Papers

The quantum focusing conjecture (QFC) is a mathematical expression of the idea that semiclassical gravity remains universally attractive. In its non-gravitational limit, the diagonal inequality is the quantum null energy condition (QNEC), which requires convexity of relative entropy with respect to the vacuum under null deformations. Rényi divergences generalize relative entropy, and positive results for the diagonal Rényi QNEC raise the question of whether they also satisfy the off-diagonal inequalities required by a full focusing principle. We show that classical correlations between distinct null generators obstruct this extension for any non-affine Rényi-type divergence satisfying data processing, tensor additivity, and matched classical-quantum conditioning.

Interactions that mix conjugate variables, such as the flux through a circuit element and the charge across it, lie outside the reach of the elementary couplings of superconducting circuits. Capacitors connect charge to charge, and inductors connect flux to flux, while no two-terminal element couples flux to charge directly. A native flux-charge coupling would thus serve as a circuit primitive in its own right, opening direct routes to non-reciprocity, protected modes, and unconventional readout. In this work, we demonstrate a flux-charge coupling by harnessing a voltage-tunable Josephson junction with parametrically modulated critical current, which mediates the interaction between a classical charge variable and a quantum flux operator. Relying on parity-selection rules in a hybrid superconducting-semiconductor fluxonium, we isolate the flux-charge coupling from other parasitic capacitive contributions and perform cross-quadrature-activated coherent control of states. Critically, we realize a flux-charge coupling that scales linearly with driving amplitude while keeping the transition energy first-order-insensitive to gate voltage. Such unconventional interaction broadens the toolbox of superconducting circuits with a critical missing component that enables the coherent coupling of conjugate variables.

Friedland et al. [PRL 129, 110402 (2022)] proposed and studied a quantum analogue of the $p$-Wasserstein distance based on quantum cost matrices and quantum couplings. They conjectured that, despite being only a semidistance in general, this quantity is a true distance for a particular quantum cost matrix and for cost matrices in a small neighborhood of it. We disprove these conjectures by exhibiting an explicit family of triples of states for which the triangle inequality fails.

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

We present electric-field-modulated electron paramagnetic resonance (EFM-EPR) measurements on centrosymmetric single crystals of the molecular spin triangle $\mathrm{[{Fe_3}O({O_2}CPh){_6}(py){_3}]ClO{_4}{\cdot}py}$ ($\bf{Fe_3}$). We provide the first observation of second harmonic EFM-EPR signal in polynuclear magnetic molecules. This signal is simulated and explained in terms of an electric-field induced modulation of the isotropic exchange in the molecule, and of their symmetry lowering resulting from a Jahn-Teller effect. Additionally, an unexpected first harmonic EFM-EPR signal is observed. Various plausible symmetry-breaking mechanisms are discussed in an attempt to explain this feature, whose observation is unexpected in a nominally centrosymmetric crystal.

We specialize Agarwal's multi-level collective spontaneous-emission formalism to the four-level case by formulating it in the fully symmetric \SU(4) representation of $N$ identical atoms. In the irreducible representation $(N,0,0)$, the occupation-number basis forms a tetrahedral weight lattice on which the six embedded $\mathfrak{su}(2)$ transition subalgebras act as ladder operators. From these algebraic factors we obtain a compact Pauli-type population-rate equation and a closed-form expression for the total emitted intensity that apply to any combination of open dipole channels. The formalism is then specialized to the seven dipole-allowed four-level topologies – tripod, inverted tripod, Y, inverted Y, double-$\Lambda$, closed cascade, and diamond – and the resulting rate equations are solved numerically for atom numbers up to $N=50$. In every case the emitted intensity develops a delayed cooperative burst whose peak height obeys a power law $I_{\mathrm{peak}}=aN^{p}$ with topology-dependent parameters $(a,p)$; the fitted exponents lie in the range $1.81\lesssim p\lesssim 1.92$, indicating a superlinear. The \SU(4) tetrahedral flow and the seven configuration-dependent transients together provide a unified geometric picture of multi-channel collective dissipation in four-level atomic ensembles.

The Baker–Campbell–Hausdorff (BCH) formula plays a critical role in many branches of mathematics and physics. It expresses the logarithm of the product of exponentials of non-commuting operators as an infinite series of nested commutators of the operators involved. The Zassenhaus formula is the dual of the BCH formula: the exponential of a sum of operators is written as an infinite product of exponentials involving the operators and their commutators. In practical computations, however, one typically has to truncate the expansions, and so understanding the error committed by the resulting approximations and eventually providing suitable bounds for this error is of paramount interest. In this work we present a general strategy to derive rigorous error bounds and explicit error constants for the BCH and Zassenhaus formulas when the operators involved are skew-adjoint, as is the case for quantum evolution problems.

