Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that could allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between nitrogen-vacancy (NV) electron spins enabling scalable entanglement. Entanglement between dipolar-coupled NV spin pairs has been demonstrated but with a limited fidelity, and its error sources have not been characterized. Here, we design and implement a robust two-qubit gate between NV electron spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of $F_{2\mathrm{q}}=(96.0\pm 2.5)\%$ under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.

How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In particular, growth profiles may differ in their degree of spatial variation and growth anisotropy; however, the criteria that distinguish observed patterns of growth from other possible alternatives are not understood. Here we exploit the mathematical formalism of quasiconformal transformations to formulate the problem of “growth pattern selection” quantitatively in the context of 3D shape formation by growing 2D epithelial sheets. We propose that nature settles on growth patterns that are the “simplest” in a certain way. Specifically, we demonstrate that growth pattern selection can be formulated as an optimization problem and solved for the trajectories that minimize spatiotemporal variation in areal growth rates and deformation anisotropy. The result is a complete prediction for the growth of the surface, including not only a set of intermediate shapes, but also a prediction for cell displacement along those surfaces in the process of growth. Optimization of growth trajectories for both idealized surfaces and those observed in nature show that relative growth rates can be uniformized at the cost of introducing anisotropy. Minimizing the variation of programmed growth rates can therefore be viewed as a generic mechanism for growth pattern selection and may help us to understand the prevalence of anisotropy in developmental programs.

One of the main interests of 2D materials is their ability to be assembled with many degrees of freedom for tuning and manipulating excitonic properties. There is a need to understand how the structure of the interfaces between atomic layers influences exciton properties. Here we use cathodoluminescence and time-resolved cathodoluminescence experiments to study how excitons interact with the interface between two twisted hexagonal boron nitride ($h$-BN) crystals with various angles. An efficient capture of free excitons by the interface is demonstrated, which leads to a population of long-lived and interface-localized (2D) excitons. Temperature-dependent experiments indicate that for high twist angles, these excitons localized at the interface further undergo a self-trapping. It consists in a distortion of the lattice around the exciton on which the exciton traps itself. Our results suggest that this exciton-interface interaction causes the broad 4-eV optical emission of highly twisted $h$-BN–$h$-BN structures. Exciton self-trapping is finally discussed as a common feature of $s{p}^2$ hybridized boron nitride polytypes and nanostructures due to the ionic nature of the B—N bond and the small size of their excitons.

In the realm of long-distance quantum communication, asynchronous measurement-device-independent quantum key distribution (AMDI-QKD) stands out for its experimental simplicity and high key rate generation. Despite these advantages, there exists a challenge in finding a balance between simplifying the laser system further and achieving high key rates. To address this challenge, we have devised a postmeasurement compensation scheme to accurately estimate the mutual frequency offset between two compact lasers using just the announced quantum-signal detection results, thereby obviating the need for optical reference light. As a result, we demonstrate an AMDI-QKD system operating at 2.5 GHz and achieving secure key rates (SKRs) of 537 and $101\mathrm{kbit}/\mathrm{s}$ at distances of 100 and 201 km, respectively, showcasing a significant key rate improvement compared to similar setups. By leveraging ultrastable lasers, we achieve the highest SKRs with measurement-device-independent security within the 100–400-km range. Over 100 km, we reach a remarkable key rate of $1.03\mathrm{Mbit}/\mathrm{s}$, which could enable real-time one-time-pad video encryption. These findings render AMDI-QKD as a promising contender for the establishment of high performance and cost-effective large-scale intercity quantum networks.

