Papers

The interplay between topology and correlation can give rise to exotic collective excitations. The integer and fractional quantum anomalous Hall (QAH) magnets recently discovered in two-dimensional (2D) flatband systems are predicted to host spin excitations distinct from those in conventional magnets. Experimentally, nevertheless, these new excitations remain largely unexplored. Here we investigate spin-valley excitations in a twisted MoTe2 moiré superlattice using resonant ultrafast pump-probe spectroscopy. We observe a metastable spin-valley excitation in the QAH magnet below T ~ 3.7 K that survives reverse magnetic field several times larger than the saturation field. The behavior of this excitation is sharply distinct from ordinary domain walls and magnons, indicating a new type of spin-valley textures unique to topological magnets. We propose that these textures are chiral domain walls with an in-plane winding of the pseudospin order parameter along the domain wall. Their metastability arises from the interplay between the topological winding in real space and the quantum geometry of the parent bands in momentum space through a universal mechanism. These chiral domain walls govern the nonequilibrium dynamics of QAH magnets and may play a central role in their stability. Our study highlights intrinsic quantum geometry effects on spin excitations in topological magnets; and provides key insights into the fundamental mechanism limiting stability of topological protection.

Non-Markovianity can be characterized by performing a series of successive measurements and analyzing departures of the corresponding outcome statistics from a Markovian probabilistic structure. Considering a system coupled with its environment via a dephasing interaction, we show that joint outcome probabilities can be written in terms of a set of two-time environment correlations. Their definition involves forward and backward propagators with different Hamiltonians, associated with a recently introduced generalization of standard Loschmidt echoes [Cormick and Budini, Phys. Lett. A 593, 132011 (2026)]. This result establishes a solid connection between quantum non-Markovianity defined in an operational (measurement-based) way and complex quantum dynamics studied through their sensitivity to dynamical perturbations. We find conditions that guarantee a Markovian (system) behavior and also determine how the generalized echoes can identify information exchanges between the system and its environment. We illustrate our ideas considering examples of spin environments that realize these different dynamical regimes.

Loschmidt echoes are a well-established method to characterize dynamical properties such as quantum chaos and sensitivity to perturbations. Here we present a straightforward generalization that identifies non-classical dynamical behavior. The generalized echoes involve four forward-backward time propagators. If these propagators do not commute, one can readily identify signatures of this property in the relations between echoes. As an example, detection of intrinsic non-commuting quantum features is analyzed in critical dynamics of a spin chain. Interestingly, this phenomenon is also observed for Gaussian dynamics and high temperature limits which are generally regarded as classical.

Spin waves are promising signal carriers for microwave control at the micrometer scale. However, realizing low-damping, tunable control of spin-wave propagation remains a central challenge. Here we use magnetic shielding by superconducting control elements to tune the local spin-wave dispersion and realize temperature-controlled refraction of spin waves in a thin-film magnetic insulator. Using magnetic imaging based on spins in diamond, we characterize the refractive index and demonstrate both positive and negative refraction as well as wavefront shaping by the superconductors. The observed refraction is explained by a geometrical analysis of the superconductivity-induced modification of the hyperbolic spin-wave dispersion. Our results demonstrate that superconductors enable tunable spin-wave optical elements, opening new opportunities for microwave control in classical or quantum information devices.

Hidden Markov models (HMMs) are widely used probabilistic models for discrete sequential data but can be limited when hidden dynamics are complex. Hidden quantum Markov models (HQMMs) generalize HMMs by replacing probability vectors with density matrices and stochastic transitions with quantum operations, enabling richer latent representations. However, existing HQMM learning methods have not consistently outperformed Expectation–Maximization (EM)-trained HMMs on data not generated by quantum processes, limiting their practical applicability. We introduce NS-RIS, Newton–Schulz Retraction-based Inference on the Stiefel manifold, a scalable algorithm for learning trace-preserving HQMMs. NS-RIS uses Newton–Schulz orthogonalization to compute a polar-factor search direction while preserving Stiefel-manifold feasibility, avoiding costly matrix decompositions. We further establish a finite-time stationarity guarantee under standard assumptions on smoothness, stochastic gradients, and finite Newton–Schulz accuracy. Empirically, NS-RIS provides the first benchmark evidence that an HQMM can significantly outperform an EM-trained HMM on data not generated by a quantum model. On synthetic HMM-generated benchmarks, NS-RIS outperforms both EM and the state-of-the-art HQMM method COSM, improving the evaluation metric by an average of 38.5% and by up to 50.6%. On a synthetic HQMM benchmark, it improves the test metric over COSM by 18.9% while reducing runtime by 12.0%. On the real-world Splice classification benchmark, NS-RIS also surpasses both EM and COSM in higher-dimensional latent regimes, reducing mean classification error by 17.9% for latent dimension 6 and 14.9% for latent dimension 8 relative to COSM. These results move HQMMs beyond a theoretical generalization of HMMs and establish them as practical and expressive models for scientific sequence data.

