We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in Calderbank-Shor-Steane stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice surgery and some of its recent generalizations are shown to be special cases of homological measurement. Using this framework, we develop a specific protocol called edge expanded homological measurement for fault-tolerant measurement of arbitrary logical Pauli operators of general quantum low density parity-check codes, requiring a number of ancillary qubits growing only linearly with the weight of the logical operator measured, and guarantee that the distance of the code is preserved. We further benchmark our protocol numerically in a photonic architecture based on Gottesman-Kitaev-Preskill qubits, showing that the logical error rates of various codes are on par with other methods requiring more ancilla qubits.

Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibit the quantum anomalous Hall effects under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show signs of extensive entropy usually attributed to local moments. The combination of these features leads to a question: Can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier orbitals? In this work, we answer the question affirmatively by proposing a minimal model for the flat topological bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wave functions that closely approximate those of the Bistritzer-MacDonald model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at $\mathrm{\Gamma }$, giving rise to a small parameter $s$ that makes the model analytically tractable. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without invoking any extra degrees of freedom. These moments are nonlocal due to topology-enforced power-law tails, yet have parametrically small overlap. We develop a systematic diagrammatic expansion in which the self-energy can be computed exactly to leading order in $s^2$ in the fluctuating moment regime and predict momentum-resolved spectral functions for future experiments to verify. Our key discovery is a charge-neutrality state we refer to as the “Mott semimetal” characterized by high flavor entropy and a Mott gap that exists throughout most of the Brillouin zone but closes at the $\mathrm{\Gamma }$ point. At $\mathrm{\Gamma }$, the spectral function contains a single Dirac cone per spin per valley and responds to perturbations in an exotic manner that is distinct from any other theoretical picture of TBG. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero quasiparticle residue at the $\mathrm{\Gamma }$ point. The model accurately reproduces results from finite-temperature thermodynamic measurements, leads to new experimental predictions, and resolves the problem of the emergence of Hubbard physics in isolated topological bands.

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in ${}^{239}\mathrm{Pu}$ nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to ${}^{239}\mathrm{Pu}$ fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate ${}^{63}\mathrm{Cu}$ and ${}^{239}\mathrm{Pu}$ total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with ${\mathrm{Al}}_2{\mathrm{O}}_3$ and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorized structure with a rank growing proportionally to its dimension remains a challenge, except when it is rotationally invariant. In this case, the information-theoretic limits and an efficient Bayes-optimal denoising algorithm, called the rotational invariant estimator, are known. Beyond this setting, few results can be found. The reason is that the model is not a usual spin system because of the growing rank dimension, nor a matrix model (as appearing in high-energy physics) due to the lack of rotation symmetry, but rather a hybrid between the two. In this paper, we make progress toward the understanding of Bayesian matrix denoising when the hidden signal is a factored matrix $\mathbf{X}{\mathbf{X}}^{⊺}$ that is not rotationally invariant. Monte Carlo simulations suggest the existence of a denoising-factorization transition separating a phase where denoising using the rotational-invariant estimator remains Bayes-optimal due to universality properties of the same nature as in random matrix theory, from one where universality breaks down and better denoising is possible, though algorithmically hard. We also argue that it is only beyond the transition that factorization, i.e., estimating $\mathbf{X}$ itself, becomes possible up to irresolvable ambiguities. On the theoretical side, we combine mean-field techniques in an interpretable multiscale fashion in order to access the minimum mean-square error and mutual information. Interestingly, our alternative method yields equations reproducible by the replica approach of Sakata and Kabashima. Using numerical insights, we delimit the portion of phase diagram where we conjecture the mean-field theory to be exact and correct it using universality when it is not. Our complete Ansatz matches well the numerics in the whole phase diagram when considering finite-size effects.

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

Antiferromagnetic materials (AFMs) have been gaining lots of attention due to their great potential in spintronics devices and the recently discovered novel spin structure in the momentum space, i.e., $C$-paired spin-valley or spin-momentum locking (CSML), where spins and valleys or momenta are locked to each other due to the crystal symmetry guaranteeing zero magnetization. Here, we systematically study CSMLs and propose a general theory and algorithm using little cogroup and coset representatives, which reveals that 12 elementary kinds of CSMLs, determined by the geometric relation of spins and valleys and the essential symmetry guaranteeing zero magnetization, are sufficient to fully represent all possible CSMLs. By combining the proposed algorithm and high-throughput first-principles calculations, we predict 38 magnetic point groups and identify 142 experimentally verified AFMs that can realize CSML. Besides predicting new materials, our theory can naturally reveal underlying mechanisms of CSMLs’ responses to external fields. As an example, two qualitatively different types of piezomagnetism via occupation imbalance or spin tilting are predicted in ${\mathrm{RbV}}_2{\mathrm{Te}}_2\mathrm{O}$. The algorithm and conclusions can be directly extended to the locking between valley or momentum and any other pseudovector degree of freedom, e.g., Berry curvature, as exemplified in ${\mathrm{RbV}}_2{\mathrm{Te}}_2\mathrm{O}$ and the new proposed piezo-Hall effect, where a strain can induce a nonzero anomalous Hall conductance. In addition, the proposed concept and methodology can be straightforwardly applied to other symmetry groups, such as spin group.

Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight $w$. For sufficiently small values of $w$ and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of $w$ values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

High-speed, nonvolatile tunability is critical for advancing reconfigurable photonic devices used in neuromorphic information processing, sensing, and communication. Despite significant progress in developing phase-change and ferroelectric materials, achieving highly efficient, reversible, rapid switching of optical properties has remained a challenge. Recently, sliding ferroelectricity has been discovered in 2D semiconductors, which also host strong excitonic effects. Here, we demonstrate that these materials enable nanosecond ferroelectric switching in the complex refractive index, substantially modulating their linear optical responses. The maximum index modulation reaches about 4, resulting in a relative reflectance change exceeding 85%. Both on and off switching occur within 2.5 ns, with switching energy at femtojoule levels. The switching mechanism is driven by tuning the excitonic peak splitting of a rhombohedral molybdenum disulfide bilayer in an engineered Coulomb screening environment. This new switching mechanism establishes a new direction for developing high-speed, nonvolatile optical memories and highly efficient, compact reconfigurable photonic devices. Additionally, the demonstrated imaging technique offers a rapid method to characterize domains and domain walls in 2D semiconductors with rhombohedral stacking.

Atomic defects underpin the properties of van der Waals materials, and their understanding is essential for advancing quantum and energy technologies. Scanning transmission electron microscopy is a powerful tool for defect identification in atomically thin materials, and extending it to multilayer and beam-sensitive materials would accelerate their exploration. Here, we establish a comprehensive defect library in a bilayer of the magnetic quasi-1D semiconductor CrSBr by combining atomic-resolution imaging, deep learning, and ab initio calculations. We apply a custom-developed machine learning work flow to detect, classify, and average point vacancy defects. This classification enables us to uncover several distinct Cr interstitial defect complexes, combined Cr and Br vacancy defect complexes, and lines of vacancy defects that extend over many unit cells. We show that their occurrence is in agreement with our computed structures and binding energy densities, reflecting the intriguing layer interlocked crystal structure of CrSBr. Our ab initio calculations show that the interstitial defect complexes give rise to highly localized electronic states. These states are of particular interest due to the reduced electronic dimensionality and magnetic properties of CrSBr and are, furthermore, predicted to be optically active. Our results broaden the scope of defect studies in challenging materials and reveal new defect types in bilayer CrSBr that can be extrapolated to the bulk and to over 20 materials belonging to the same FeOCl structural family.

A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits’ coherence time by 3 orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states $|{\mathrm{\Phi }}^{+}⟩$ and $|{\mathrm{\Psi }}^{+}⟩$ in less than or equal to $313\mathrm{\mu }\mathrm{s}$ with fidelities up to ${98}_{-3}^{+2}\%$ in a static magnetic gradient of only $19.09\mathrm{T}/\mathrm{m}$. At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.

The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is challenging. We formulate an efficiently implementable multiscale entanglement renormalization ansatz model of AdS/CFT, providing a mapping between a ($1+1$)-dimensional critical spin system and a ($2+1$)-dimensional bulk theory. Using a combination of numerics and analytics, we show that the bulk theory arising from this optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have one- and two-particle energies matching the predictions for matter coupled to AdS gravity at long distances, thus displaying key features of AdS physics. We show that these potentials arise as a direct consequence of entanglement renormalization and discuss how this approach can be used to efficiently simulate bulk dynamics using realistic quantum devices.