Quantum error correction is necessary to perform large-scale quantum computation but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit numbers, but performing computation while maintaining low space cost has required serialization of operations and extra time costs. In this work, we design fast and parallelizable logical gates for qLDPC codes and demonstrate their utility for key algorithmic subroutines such as the quantum adder. Our gate gadgets utilize transversal logical cnots between a data qLDPC code and a suitably constructed ancilla code to perform parallel Pauli product measurements (PPMs) on the data logical qubits. For hypergraph product codes, we show that the ancilla can be constructed by simply modifying the base classical codes of the data code, achieving parallel PPMs on a subgrid of the logical qubits with a lower space-time cost than existing schemes for an important class of circuits. Generalizations to 3D and 4D homological product codes further feature fast PPMs in constant depth. While prior work on qLDPC codes has focused on individual logical gates, we initiate the study of fault-tolerant compilation with our expanded set of native qLDPC code operations, constructing algorithmic primitives for preparing $k$-qubit Greenberger-Horne-Zeilinger states and distilling or teleporting $k$ magic states with $O(1)$ space overhead in $O(1)$ and $O(\sqrt{k}\log k)$ logical cycles, respectively. We further generalize this to key algorithmic subroutines, demonstrating the efficient implementation of quantum adders using parallel operations. Our constructions are naturally compatible with reconfigurable architectures such as neutral atom arrays, paving the way to large-scale quantum computation with low space and time overheads.

While the physics of disordered packing in nongrowing systems is well understood, unexplored phenomena can emerge when packing takes place in growing domains. We study the arrangements of pigment cells (chromatophores) on squid skin as a biological example of a packed system on an expanding surface. We find that relative density fluctuations in cell numbers grow with spatial scale. We term this behavior “hyperdisordered,” in contrast with hyperuniform behavior in which relative fluctuations tend to zero at large scales. We find that hyperdisordered scaling, akin to that of a critical system, is quantitatively reproduced by a model in which hard disks are randomly inserted in a homogeneously growing surface. In addition, we find that chromatophores increase in size during animal development but maintain a stationary size distribution. The physical mechanisms described in our work may apply to a broad class of growing dense systems.

We propose a “minimal” fractional topological insulator (mFTI), motivated by the recent experimental report on the fractional quantum spin-Hall effect in a transition metal dichalcogenide moiré system. The observed effect suggests the possibility of a topological state living in a pair of half-filled conjugate Chern bands with Chern numbers $C=\pm 1$. We propose the mFTI as a novel candidate topological state in the half-filled conjugate Chern bands. The mFTI is characterized by the following features. (1) It is a fully gapped topological order (TO) with 16 Abelian anyons if the electron is considered trivial (32 including electrons), (2) the minimally charged anyon carries electric charge $e^{*}=e/2$, together with the fractional quantum spin-Hall conductance, implying the robustness of the mFTI’s gapless edge state whenever time-reversal symmetry and charge conservation are present, and (3) the mFTI is minimal in the sense that it has the smallest total quantum dimension (a metric for the TO’s complexity) within all the TOs that can potentially be realized at the same electron filling and with the same Hall transports; the mFTI is also the unique minimal TO that respects time-reversal symmetry. (4) The mFTI is the common descendant of multiple valley-decoupled “product TOs” with larger quantum dimensions. It can also be viewed as the result of gauging multiple symmetry-protected topological states. Similar mFTIs are classified and constructed for a pair of $1/q$-filled conjugate Chern bands. We further classify the mFTIs via the stability of the gapless interfaces between them.

Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit average symmetries—symmetries that keep the total ensemble invariant but not on each individual state. In this work, we present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, we formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics. Notably, we discover that (1) the definition and classification of ASPT phases in decohered and disordered systems exhibit subtle differences, (2) despite these differences, ASPT phases in both settings can be classified and characterized under a unified framework of defect decoration and spectral sequence, (3) this systematic classification uncovers a plethora of ASPT phases that are intrinsically mixed, implying they can exclusively manifest in decohered or disordered systems where part of the symmetry is average, and (4) similarly for ASET, we find intrinsically disordered phases exhibiting exotic anyon behaviors—the ground states of such phases necessarily contain localized anyons, with gapless (yet still localized) excitation blue spectra.