The Equation of State (EoS) of Nuclear Matter at high densities, and particularly that of neutron stars, resists $\mathit{ab}$ $\mathit{initio}$ Quantum Chromodynamics (QCD) computations due to the notorious sign problem of Lattice Gauge Theory at finite chemical potential. A quantum computer deploying QCD in canonical quantization should be able to make substantial progress. We set some basic goals for a future quantum computer to predict the EoS, and thus the basic static observables of the star (mass, radius and Tidal deformability, for example). We then develop the basic theory to address the canonical Hamiltonian in Weyl (time-axial) gauge expressed in normal modes, together with the squared Gauss operator $\mathcal{G}^2$ necessary to execute energy minimization algorithms restricted to the physical Fock subspace. Finally, we deploy our particle-quantum register encoding of a generic field theory to demonstrate QCD at finite chemical potential for a few (three-four) particles with a modest number of momentum modes, by simulating the quantum computer on a classical cluster. This opens the possibility for effective quantum computers to constrain the microscopic physics of neutron stars simultaneously to the operation of third–generation gravitational wave detectors such as the Einstein Telescope, providing more detailed predictions than has been possible until now.

In the process of charging a quantum battery, quantum jumps play a detrimental role because they induce transitions from higher to lower energy levels, leading to energy dissipation. This be- havior directly opposes the fundamental objective of the charging protocol, which is to increase the population of higher-energy states and store usable energy in the system. Furthermore, decoherence introduced by randomness of quantum jumps leads to a mixed state, thereby reducing the amount of energy that can be extracted from the charged quantum battery. Here, we propose a quantum battery comprising an ensemble of three-level atoms in the {\Lambda} configuration to store energy in the metastable state over a long time. We demonstrate that, when spontaneous atomic transitions are restricted to occur solely from the excited state to a metastable state, with decay to the ground state completely suppressed, quantum jumps acquire a constructive character. Under these con- ditions, they drive the quantum battery to a fully charged state, render the entire stored energy extractable, and shorten the duration of the second stage of the charging protocol.

We study the single-particle Green's function $G(x,t)=\langle \sigma^-_x(0)\sigma^+_0(t)\rangle$ in one-dimensional particle-number-conserving random unitary circuits coupled to an external bath. For fixed spacetime disorder, we argue that $G(x,t)$ is governed, in both the strong- and weak-noise limits, by directed waves in a random medium. We find Kardar-Parisi-Zhang (KPZ) scaling in the wandering statistics of the normalized spatial distribution $p(x,t)\propto |G(x,t)|^2$ and in the associated free energy. In particular, its center $\langle x(t)\rangle\equiv\sum_x x\, p(x,t)$ wanders on a length-scale $\mathcal{O}(t^{2/3})$, while sample-to-sample fluctuations of $-\log\sum_x |G(x,t)|^2$ scale as $t^{1/3}$. At weak noise $\gamma \ll 1$, the crossover to the strong-disorder fixed point occurs at a parametrically long time $\mathcal{O}(\gamma^{-3/2})$. These predictions are confirmed numerically using tensor-network simulations of the noisy operator dynamics in individual circuits at moderate noise, and of a phase-annealed proxy retaining hopping disorder at weak noise.

We investigate Bell correlations for a free real quantum scalar field on the noncommutative Moyal plane. Although the free field dynamics and the one-particle sector remain unchanged, the deformation enters through twisted multiparticle statistics and its Fock-space dressing representation. A classical external source coupled locally to the twist-dressed quantum field prepares coherent superpositions of momentum-pair configurations propagating toward two spacelike-separated laboratories. The momentum-dependent twist phases are generally nonfactorizable and generate entanglement between the corresponding wave-packet modes. We show that suitable local mode measurements lead to a violation of the CHSH Bell inequality. The resulting correlations provide an operational probe of the noncommutative structure encoded in the multiparticle sector of the quantum field.