The spectral condition number is a widely adopted measure of worst-case cost for quantum linear system solvers. Yet it can significantly overestimate the actual runtime for a typical problem instance. We present two quantum algorithms that produce the normalized solution $|x\rangle$ of linear system $Ax=| b \rangle$ to accuracy $\epsilon$ with complexity independent of the condition number $\kappa=\lVert A^{-1}\rVert$. We focus on the standard input model where $A$ is accessed through a block encoding and $| b \rangle$ is prepared by a unitary. But we also introduce an affine dilation model that encodes $A$ and $| b \rangle$ jointly, allowing further refinements of the query complexity. Our truncation-based solver makes an optimal number of queries to $| b \rangle$ and $\operatorname{\mathbf{O}}\left(\kappa_{\mathrm{eff}}\operatorname{polylog}\left(\frac{\kappa_{\mathrm{eff}}}{\epsilon}\right)\right)$ queries to $A$. We prove a family of upper bounds on the effective condition number, including $\kappa_{\mathrm{eff}}\leq\frac{\lVert(A^\dagger A)^{-t/2}|x\rangle\rVert^{1/t}}{\epsilon^{1/t}}$ for positive even integer $t$ and $\kappa_{\mathrm{eff}}\leq\frac{\lVert A^{-1\dagger}(A^\dagger A)^{-(t-1)/2}|x\rangle\rVert^{1/t}}{\epsilon^{1/t}}$ for positive odd $t$, overcoming the $\kappa$-barrier. Our filtering-based solver is extremely simple with a favorable runtime prefactor. In particular, the solver has query complexity $3\frac{\lVert A^{-1\dagger}|x\rangle\rVert}{\epsilon}$ to leading order when the solution norm is known. We then present a similarly simple solution norm estimator with the same asymptotic cost up to logarithmic factors. Our quantum linear system solvers thus substantially improve a recent algorithm of Li, enabling faster quantum linear system solving beyond the condition number.

The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time ($T_1$). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an ab initio acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of $T_1$ without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.

Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring the application of quantum computation techniques. We propose a hybrid quantum-classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths, consisting of a reference path and a target path for classification, using either classical or quantum variational linear solvers (VQLS). These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.

Polarization measurements of a classical 1550-nm signal are collected and analyzed on 15-km hybrid aerial-inground fiber connections over 11 months. The spectral area and spectral moments of mHz-resolution Fast-Fourier-Transform (FFT) of these measurements are extracted, and related to temperature, humidity, wind speed, and time of day. Spectral area correlations show a strong diurnal structure: daytime maxima align with temperatures/wind speed peaks and humidity dips, with lower levels during the night. These diurnal patterns also show seasonality, with higher mean and variance in summer than winter. A random forest regressor is used to estimate FFT features from environmental measurements, informed by a theoretical model

Multi-stage cryogenic readout chains with a wide bandwidth and added noise within a few quanta of the quantum limit are frequently constructed using traveling-wave parametric amplifiers (TWPAs) as the first stage, and a semiconductor amplifier as the second stage. Unfortunately for highly-scaled superconducting detector arrays, or quantum information systems, and space-based observatories, the power dissipation of the semiconductor amplifier becomes problematic from the perspective of available cryogenic cooling power at \mbox{3~K to 4~K}. Here we demonstrate a readout chain based on a two-stage kinetic inductance TWPA (KTWPA). This quantum-amplifier-based-readout-chain (QARC) provides sufficient gain that a cryogenic semiconductor follow-on amplifier can be eliminated without degradation of the system noise. In this way, the QARC dissipates approximately three orders of magnitude less power than readout chains containing semiconductor amplifiers while adding noise of less than 2~quanta over a 1~GHz bandwidth. In addition, by leveraging the high power handling of kinetic inductance technology, the QARC maintains an input compression point of -93~dBm, which exceeds that of many contemporary Josephson-junction-based parametric amplifiers.