Polaritons, formed by strong light-matter interactions, open new avenues for studying topological phases, where the spatial and time symmetries can be controlled via the light and matter components, respectively. However, most research on topological polaritons has been confined to hexagonal photonic lattices featuring Dirac cones at large wave numbers. This restricts key topological properties and device performance, including sub-meV gap sizes that hinder further experimental investigations and future applications of polariton Chern insulator systems. In this study, we move beyond the traditional Dirac cone framework and introduce two alternative band structures in photonic crystals (PhCs) as promising platforms for realizing polariton Chern bands: bands with symmetry-protected bound states in the continuum and bands with symmetry-protected degeneracies at the $\mathrm{\Gamma }$ points. These band structures are prevalent in various PhC lattices and have features crucial for experimental studies. We show examples of higher Chern number bands, more uniform Berry curvature distributions, and experimentally feasible systems capable of achieving topological gap greater than 10 meV. Our findings show the broad applicability of polariton Chern bands in 2D PhCs and provide design principles for enhancing the functionality and performance of topological photonic devices, opening up exciting possibilities for better understanding and using topological physics.

We propose a tensor network approach known as the locally purified density operator (LPDO) to investigate the classification and characterization of symmetry-protected topological phases in open quantum systems. We extend the concept of injectivity, originally associated with matrix product states and projected entangled pair states, to LPDOs in $(1+1)\mathrm{D}$ and $(2+1)\mathrm{D}$ systems, unveiling two distinct types of injectivity conditions that are inherent for short-range entangled density matrices. Within the LPDO framework, we outline a classification scheme for decohered average symmetry-protected topological (ASPT) phases, consistent with earlier results obtained through spectrum sequence techniques. However, our approach offers an intuitive and explicit construction of ASPT states with the decorated domain-wall picture emerging naturally. We illustrate our framework with ASPT phases protected by a weak global symmetry and strong fermion parity symmetry and then extend it to a general group structure. Moreover, we derive both the classification data and the explicit forms of the obstruction functions using the LPDO formalism, particularly in the case of nontrivial group extension between strong and weak symmetries, where intrinsic ASPT phases may emerge. We demonstrate constructions of fixed-point LPDOs for ASPT phases in both $(1+1)\mathrm{D}$ and $(2+1)\mathrm{D}$ and discuss their physical realization in decohered or disordered systems. In particular, we construct examples of intrinsic ASPT states in $(1+1)\mathrm{D}$ and $(2+1)\mathrm{D}$ using the LPDO formalism.

We analyze the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement entropy of such postmeasurement states, we prove that macroscopic long-ranged entanglement is generated above some constant critical depth in several natural classes of circuit architectures, which include brickwork circuits and random holographic tensor networks. This behavior had been conjectured based on previous works, which utilize nonrigorous methods such as replica theory calculations, or work in regimes where the local Hilbert space dimension grows with system size. To establish our lower bound, we develop new replica-free theoretical techniques that leverage tools from multiuser quantum information theory, which are of independent interest, allowing us to map the problem onto a statistical mechanics model of self-avoiding walks without requiring large local Hilbert space dimension. Our findings have consequences for the complexity of classically simulating sampling from random shallow circuits and of contracting tensor networks. First, we show that standard algorithms based on matrix product states which are used for both these tasks will fail above some constant depth and bond dimension, respectively. In addition, we also prove that these random constant-depth quantum circuits cannot be simulated by any classical circuit of sublogarithmic depth.