Shadow Tomography is a fundamental problem in quantum information theory. Given multiple copies of an unknown $d$-dimensional quantum state $\rho$ and a known collection of observables $E_1,\ldots,E_M$, the goal is to estimate all expectation values $\{\text{Tr}(\rho E_i)\}_{i=1}^M$ to additive accuracy $\varepsilon$ with probability at least $1-\delta$. An elusive open question from the seminal shadow tomography work of Aaronson is whether this task admits a dimension-independent sample complexity with only polylogarithmic dependence on $M$, as suggested by the best-known lower bounds. In this work, we propose two different quantum protocols for shadow tomography with the best sample complexity \[ O\left( \frac{\log(M)\log(M/\delta)}{\varepsilon^2} \right), \] which is polylogarithmic in the number of observables and independent of the dimension of the unknown state, thereby answering Aaronson's original question while also providing an exponential improvement in the prior best dimension independent sample complexity of shadow tomography from Sinha (STOC 2025) and, more recently, Chen, O'Donnell, Pelecanos, and Wright. Our approach first reduces the general shadow tomography problem to a finite-ensemble estimation problem via a minimax argument. We then develop an observable-independent protocol that repeatedly applies the pretty-good measurement while updating the prior distribution over the finite ensemble according to the measurement outcomes. A tail analysis of the resulting estimation error yields simultaneous accuracy guarantees for all observables and a cubic-logarithmic upper bound. We also introduce a refined recovery-label measurement for the same finite ensemble, which yields the bound in our main theorem.

The geometry of quantum states has emerged as a key ingredient in understanding the linear and nonlinear responses of quantum materials. To date, however, the connection between geometry and nonlinear response is best understood for clean, noninteracting systems at zero temperature. In this work, we develop a theory of multi-state geometry for density matrices and use it to derive sum rules for second-order rectification, making no assumptions about the strength of disorder or interactions. We first show that perturbation theory for thermal density matrices gives rise to two dual information-theoretic connections and an almost complex structure. We introduce a complex, quantum generalization of the Amari-Chentsov tensor of classical information theory, the cQAC tensor, which captures the multi-state geometry of the perturbed density matrix. We derive a zero-temperature sum rule for the frequency-integrated DC rectification response of an insulator as a difference between a ground state third cumulant and the complex distortion tensor, a multi-state geometric quantity built from the cQAC tensor. This generalizes known single-particle sum rules for the shift and nonlinear Hall currents to many-body systems and general perturbations. Specializing to the shift current, we resolve the geometric contribution for multiband insulators into particle-like and hole-like terms. We verify the sum rule numerically in a generalized Kane-Mele model, finding that the geometric contribution can dominate the integrated response. Finally, we show that although the splitting of the sum rule into cumulant and geometric contributions does not survive at nonzero temperature, the measured sum rule for insulators differs from its zero-temperature form by corrections exponentially small in the gap, allowing low-temperature rectification measurements to probe the multi-state geometry of insulators.

Rare fluctuations in physical systems depend on the detailed microphysics responsible for the fluctuations. In classical statistical systems, the large deviation principle has elucidated the role of semi-classics in describing this regime, and has simultaneously provided a the mathematical foundation of statistical mechanics. Large deviation theory for quantum system is considerably less developed. As all physical systems are fundamentally quantum mechanical, this leaves a major gap in our understanding of rare fluctuations relevant to statistical physics, cosmology, and more. In this paper, we develop the practical aspects of the theory of large deviations relevant for calculating rare events in physical systems from quantum walks to cosmology. We first analyze the case of the anharmonic oscillator coupled to a bath, showing explicitly how the system evolves from dominantly statistical (e.g. thermal) to quantum fluctuations. We then generalize these results, showing that the dominant rare fluctuations minimize the measurement-induced relative entropy. This perspective provides a thermodynamic description of a wide range of open quantum systems. We apply these results to random walks that arise in cosmology through stochastic inflation. We show that the evolution of the density matrix of long wavelength fields on a fixed de Sitter background breaks the KMS symmetry, giving rise to a stationary density matrix that does not respect detailed balance.