Quantum error correction compatible with continuous symmetries is a fundamental problem in quantum information and a possible route to robust analog quantum simulation. Because the Eastin-Knill theorem forbids exact codes with continuous transversal symmetries, we construct explicit $SU(d)$-covariant approximate codes that exploit permutation symmetry to spread logical information uniformly across all physical subsystems. For one-, two-, and three-qudit erasures at known locations, we prove worst-case purified-distance scaling $O(1/N)$, which matches known approximate Eastin-Knill lower bounds up to constants, and we extend the reduced-state analysis to general flagged local noise. Exact permutation symmetry of this kind is available only up to three erased sites; for an arbitrary fixed number $k$ of erased sites, we instead show that Haar-random and efficiently sampled encodings achieve worst-case distance $O(\sqrt{k}/N)$ with probability exponentially close to one. For single-qudit erasure, we construct an explicit near-optimal decoder from the Petz recovery map. We then use these codes as building blocks for encoded analog dynamics. Symmetry-preserving Hamiltonians generate block-structured dynamical Lie algebras implementable transversally, while controlled symmetry-breaking terms serve as non-transversal resources for universal dynamics. These results provide explicit non-Abelian covariant codes and a framework for robust analog quantum simulation.

The distribution of entangled photon pairs over standard optical fiber is a fundamental requirement for the realization of the quantum internet. However, real-world deployment is severely bottlenecked by the interplay of amplitude damping (photon loss) and phase noise (birefringence). In this paper, we numerically investigate the degradation of dual-rail polarization entanglement in telecom C-band fiber links. We demonstrate a critical disparity between the physical survival of quantum correlations and their practical utility in standard communication protocols. By evaluating the unconditional logarithmic negativity against the post-selected teleportation fidelity, we identify a distinct “operational collapse region” – a distance window where the channel retains true quantum entanglement, yet standard coincidence-based detection architectures fail to provide any advantage over classical strategies. Furthermore, we reveal that the width of this inaccessible region exhibits a non-monotonic dependence on the phase noise rate, implying that simply minimizing fiber dephasing does not necessarily optimize the operational efficiency of the network. These findings provide vital guidelines for the design of practical quantum communication links.

The emergence of Quantum Software Engineering (QSE) responds to the need for systematic, disciplined, and quantifiable approaches to the development, operation, and maintenance of quantum software. Within this context, quantum computer certification represents a significant challenge: verifying that quantum devices produce valid entangled states despite hardware imperfections, noise, and decoherence. This paper presents QAccCert, a hybrid certification framework developed following QSE principles, demonstrating how heterogeneous technologies like FPGAs and Artificial Intelligence can be integrated for quantum processing. The framework implements entanglement certification through CHSH inequality violation in ideal quantum simulations using Qiskit AerSimulator. Through LLM-guided optimization, the system achieves 99.94% of the theoretical maximum of $2\sqrt{2}$, evidencing more efficient parameter space exploration than random search. These simulated results illustrate how QSE methodologies, combined with strategic technology interconnection, can be applied for practical and scalable quantum certification on real NISQ hardware in future work. This study provides a concrete case study of systematic quantum software development.

We present a geometric interpretation of the sum photon blockade effect in multimode quantum optical systems, such as semiconductor microresonators. The blockade condition \(c^{(n)} \cdot v = 0\) reflects the orthogonality of the \(n\)-photon amplitude vector to a target mode vector in an \(N\)-dimensional Hilbert space, visualized as the confinement of the state to a hyperplane. A key result is the calculation of the maximum probability of the system remaining in the blockade subspace under the influence of decoherence processes (in particular, dephasing), which determines the practical feasibility and robustness of the effect. This approach extends to higher-order correlators \(g^{(2)}_\Sigma\) and cross-correlations, enabling the design of scalable quantum devices. We introduce the concept of "dark-state typicality": as the number of modes \(M\) increases, the dark subspace annihilated by the collective mode operator asymptotically occupies a unit fraction of the \(n\)-boson Hilbert space. This allows the transition from fragile, finely tuned mechanisms to macroscopically robust non-classical light in large multimode bosonic architectures. We consider continuum collective modes, hypotheses on correlation zeros and invariant manifolds, as well as the relationship between blockade and entanglement.