Proximity ferroelectricity has recently been reported as a new design paradigm for inducing ferroelectricity, where a nonferroelectric polar material becomes a ferroelectric one by interfacing with a thin ferroelectric layer. Strongly polar materials, such as AlN and ZnO, which were previously unswitchable with an external field below their dielectric breakdown fields, can now be switched with practical coercive fields when they are in intimate proximity to a switchable ferroelectric. Here, we develop a general Landau-Ginzburg theory of proximity ferroelectricity in multilayers of nonferroelectrics and ferroelectrics to analyze their switchability and coercive fields. The theory predicts regimes of both “proximity switching,” where the multilayers collectively switch, and “proximity suppression,” where they collectively do not switch. The mechanism of the proximity ferroelectricity is an internal electric field determined by the polarization of the layers and their relative thickness in a self-consistent manner that renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier. Further reduction in the coercive field emerges from charged defects in the bulk that act as nucleation centers. The application of the theory to proximity ferroelectricity in ${\mathrm{Al}}_{\mathrm{x}\text{−}1}{\mathrm{Sc}}_{\mathrm{x}}\mathrm{N}/\mathrm{AlN}$ and ${\mathrm{Zn}}_{1\text{−}\mathrm{x}}{\mathrm{Mg}}_{\mathrm{x}}\mathrm{O}/\mathrm{ZnO}$ bilayers is demonstrated. The theory further predicts that dielectric-ferroelectric and paraelectric-ferroelectric multilayers can potentially lead to induced ferroelectricity in the dielectric or paraelectric layers, resulting in the entire stack being switched, an exciting avenue for new discoveries. This thawing of “frozen ferroelectrics,” paraelectrics, and potentially dielectrics with high dielectric constants promises a large class of new ferroelectrics with exciting prospects for previously unrealizable domain-patterned optoelectronic and memory technologies.

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited scalability of current near-term algorithms. Meanwhile, assuming a typical architecture for fault-tolerant quantum computing (FTQC), realistic applications inevitably require a vast number of qubits, typically exceeding ${10}^6$, which seems far beyond near-term realization. In this work, to bridge the gap between the NISQ and FTQC eras, we propose an alternative approach to achieve practical quantum advantages on early-FTQC devices. Our framework is based on partially fault-tolerant logical operations to minimize spatial overhead and avoids the costly distillation techniques typically required for executing non-Clifford gates. To this end, we develop a space-time efficient state preparation protocol to generate an ancillary non-Clifford state consumed for implementing an analog rotation gate with an arbitrary small angle $\theta$ and a remarkably low worst-case error rate below $\mathcal{O}(|\theta |p_{\mathrm{ph}})$, where $p_{\mathrm{ph}}$ is the physical error rate. Furthermore, we propose several error suppression schemes tailored to our preparation protocol, which are essential to minimize the overhead for mitigating errors. Based on this framework, we present several promising applications that leverage the potential of our framework, including the Trotter simulation and quantum phase estimation (QPE). Notably, we demonstrate that our framework allows us to perform the QPE for an $(8\times 8)$-site Hubbard model with fewer than $6.8\times {10}^4$ qubits and an execution time of 10.6 days (or 14 min with full parallelization) under $p_{\mathrm{ph}}={10}^{-4}$, which is significantly faster than recent classical estimation with tensor network techniques (density matrix renormalization group and projected entangled pair states).

The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moiré flat bands are intrinsically resilient against certain types of disorder. Here, we investigate the robustness of moiré flat bands in the chiral limit of the Bistritzer-MacDonald model—applicable to both platforms in certain limits—and demonstrate drastic differences between the first magic angle and higher magic angles in response to chiral symmetric disorder that arise, for instance, from lattice relaxation. We understand these differences using a hidden constant of motion that permits the decomposition of the non-Abelian gauge field induced by interlayer tunnelings into two decoupled Abelian ones. At all magic angles, the resulting effective magnetic field splits into an anomalous contribution and a fluctuating part. The anomalous field maps the moiré flat bands onto a zeroth Dirac Landau level, whose flatness withstands any chiral symmetric perturbation such as nonuniform magnetic fields due to a topological index theorem—thereby underscoring a topological mechanism for band flatness. Only the first magic angle can fully harness this topological protection due to its weak fluctuating magnetic field. In higher magic angles, the amplitude of fluctuations largely exceeds the anomalous contribution, which we find results in a physically meaningless chiral operator and an extremely large sensitivity to microscopic details and an exponential collapse of the single-particle gap. Through numerical simulations, we further study various types of disorder and identify the scattering processes that are enhanced or suppressed in the chiral limit. Interestingly, we find that the topological suppression of disorder broadening persists away from the chiral limit and is further accentuated by isolating a single sublattice polarized flat band in energy. Our analysis suggests the Berry curvature hot spot at the top of the $K$ and $K^{\prime }$ valence band in the transition metal dichalcogenide monolayers is essential for the stability of its moiré flat bands and their correlated states.