As quantum computing matures, there is an increasing need for deeper and longer experiments to characterize quantum devices precisely and higher circuit throughput to validate more domain applications. However, this need is hindered by a memory bottleneck at the quantum control system layer, arising from the limited capacity of on-chip block random-access memory (BRAM) and the non-deterministic latency of dynamic random-access memory (DRAM). To break this bottleneck, we present Ant-Q, a memory hierarchy design for the QubiC 2.0 control system that integrates DRAM with BRAM to support pipelined quantum circuit execution while keeping inter-circuit timing deterministic whenever each circuit outlasts the refill of the next. A switch between command buffers then takes a constant 134 ns and, inside a circuit, acts on the qubit as a 144 ns idle. On the bench, Ant-Q runs deep one- and two-qubit randomized benchmarking beyond the command capacity of the baseline. For circuits with at least 1000 shots, it reduces the time the board spends beyond the circuit execution from 18.91%-104.54% to at most 0.53% of the execution time, and it improves the board-level throughput of 30-circuit batches by 51.06% against a baseline with the same shared tables (59.90% against the stock baseline). On a transmon qubit, Ant-Q executes a 5101-Clifford sequence and acquires uninterrupted 100 s Ramsey records with 0.01 Hz frequency spacing. In simulations, these records detect 1/f frequency noise of 1.37 and 1.62 times lower spectral density than the same records split into the 2.048 s runs of the baseline. The measured spectra resolve no 1/f component and match the measurement floor from 0.1 to 100 Hz. Ant-Q has been merged into the open-source QubiC gateware and software.

Quantum data hiding asks how much distinguishing power can be lost when global measurements are restricted to local measurements and classical communication. In this work, we establish sharp results and improved bounds for several natural classes of restricted measurements. For bipartite systems on $\mathbb C^n\otimes\mathbb C^m$, we prove that the optimal data-hiding ratios against separable and LOCC measurements are both $\min\{n,m\}$. This result follows from a stronger result that, for every $2\le p\le\infty$, the largest centered Schatten $p$-ball whose associated binary measurements are implementable by finite-round LOCC has radius $\min\{n,m\}^{2/p-1}$. This strengthens the classic separable-ball theorems, while also providing an explicit finite-round LOCC implementation. For Alice-first one-way LOCC with Alice's local dimension equal to $n$, we prove that the optimal ratio is $(1+o(1))n$, with the upper bound obtained from a Gaussian rank-one POVM. For local operations without communication, we improve the universal upper bound to $(\pi\sqrt3/4+o(1))\min\{n,m\}$.

We apply time-reversal symmetry to quantum codes and show that it imposes parity selection rules on the physical error algebra. A time-reversal-invariant logical qubit on an odd number of spins is a Kramers doublet, forcing every even-weight Pauli to act as a scalar. Consequently, all even-weight Knill–Laflamme conditions hold automatically, so single-qubit error detection implies correction. We then reinterpret the Rains shadow enumerator through time reversal: each coefficient is a sum of error-resolved overlaps between a code and its time-reversed image.

The precision of transport observables can be bounded by the entropy production and the activity of the transport process via kinetic and thermokinetic uncertainty relations. In linear bosonic systems, such uncertainty relations can provide tight bounds when the activity is replaced by a local activity of the measurement contact of interest—even in the strong-coupling regime. How much nonlinearities (or interactions) impact the validity and predictiveness of these local bounds and how much this impact depends on the concrete definition of activity are open questions that we address for two experimentally relevant model systems, a harmonic oscillator network and the intrinsically nonlinear spin-boson model. We thereby provide experimentally testable predictions on how nonlinearities impact or even break local kinetic and thermokinetic precision bounds.

We develop a fully quantized theory of nonlinear Compton scattering driven by a single-mode quantum field. Exact quantum-Volkov states retain pump depletion, back-action, and final-state correlations through displaced or squeezed-displaced Fock-state ladders. A finite Fock-state pump produces discrete photon-transfer edges and a terminal spectral cutoff. In the bright, weakly depleted regime, the exact theory reduces to a Wigner-function weighted-average of scattering probabilities evaluated at fixed complex field amplitudes, with ordinary and generalized Bessel functions describing the harmonic structure for circular and linear polarization, respectively. For squeezed coherent light, the squeezing angle controls the high-energy emission through photon-number fluctuations.