We describe a quantum algorithm for the Planted Noisy $k\mathrm{XOR}$ Problem (also known as Sparse Learning Parity with Noise) that achieves a nearly quartic (fourth-power) speedup over the best known classical algorithm while using exponentially less space. Our work generalizes and simplifies prior work of Hastings [Quantum 4, 237 (2020)], by building on his quantum algorithm for the tensor principal component analysis (PCA) problem. We achieve our quantum speedup using a general framework based on the Kikuchi method (recovering the quartic speedup for Tensor PCA), and we anticipate it will yield similar speedups for further planted inference problems. These speedups rely on the fact that planted inference problems naturally instantiate the guided sparse Hamiltonian problem. Since the Planted Noisy $k\mathrm{XOR}$ Problem has been used as a component of certain cryptographic constructions, our work suggests that some of these are susceptible to superquadratic quantum attacks.

The spin-$1/2$ kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the reports of $1/9$ magnetization plateau and magnetic oscillations in a kagome antiferromagnet ${\mathrm{YCu}}_3{(\mathrm{OH})}_6{\mathrm{Br}}_2[{\text{Br}}_x{(\mathrm{OH})}_{1-x}]$ (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here, we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 T) down to 0.46 K, and the $1/9$ plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of $1/9$ plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states contributed by other spinon Fermi surfaces. Surprisingly, the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near 30 T above the $1/9$ plateau which is another hallmark of fermionic excitations in the specific heat. This combination of gapless behavior and the double-peak structure strongly suggests that the $1/9$ plateau in YCOB is nontrivial and hosts fermionic quasiparticles.

The discovery of multiple superconducting phases in ${\mathrm{UTe}}_2$ boosted research on correlated-electron physics. This heavy-fermion paramagnet was rapidly identified as a reference compound to study the interplay between magnetism and unconventional superconductivity with multiple degrees of freedom. The proximity to a ferromagnetic quantum phase transition was initially proposed as a driving force to triplet-pairing superconductivity. However, we find here that long-range incommensurate antiferromagnetic order is established under pressure. The propagation vector ${\mathbf{k}}_{\mathbf{m}}=(0.07,0.33,1)$ of the antiferromagnetic phase is close to a wave vector where antiferromagnetic fluctuations have previously been observed at ambient pressure. These elements support that ${\mathrm{UTe}}_2$ is a nearly antiferromagnet at ambient pressure. Our work appeals for theories modeling the evolution of the magnetic interactions and electronic properties, driving a correlated paramagnetic regime at ambient pressure to a long-range antiferromagnetic order under pressure. A deeper understanding of itinerant-$f$-electron magnetism in ${\mathrm{UTe}}_2$ will be a key for describing its unconventional superconducting phases.

Exotic quantum solids can host electronic states that spontaneously break rotational symmetry of the electronic structure, such as electronic nematic phases and unidirectional charge density waves (CDWs). When electrons couple to the lattice, uniaxial strain can be used to anchor and control this electronic directionality. Here, we reveal an unusual impact of strain on unidirectional “smectic” CDW orders in kagome superconductors ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ using spectroscopic-imaging scanning tunneling microscopy. We discover local decoupling between the smectic electronic director axis and the direction of anisotropic strain. While the two can generally be aligned along the same direction in regions of a small CDW gap, the tendency for alignment decreases in regions where the CDW gap is the largest. This feature, in turn, suggests nanoscale variations in smectic susceptibility, which we attribute to a combination of local strain and electron correlation strength. Overall, we observe an unusually high decoupling rate between the smectic electronic director of the three-state Potts order and anisotropic strain, revealing weak smectoelastic coupling in the CDW phase of kagome superconductors. This finding is phenomenologically different from the extensively studied nematoelastic coupling in the Ising nematic phase of Ising nematic phase of Fe-based superconductor bulk single crystals, providing a contrasting picture of how strain can control electronic unidirectionality in different families of quantum materials.

Spin-boson models involving many interacting spins and bosons are ubiquitous in quantum simulation platforms. At the same time, characterizing the dynamics of these quantum systems represents a significant challenge. Here, we consider general spin-boson models where bosons are subject to Markovian dissipation (e.g., due to cavity loss). We present an exact hybrid quantum-classical stochastic approach where the solution of a classical stochastic equation—mimicking the bosonic modes—is input into a quantum stochastic equation for the spins. Furthermore, the spins are effectively decoupled for each stochastic realization, which nevertheless comes at the expense of sampling over unphysical states. In contrast with existing stochastic approaches based on the influence functional formalism, we place no restriction (factorizability or Gaussianity) on the initial state, or the spin-boson coupling (except that it be linear in the bosonic operator). Markovian dissipation, being at the heart of our approach, renders the stochastic equations Markovian even in the strong coupling regime. Furthermore, it ensures hermiticity (though not positivity) of the density matrix for each realization, thus improving the convergence of stochastic sampling. Interestingly, we find a condition on the classical simulability of the system based solely on the single atom cooperativity even in a many-body setting. We benchmark and showcase the utility of our approach in several examples, specifically in cases where a direct numerical computation is unfeasible.