Donor spin systems host a native Hilbert space whose dimension exceeds that of a qubit, meaning they can be used as qudits. Here we study a \ce{Si{:}P} donor spin system through leakage-aware randomized benchmarking (RB) of native ququart $\mathcal{C}_4$ and encoded two-qubit $\mathcal{C}_2^{\otimes 2}$ Clifford groups. We implement adiabatic ramps to operate electron dipole spin resonance (EDSR) pulses at the ionization point, where the electron is shared halfway between the donor and the interface, and to operate electron spin resonance (ESR) pulses near the interface, motivated by the sensitivity of the effective magnetic field to charge noise at the ionization point. By placing the electron near the ionization point only during EDSR control and using sufficiently long displacement ramp durations, leakage outside the computational basis is strongly suppressed, which is crucial for optimized qudit control. We find in our analysis based on leakage RB that $\mathcal{C}_4$ consistently achieves $\sim 40$–$50\%$ lower (lower-bound) error rates $\varepsilon^{\mathrm{LB}}_\mathrm{PT}$ with respect to $\mathcal{C}_2^{\otimes 2}$, due to its reduced circuit complexity. These results indicate that donor spin qudits benefit from genuine qudit operation as opposed to imposed encoded qubit operation.

We provide a thorough study of the properties of the Boulware vacuum in the spacetime of a spherical, static thin shell with a Minkowski interior. To this end, we calculate the renormalized vacuum polarization and stress-energy tensor of massless scalar fields via the extended-coordinate prescription, paying particular attention to their scaling as the shell approaches the black hole limit. Near the surface of the thin shell, we obtain the expected leading-order singular behavior of both quantities via two independent methods: a high-frequency approximation for the modes, and a weak-field approximation. At the center of the shell we find non-local, Casimir-like contributions that remain finite in the black hole limit, and whose backreaction effects we compute via the semiclassical Einstein equations. Away from these regions amenable to analytic treatment, we obtain numerical results for a wide range of shell compactnesses and field couplings. In the black hole limit, we show that the vacuum polarization and renormalized stress-energy tensor outside the shell quickly approach the ones generated by a Schwarzschild black hole, suggesting a possible universality in the vacuum outside highly compact horizonless objects. This work addresses the conceptual and technical aspects necessary for computing renormalized expectation values in matter configurations, laying the foundations for future explorations on the subject.

A fundamental question in PAC learning is determining the number of labeled examples required to learn a concept class to a desired accuracy and confidence. In classical learning theory, this quantity is characterized by the VC-dimension, while several quantum generalizations have established analogous results when examples are provided in quantum superposition. In this work, we study a distinct quantum PAC-learning model in which concepts are functions acting on quantum states. We demonstrate that the VC-dimension, although still relevant, fails to fully capture the sample complexity of this model. To further characterize this setting, we develop a new lower bound on the required number of samples and establish an upper bound when the states in the domain are linearly independent. Remarkably, this upper bound has a form similar to the classical PAC-learning bound. We further examine a setting in which the learner receives more informative data and show that the limitations of the VC-dimension persist in this extended model.

Quantum thermometry based on single-qubit sensor configurations enables the precise estimation of the temperature of a cosmological Anti-de Sitter (AdS) spacetime. In this work, we characterize the achievable estimation accuracy using the Quantum Fisher Information (QFI) and the associated quantum signal-to-noise ratio. For the first time, we introduce an ancillary Unruh-DeWitt detector between the sensor and the thermal bath, enhancing thermometric sensitivity by channeling temperature-dependent information into the probe qubit's coherence. We examine how detector acceleration in AdS space and the choice of boundary conditions modify the probe's thermal sensitivity. Despite the differing geometries, a unified phenomenology emerges: we characterize the scaling of the QFI with respect to temperature, detector energy gap, spacetime curvature, and interaction time. Finally, we identify optimal state preparation and measurement strategies that maximize the QFI, thereby establishing the fundamental limits of precision for non-Markovian sensing in curved spacetime.

The Born rule for computing probabilities of the outcomes of measurements is an indispensable ingredient of quantum mechanics. The standard textbook description of this rule gives the impression that it implies the unitarity of time evolution. This view relies on the argument that unless the dynamics is unitary, the probabilities of finding all possible outcomes of a measurement do not add up to 1, i.e., the total probability is not conserved. We show that this argument is flawed, and that the general expression for the Born rule ensures the conservation of total probabilities even when the dynamics of a quantum system is not unitary. This applies to the dynamics of ensembles of quantum systems in both pure and mixed states. We discuss the status of the local conservation of probabilities and the arguments against the plausibility of non-unitary time evolutions that are based on the identification of the Hamiltonian operator with the energy observable.