Topologically ordered phases naturally realize quantum error correction through nonlocal encoding of quantum information. More recently, conformal field theories have been shown to realize approximate quantum error-correcting codes, but such constructions generally require fine tuning to criticality. Here we introduce a family of approximate quantum error-correcting codes realized by the chiral edges of two-dimensional topologically ordered phases. The proposed encoding combines the robustness of a gapped topological bulk with the flexibility of gapless edge conformal field theories. To characterize its robustness, we study coherent-information loss under local erasure. We derive an exact expression relating coherent-information loss to relative entropy, reducing the recoverability problem to universal properties of the edge theory. This leads to power-law scaling of coherent-information loss with the size of the erased region. We further show that, for geometrically local erasures near one edge, the two-dimensional chiral edge code is at least as robust as the dimensionally reduced CFT code, and is strictly more robust in several representative examples. For Abelian code subspaces, we further construct a power-law-range recovery map supported on the erased region together with a power-law-range buffer; this recovery map depends only on the code subspace, not on the unknown encoded state. We provide numerical calculations for lattice realizations of compact free boson and Ising CFT examples that support the theoretical predictions of the power-law exponents.

Syndrome-measurement timing is usually treated as a fixed clock cycle of a quantum error-correcting code. For quantum memories, however, the inter-round interval is itself an optimizable control parameter: measuring too rarely allows idling errors to accumulate, whereas measuring too often introduces measurement-induced faults. We propose a phenomenological logical-noise model for this trade-off and analytically show that the optimal syndrome-measurement interval is inversely proportional to the code distance and that this produces an exponential reduction of logical-error rates in the distance relative to constant-interval schedules. Furthermore, for time-dependent idling noise, we develop an adaptive timing strategy based on the measured syndrome activity that outperforms every fixed-interval protocol, with largest gains for short but strong noise bursts. Simulations of rotated surface-code memories with matching decoding validate the phenomenological model, the distance-dependent optimum, and the adaptive-strategy improvement. Moreover, with the experimental noise parameters reported by Google in Nature 638 (2025), our model predicts reductions in logical-error rates per unit time of up to $40\%$.

Non-Gaussian states can exhibit large quantum Fisher information (QFI) in quantum sensing. In optical systems, however, its generation is often probabilistic via the boson-sampling type conditional operation and thus its generation rate is limited. This probabilistic generation of non-Gaussian resource should be taken into account for evaluation of the sensing performance. Then a natural question arising is whether the use of heralded probabilistic non-Gaussian states is better than that of the original deterministic Gaussian states for quantum sensing. In this paper, we answer to this question for single-parameter phase-estimation. By using photon-number conservation in passive linear optical systems, we show that heralded state preparation before parameter encoding can be mapped to a postselection problem after parameter encoding for phase estimation. This mapping allows the success probability of heralding to be included naturally in the metrological performance. We introduce an effective quantum Fisher information (EQFI), defined as the success-probability-weighted QFI of the heralded outputs, and prove that it cannot exceed the QFI of the original Gaussian inputs. The result highlights the importance of resource counting in quantum sensing toward better understanding of the resource efficient advantage of optical quantum sensing.

To probe a bipartite quantum system, one may use arbitrary global operators or restrict to product operators acting separately on the two subsystems. We determine the sharp universal comparison between the resulting norms. For every $z\in M_n\otimes M_m$, we prove $\|z\|_1\leq\sqrt{2}\min\{n,m\}\|z\|_\varepsilon$, where $\|\cdot\|_1$ is the trace norm and $\|\cdot\|_\varepsilon$ is the injective tensor norm associated with the trace norms on $M_n$ and $M_m$. To prove the upper bound, we establish an $L_1$ noncommutative Khintchine inequality whose random coefficients are the entries of a Haar unitary. We also show that the coefficient $\sqrt{2}$ is sharp. As applications, we show that the same sharp constant governs the gap between bipartite correlation measured in trace norm and that measured by a correlation function, and obtain an improved universal upper bound for quantum data hiding. The upper bound has also been formalized and machine-checked in Lean.

Mobile impurities provide a powerful means of probing correlated and topological quantum matter, through their dressing by the surrounding medium and the practical probes granting access to the resulting composite object. Motivated by the recent observation of anyon-impurity composites in the solid state, as well as recent realizations of Laughlin-type states in engineered lattice systems, we investigate the formation of a bound state between a mobile impurity and a single pinned quasihole in the interacting Harper-Hofstadter model deep in the fractional Chern insulator regime. Combining analytical arguments with large-scale numerical simulations, we characterize the structure, energetics, and stability of hybrid anyon-impurity bound states, and show that their binding energy provides direct access to the fractional charge of the quasihole under conditions that we identify. We further demonstrate that the composite object can be coherently transported by externally steering the quasihole pinning potential. Our results establish a realistic pathway for controlled anyon-impurity manipulation in quantum-engineered platforms, enabling experimentally feasible protocols for braiding.