The recent laser excitation of the low-lying ${}^{229}\mathrm{Th}$ isomer transition has started a revolution in ultralight dark matter searches. The enhanced sensitivity of this transition to the large class of dark matter models dominantly coupling to quarks and gluons will ultimately allow us to probe coupling strengths 8 orders of magnitude smaller than the current bounds from optical atomic clocks, which are mainly sensitive to dark matter couplings to electrons and photons. We argue that, with increasing precision, observations of the ${}^{229}\mathrm{Th}$ excitation spectrum will soon give the world-leading constraints. Using data from the pioneering laser excitation of ${}^{229}\mathrm{Th}$ by Tiedau et al. [Phys. Rev. Lett. 132, 182501 (2024)], we present a first dark matter search in the excitation spectrum. While the exclusion limits of our detailed study of the lineshape are still below the sensitivity of currently operating clock experiments, we project the measurement of Zhang et al. [Nature (London) 633, 63 (2024)] to surpass it.

Materials where flattened electronic dispersions arise from destructive phase interference, rather than localized orbitals, have emerged as promising platforms for studying emergent quantum phenomena. Crucial next steps involve tuning such flat bands to the Fermi level, where they can be studied at low energy scales, and assessing their potential for practical applications. Here, we show that the interplay of highly dispersive and ultraflat bands inherent to these systems can lead to extreme interband scattering-induced electron-hole asymmetry, which can be harnessed in thermoelectrics. Our comprehensive theoretical and experimental investigation of ${\mathrm{Ni}}_3{\mathrm{In}}_{1-x}{\mathrm{Sn}}_x$ kagome metals supports this concept, showing that it could lead to thermoelectric performance on par with state-of-the-art semiconductors such as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. In ${\mathrm{Ni}}_3\mathrm{In}$, scattering-induced electron-hole asymmetry is, however, subdued by an exotic conduction mechanism arising from quantum tunneling of charge carriers between Dirac bands, unrelated to the flat band itself. We outline strategies to selectively switch off this tunneling transport through negative chemical pressure or strain. Our study proposes a new direction to explore in topological flat-band systems and vice versa introduces a novel tuning knob for thermoelectric materials.

Identifying efficient pathways to modulate quantum coherence is a crucial step toward realizing ultrafast switching of macroscopic orders, which requires the microscopical understanding of the interplay between multidegrees of freedom. Here, we demonstrate an all-optical method to control the coherent electron and lattice excitation in a prototypical nodal-line semimetal ZrSiS. We show the displacive excitation of two coherent Raman-active phonon modes, which results in a mode-selective renormalization of its topological band structure comparable with previous experimental observations. We subsequently realize an effective manipulation of the coherent lattice vibration, not only for their amplitude, but also a $\pi$-phase shift by tuning the laser intensity and frequency. We pinpoint that such a phase shift originates from the photoinduced carrier redistribution and can, in turn, determine the quasiparticle renormalization, for example, to induce an ultrafast topological Lifshitz transition, which we anticipate can be detected by pump-probe transport measurements. These results address the requirements for a directional pumping of coherent phonons with laser fields and provide the opportunity to explore exotic nonequilibrium physics.

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of approximately 50 qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and, therefore, how much infidelity is suffered) in generating highly entangled states. Here, we describe recent hardware upgrades to Quantinuum’s H2 quantum computer, enabling it to operate on up to 56 qubits with arbitrary connectivity and 99.843(5)% two-qubit gate fidelity. We define a class of circuits with random geometries that become hard to classically simulate in very low depth and implement them utilizing the flexible connectivity of H2. A careful analysis demonstrating the fast saturation of classical simulation complexity with depth indicates that H2 can yield data well beyond the reach of state-of-the art classical simulation methods at unprecedented fidelities. We find that the considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the quantum charge-coupled device architecture as continued progress is made toward building larger machines.