we test our map between lattice and continuum defects in detail. We also point out a no-go result, which implies that a single $(2+1)\mathrm{D}$ Dirac cone in symmetry class AII is incompatible with a commuting $C_M$ rotational symmetry with $(C_M{)}^M=+1$.

Executing quantum logic in cryogenic quantum computers requires a continuous energy supply from room-temperature control electronics. This dependence on external energy sources creates scalability limitations due to control channel density and heat dissipation. Here, we propose quantum batteries (QBs) as intrinsic quantum energy sources for quantum computation, enabling the thermodynamic limit of zero dissipation for unitary gates. Unlike classical power sources, QBs maintain quantum coherence with their load—a property that, while theoretically studied, remains unexploited in practical quantum technologies. We demonstrate that initializing a bosonic QB in a Fock state can supply the energy required for arbitrary unitary gates regardless of the circuit’s depth, via the recycling of precharged energy. Crucially, allowing QB-qubit entanglement during computation lowers the QB’s initial energy requirements below established energy-fidelity bounds. This scheme facilitates a universal gate set controlled by a single parameter per qubit: its resonant frequency. The relative detuning of each qubit from the QB’s resonant frequency qualitatively gives rise to two gate types: off resonance and around resonance. The former facilitates dispersive gates that allow multiqubit parity probing while the latter enables energy exchange between the QB and the qubits, driving both population transfer and entanglement generation. This mechanism utilizes the all-to-all connectivity of the shared-resonator architecture to go beyond the standard single- and two-qubit native gates of current platforms with multiqubit gate timescales of few $\pi /g$, where $g$ is the qubit-resonator coupling. The resultant speedup also includes superextensive gates between symmetric Dicke states, characteristic of QB systems. Using a QB eliminates the need for individual drive lines, significantly reducing wiring overhead and potentially quadrupling the number of qubits that can be integrated within cryogenic systems, thereby offering a scalable architecture for quantum computing.

The isospin flavors in condensed matters can be continuously broken, forming various symmetry-broken quantum states. In moiré crystals, the competition between different isospin configurations can be effectively tuned by the twist angles and stacking orders. Here we report twisted double rhombohedral-trilayer-graphene as a new twisted crystalline flatband system showing rich moiré dependent topological phenomena. In devices with small twist angles, programmable Chern insulators with Chern number $C=3$ at integer moiré filling $v=1$ have been observed. We have further revealed an exotic hidden order which can quench the Chern insulator as well as multiple first-order transitions between different symmetry-broken phases. Interestly, in the device with a slightly larger twist angle, multiple Chern insulators with $C=1$ at fractional moiré fillings including $v=1/4$, $1/3$, and $1/2$ have been observed, whereas the Chern insulator at $v=1$ is absent. Our study demonstrated the twisted flatbands form rhombohedral-multilayer-graphene as a new platform to study tunable high Chern insulators as well as new devices for quantum storage and computation.

Gallium nitride (GaN) as a direct band gap semiconductor played a central role in the historical development of efficient blue light-emitting diode and laser diode, in which its intrinsic wide band gap shrinks through the addition of indium (In), thus tuning the color of the light by changing the chemistry. This alloying approach, however, does not allow for dynamic and reversible modulation of the band gap and emission color. Here we show that ultralarge tensile elastic strain can be introduced in microfabricated single crystal GaN microbridges and offer an unprecedented opportunity to modulate its band structure and optoelectronic properties continuously through deep elastic strain engineering. The elastic strain-induced energy band gap modulation was characterized and quantified by in situ cathodoluminescence (CL) as well as via strained GaN devices inside a scanning electron microscope. The CL emission of deeply strained ($>5\%$) GaN microbridges has shown substantial band gap reduction from $\sim 3.4$ to 2.96 eV ($\sim 365$ to 420 nm in wavelength), making its optical emission shift from invisible or UV to the blue visible regime. Experimental results agree well with ab initio calculation of the change in band gap with increased strain. This dynamic, reversible, and well-controllable strain engineering would facilitate novel device applications in power electronics and optoelectronics.