Quantum optimization has attracted growing interest as quantum hardware continues to improve, yet state-of-the-art classical solvers remain a formidable benchmark for practical utility. Rather than seeking a fully quantum replacement for classical optimization, we propose a hybrid strategy that uses quantum information to enhance leading classical heuristics. Specifically, we introduce a warm-start method based on local correlators obtained from the Quantum Approximate Optimization Algorithm (QAOA), and use this information to initialize the Burer-Monteiro (BM) rank-two relaxation. We demonstrate numerically that, compared to a random, multi-start initialization baseline (a standard strategy used for BM), this quantum-informed initialization offers a significant head start, i.e., high-quality solutions with very small number of iterations, for two problem classes – random Erdős Rényi graphs with edge density of $10\%$ (ER-10) and fully-connected Sherrington Kirkpatrick (SK) spin glass models, at $n=500$ and $n=1000$ qubits. At the same time, given enough iterations, the random baseline often eventually catches up and slightly outperforms the warm-start strategy on average, an effect visibly stronger for $n=500$ than for $n=1000$. The results demonstrate an exploitation/exploration tradeoff of using WS to quickly arrive at very good solutions vs exploring slightly better solutions with a larger iterations budget via a standard strategy. Our results highlight how low-depth quantum circuits can provide useful structural information for classical optimization and suggest a promising route toward near-term quantum utility through quantum-assisted initialization.

We derive two quantum fluctuation relations for systems undergoing repeated projective measurements. These fluctuation relations characterize the work that can be extracted from a quantum device when a first-detection event triggers a mechanical operation leading to positive work production. The correction to the standard quantum Jarzynski equality depends logarithmically on the mean first-detection time for the time-reversed dynamics. Application of Jensen's inequality leads to fundamental limits on both the total work involved in the repeated measurements and final mechanical operation, and the extracted work alone. The general case of a device connected to an external environment is also considered.

We construct explicit error-detecting surgery gadgets—small systems of auxiliary qubits and checks—for the high-rate Iceberg codes $[[2N,2N-2,2]]$, to perform fault-detected measurements of logical Pauli products. The construction follows the perspective of surgery as the gauging of a logical operator, regarded as a symmetry of the code. We give a complete classification of logical Pauli operators under the permutation automorphism group of the Iceberg code, reducing the construction to one gadget per orbit, and we verify with circuit-level simulations that the gadgets are fault-detecting, with the expected post-selected logical error rate. The gadgets require reconfigurable long-range connectivity, available on platforms such as neutral-atom arrays, making an error-detected demonstration of Pauli-based computation a natural near-term experiment. The paper doubles as a self-contained introduction to gauging and code surgery, developed alongside a simple worked example.

Compact cesium beam clocks are major frequency references for deployable timing systems. However, further improvement of their short-term frequency stability is limited by the clock signal-to-noise ratio (SNR). Although two-laser optical pumping can increase the effective atomic utilization, the achievable clock SNR has long been limited by laser-induced frequency-to-amplitude noise conversion. Here, we demonstrate a compact dual-Faraday-laser-pumped (DFP) Cs beam clock enabled by a low-frequency-noise atom-referenced laser architecture. The intracavity Faraday anomalous dispersion optical filter provides inherent alignment to the Cs D$_2$ resonances, while modulation transfer spectroscopy offers suppressed frequency noise and drift. The resulting laser system supports robust turnkey operation with a Lorentzian linewidth of 2.12 kHz. The DFP Cs clock achieves a clock SNR of 46,365 in a 1-Hz bandwidth and a fractional Allan deviation of $7.7\times 10^{-13}/\sqrt\tau$ , with Hadamard deviation reaching $7.7\times 10^{-15}$ at 10,000 s. This work pushes the fractional frequency stability of a compact Cs beam clock into the $10^{-13}/\sqrt\tau$ regime, providing a pathway toward high-performance Cs frequency references for field-deployable precision timing, navigation, and synchronization.