We investigate the subsystem entanglement asymmetry in random quantum automaton ensembles, which are generated by permuting the basis states in the Hilbert space and applying global phase shifts. We compute the ensemble average of the $U(1)$ subsystem asymmetry in different connectivity geometries, showing that the late-time limit of the ensemble associated to a 2-local circuit geometry coincides with the all-to-all ensemble average. By focusing on different subsystem sizes, we demonstrate that, similarly to Haar-random circuits, the system locally symmetrizes. However, in sharp contrast to the Haar-random setting, the scale at which symmetrization happens depends on the initial state, a phenomenon we associate with the interplay of conservation of the participation entropy and the uniform exploration of charge sectors. Additionally, we connect the growth of the subsystem asymmetry to the subsystem coherence and show that their growth is characterized by the same symmetrization scale.

Designing fault-tolerant quantum circuits that are both algorithmically correct and hardware compatible remains a major bottleneck in the transition to scalable quantum computing. We introduce RubriQ, a scalable framework that formulates circuit synthesis as a large language model (LLM) code-generation task, optimized via group relative policy optimization (GRPO). Unlike conventional black-box neural critics, RubriQ employs a domain-grounded programmatic rubric as the reinforcement learning reward function, evaluating circuits for T-gate reduction, hardware topology compliance, and unitary fidelity. To support high-throughput training, RubriQ integrates GPU-accelerated CUDA-Q simulation directly into the reinforcement learning (RL) loop and is deployed on NERSC Perlmutter using DeepSpeed ZeRO2 across multinode NVIDIA A100 clusters. On benchmark tasks, RubriQ achieves a mean T-gate compression of 3.31x, significantly outperforming sparse-reward RL baselines (2.05x), converging 2-3x faster, and maintaining less than 1% hardware-constraint violations. Validated on IBM and IonQ quantum processors, RubriQ establishes an automated, high-performance computing (HPC)-driven pipeline for generating hardware-ready, fault-tolerant quantum circuits at scale.

This study develops a hybrid quantum-classical framework for constrained vehicle routing problems, focusing on the pickup-and-delivery problem with time windows. Instead of casting the full routing problem as a stand-alone quantum optimization task, we embed shallow quantum samplers inside the repair phase of an Adaptive Large Neighbourhood Search (ALNS) heuristic. A Deep Q-Network controller decides whether each reduced repair subproblem should be handled by a classical repair heuristic or by a quantum sampler, using features that describe the local repair structure and predicted hardware reliability. IBM Heron experiments are used to calibrate an empirical noise-aware model for local quantum repair circuits. Across the tested instances, quantum repair is admissible in only about 16% of reduced repair states and is not superior on average. However, under selected matched repair budgets, quantum-enabled repair reduces the final gap relative to standard ALNS in 29 of 36 tested settings. These results suggest that near-term quantum sampling is most useful as a selective local repair mechanism rather than as a replacement for classical routing heuristics.

Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.

The performance of variational quantum algorithms depends in general on the structure of the parametrized quantum circuit, but the most common ansätze are typically based on local couplings. Motivated by the extended connectivity available with neutral atoms and trapped ions, we examine when structured long-range connectivity provides a useful resource, focusing on sparse power-of-two (PWR2) coupling graphs. Using dynamical Lie-algebra analysis, approximate unitary-design diagnostics, and finite-depth measures of expressibility and entanglement, we examine how these geometries enlarge the accessible operator space. This enlarged space alone is not sufficient to ensure trainability of the parameterized circuit for given target problems, and we explore performance across example problems with and without long-range coupling, identifying where sparse coupling graphs are or are not likely to provide an advantage. We also introduce a variational scheme that maps hierarchical long-range Hamiltonians to geometrically local ones that can be optimized with short-range circuits. Together, these results identify circuit geometry and qubit reconfigurability as task-dependent resources for variational algorithms, relevant to ongoing developments in quantum hardware with long-range connectivity.