Controlling electrically stimulated quantum light sources (QLSs) is key for developing integrated and low-scale quantum devices. The underlying mechanisms leading to electrically driven quantum emission, however, are complex, as a large number of electronic states of the system can be involved and, thus, impact the emission dynamics. Here, we use a scanning tunneling microscope to electrically excite a model QLS, namely, a single ZnPc molecule, and disentangle the interplay of charge transfer and excited state formation. The luminescence spectra reveal two lines, associated to the emission of the neutral (exciton) and positively charged (trion) ZnPc, both exhibiting single-photon source behavior. In addition, we find a correlation between the charged and neutral emission, specifically, the signature of a photon cascade in which the radiative decay of the molecular trion is followed by the formation and decay of the exciton. By adjusting the charging vs discharging rate, we show that we can control these emission statistics. This generic strategy is further established by a comprehensive rate equation model comprising a variety of states that mediate excited state formation in the electrically driven single and cascaded photon emission process, revealing the complex internal dynamics of the molecular junction.

Significant progress toward a theory of high-temperature superconductivity in cuprates has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions, while essential for constructing a comprehensive theory, remain challenging due to the complex relationship between real materials and the parameters of the effective models. By combining cluster dynamical mean-field theory and density functional theory in a charge-self-consistent manner, here we show that the goal of material-specific predictions for high-temperature superconductors from first principles is within reach. To demonstrate the capabilities of our approach, we take on the challenge of explaining the remarkable physics of multilayer cuprates by focusing on the two representative ${\mathrm{Ca}}_{(1+n)}{\mathrm{Cu}}_n{\mathrm{O}}_{2n}{\mathrm{Cl}}_2$ and ${\mathrm{HgBa}}_2{\mathrm{Ca}}_{(n-1)}{\mathrm{Cu}}_n{\mathrm{O}}_{(2n+2)}$ families. We shed light on the microscopic origin of many salient features of multilayer cuprates, in particular, the $n$ dependence of their superconducting properties. The growth of $T_c$ from the single-layer to the trilayer compounds is here explained by the reduction of the charge transfer gap and, consequently, the growth of superexchange $J$ as $n$ increases. The origin of both is traced to the appearance of low-energy conduction bands reminiscent of standing wave modes confined within the stack of ${\mathrm{CuO}}_2$ planes. We interpret the ultimate drop of $T_c$ for $n\ge 4$ as a consequence of the inhomogeneous doping between the ${\mathrm{CuO}}_2$ planes, which prevents the emergence of superconductivity in the inner planes due to their insufficient effective hole doping, as we also highlight the existence of a minimal doping (4%) required for superconductivity to appear in one of the planes. We explain material-specific properties such as the larger propensity of ${\mathrm{HgBa}}_2{\mathrm{Ca}}_{(n-1)}{\mathrm{Cu}}_n{\mathrm{O}}_{(2n+2)}$ to superconduct compared with ${\mathrm{Ca}}_{(1+n)}{\mathrm{Cu}}_n{\mathrm{O}}_{2n}{\mathrm{Cl}}_2$. We also find the coexistence of arcs and pockets observed with photoemission, the charge redistribution between copper and oxygen, and the link to the pseudogap. Our work establishes a framework for comprehensive studies of high-temperature superconducting cuprates, enables detailed comparisons with experiment, and, through its ab initio settings, unlocks opportunities for theoretical material design of high-temperature superconductors.

Predicting the emergent properties of impurities immersed in a quantum bath is a fundamental challenge that can defy quasiparticle treatments. Here, we measure the spectral properties and real-time dynamics of mobile impurities injected into a weakly interacting homogeneous Bose-Einstein condensate, using two broad Feshbach resonances to tune both the impurity-bath and intrabath interactions. For attractive impurity-bath interactions, the impurity spectrum features a single branch, which away from the resonance corresponds to a well-defined attractive polaron; near the resonance, we observe dramatic broadening of this branch, suggesting a breakdown of the quasiparticle picture. For repulsive impurity-bath interactions, the spectrum features two branches: the attractive branch that is dominated by excitations with energy close to that of the Feshbach dimer, but has a many-body character, and the repulsive polaron branch. Our measurements show that the behavior of impurities in weakly interacting baths is remarkably universal, controlled only by the bath density and a single dimensionless interaction parameter.

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.