Can one neural wave function describe both a Bose condensate and a chiral topological liquid? We introduce ChernFormer, which combines a fermionic transformer with a fixed Chern-Simons phase that attaches one statistical vortex to every particle pair. Each factor changes sign under exchange, so their product is exactly bosonic. The fixed phase changes statistics but not probability, making every bosonic learning problem equivalent to a fermionic one with the same approximation error and overlap. With enough capacity, ChernFormer can approximate any normalizable bosonic wave function on the plane at fixed particle number. A finite, smooth network still vanishes when particles meet, yet this contact hole can shrink while the wave function and condensate fraction approach those of a nodeless condensate. Following the needle-in-a-haystack target-reconstruction benchmark introduced in \cite{NazaryanGaggioliTengFu2025}, we test ChernFormer on the Kalmeyer–Laughlin ground state and its first two chiral edge states. The overlap curves stay close to unity through their largest sampled sizes, while independent amplitude and phase maps at $N=20$ for all three states recover both local Laughlin vortices and the collective edge vortex. By contrast, a continuous, nonzero product of identical particle-wise factors misses these elementary edge sectors. ChernFormer therefore provides one variational language for conventional bosonic order and chiral topological matter.

Solving the Vehicle Routing Problem (VRP) in Stochastic Transportation Networks (STNs), a core task in Intelligent Transportation Systems (ITS), introduces estimation challenges for stochastic path travel times and the resulting VRP objective function. These challenges have typically been addressed through computationally expensive sampling-based techniques such as Monte Carlo simulation, whose performance depends on sample size, the sampling strategy, and the underlying travel time distributions. To address these issues, this study proposes and validates a quantum computing technique, Quantum Amplitude Estimation (QAE) for path-level travel time estimation in STNs. Without relying on sampling or prior assumptions of the travel time distribution, the proposed framework encodes all feasible travel time realizations into a quantum superposition, enabling a theoretical quadratic speed-up over Monte Carlo simulation. Four QAE variants are implemented in IBM's Qiskit framework, namely Canonical AE (CAE), Iterative AE (IAE), Maximum Likelihood AE (MLAE), and Faster AE (FAE), together with four rotation-angle scaling strategies for handling different discrete travel time distributions. Experiments on a small-scale STN show that the choice of scaling method and rotation-angle range significantly affects estimation accuracy, while the four QAE variants produce comparable estimates across all tested conditions, with IAE exhibiting the most stable overall performance. The results provide practical guidance on parameter selection for future hybrid quantum-classical optimization frameworks in ITS applications.

Cold heavy molecules are promising systems for exploring nuclear $\mathcal{P}$- and $\mathcal{CP}$-violating phenomena in search of new physics beyond the Standard Model. However, most proposed experimental strategies and their early realizations to date have been limited to proof-of-principle molecular species with effectively spin-zero nuclei that are not sensitive to nuclear symmetry-violating phenomena. Here, we introduce a comprehensive experimental toolbox that integrates cooling, trapping, coherent state manipulation, and a complete precision-measurement protocol that is applicable to molecules carrying relevant nuclear spins. Using ${}^{137}$Ba${}^{19}$F and nuclear-spin-dependent parity violation (NSD-PV) as representative species and benchmark application, respectively, our approach achieves a projected statistical sensitivity roughly two orders of magnitude beyond comparable molecular beams by combining techniques already demonstrated individually in current experiments. This level of precision could provide realistic experimental access not only to the enhanced NSD-PV signals arising from the heavy ${}^{137}$Ba nucleus within this molecule but also to the contributions from the lighter ${}^{19}$F nucleus, bringing direct benchmarks of nuclear ab initio theory within reach. We further identify a candidate magic wavelength as a route to second-scale rotational coherence in future experiments. The techniques developed here can be transferred to measurements of nuclear Schiff and magnetic quadrupole moments in molecules containing deformed nuclei, establishing a general platform for laboratory searches for nuclear symmetry violations.

We investigate the open quantum dynamics of a system of two masses interacting with an environment of linearized gravitational waves. We formulate the analysis in terms of the observable proper distance between the two masses, and show that the canonical variables obtained from the standard Lagrangian, expressed in terms of the Fermi normal coordinates, are not suitable for an effective description of the system. We resolve this issue through a unitary transformation that provides a physically meaningful system–environment decomposition and derive the master equation to leading order in $G$. Its dissipative sector reproduces the classical energy loss due to gravitational-wave emission, while the noisy contributions suppress coherences between states with different mass quadrupole, or effectively, different proper separations. In the regime where the proper distance can be described by considering small quantum fluctuations around an average distance $l_0$, the dynamics reduces to a Caldeira–Leggett-type equation, with a decoherence rate dependent on the baseline length $l_0$.