Non-Markovian behavior in quantum systems is often studied in the context of bipartite systems consisting of a system of interest and an environment – tracing over the environment results in non-Markovian behavior for the subsystem of interest. One may get a Markovian limit in certain regimes, which is studied using the Lindblad master equation, and corrections to this behavior can be obtained by techniques such as the Nakajima-Zwanzig formalism. In this paper, we obtain an exact non-Markovian equation for the dynamics of a simple model system that consists of a direct sum rather than a tensor product of two pieces, namely, a discrete state and an infinite ladder. This system, called the Bixon-Jortner model, was first developed in the quantum chemistry literature but has been utilized by the quantum optics community as a model system with interesting behavior, including a Wigner-Weisskopf limit of exponential decay. We attack the time evolution problem of this system directly in time-domain, and start with an integrodifferential equation describing the time evolution of the discrete state. Using tools from mathematical physics, we transform this equation to a delay differential equation, which makes the non-Markovianity completely transparent, and then we solve the delay equation using an intuitive ansatz. This allows us to obtain the analytic form of the dynamics directly in time domain, and demonstrate decay and revival behaviors coming from the aforementioned delay differential equation. We believe the explicit form of the time-domain non-Markovian equation we obtain and the accessibility the solution techniques we use make our results a useful case study of non-Markovianity in quantum systems.

We propose a novel approach to the minimax estimation of high-order functionals from the perspective of quantum computing. Specifically, for any real number $\alpha \gg 1$, we present two estimators, one for the classical functional $\mathrm{F}_\alpha(P) = \sum_{i=1}^S p_i^\alpha$ of a discrete distribution $P$ and the other for the quantum functional $\mathrm{F}_\alpha(\rho) = \operatorname{tr}(\rho^\alpha)$ of a mixed state $\rho$. These functionals have close connections with the Rényi entropy and the Tsallis entropy. We show that both estimators achieve the minimax optimal $L_2$ rate $\alpha \mathsf{n}^{-1}$ in the range $\alpha \lesssim \mathsf{n} \lesssim \alpha^{3-o(1)}$, where the support size $S$ of $P$ or the dimension of $\rho$ can be much larger than the number of samples $\mathsf{n}$. As a result, both estimators achieve the optimal sample complexity $\mathsf{n} \asymp \alpha$, improving upon the prior best upper bounds $O(\alpha^2)$ established by Jiao, Venkat, Han, and Weissman (IEEE Trans. Inf. Theory 2017) for classical functionals and Chen and Wang (COLT 2025) for quantum functionals. Our estimators are constructed under a unified framework using quantum primitives and run in linear time on a quantum computer. This work reveals an unexpected path from quantum computing to statistics, suggesting a conceptually new methodology for functional estimation. It adds to the growing list of quantum proofs for classical theorems.

We consider a multiplexed quantum repeater that distributes entanglement between two end nodes. Multiplexing is achieved through optical integration of many quantum chips. Each chip hosts an optically addressable communication qubit and a separate memory qubit. The communication qubit serves as an entanglement generation interface between different quantum chips, and the memory qubit can be used to store entanglement. The quantum chips on the repeater are interconnected using a reconfigurable router, which makes it possible to dynamically assign quantum chips for entanglement generation with either of the two end nodes in every end-to-end communication cycle. We propose a dynamic multiplexing policy in which after an entangled link has been established with one of the end nodes, all remaining quantum chips are assigned to the opposite end node. We compare this dynamic policy to a policy in which the assignment of quantum chips to end nodes is fixed. We consider a parameter regime where on average less than one entangled link is generated per end-to-end communication cycle, which is the relevant regime for near-term quantum networks. We show that in this regime, the dynamic multiplexing policy can lead to a significant improvement in fidelity over a fixed policy, while marginally improving the rate. Moreover, even though the dynamic multiplexing policy requires a deeper, and hence, more lossy, router than the fixed policy, it can still achieve higher secret key rates in the parameter regime studied. This makes dynamic multiplexing with a many-quantum-chip repeater especially relevant for the development of near-term quantum networks.

With a single clear exception, every NISQ-era flagship demonstration of 'quantum advantage' has, within eighteen months of its announcement, been classically reproduced, shown to rest on classically tractable structure, or closed by a simulability theorem. Six theoretical results from 2024 through April 2026 explain the pattern: the regions of circuit-space NISQ hardware can run with sufficient fidelity coincide with the regions classical algorithms compress efficiently, because the features that admit one (low effective depth, strong algebraic structure, geometric locality) are the features that admit the other. This reading dates the NISQ programme from its 2018 articulation as an interim retreat from the unmet conditions of the 1996 threshold theorems, characterises the eight years that followed as a closed loop in which the demonstrations the hardware could run were drawn from regions classical methods could already reach, and locates the exit from the loop where the threshold theorems originally located it: in fault tolerance. The empirical pattern could in principle break with a demonstration that escapes the current simulability results. After eight years and more than thirty advantage-class announcements, the burden of producing such a demonstration falls to the defenders of NISQ.