In this article, we solve the Duffin-Kemmer-Petiau (DKP) equation in the presence of the Woods-Saxon potential barrier and well for spin-one particles. We derive the scattering solution in terms of the Gaussian hypergeometric function ${}_2F_1(a, b; c; z)$, the regularized Gaussian hypergeometric function ${}_2\tilde{F}_1(a, b; c; z)$, and the Gamma function $\Gamma(x)$. Our analysis reveals the presence of transmission resonances. To observe these resonances, we calculate and plot the transmission $T$ and reflection $R$ coefficients for various parameters of the Woods-Saxon potential barrier. Our results are compared with those obtained for the square potential barrier and the cusp potential barrier, which represent limiting cases of the Woods-Saxon potential barrier. Furthermore, we investigate the bound state solutions, determining the critical turning point $V_{cr}$ to study particle-antiparticle creation and compute the norm $N$. Finally, we also compare our results with those obtained for the square potential well and the cusp potential well, confirming that pair creation occurs in both potential wells.

Recent advancements in quantum computing (QC) and machine learning (ML) have fueled significant research efforts aimed at integrating these two transformative technologies. Quantum machine learning (QML), an emerging interdisciplinary field, leverages quantum principles to enhance the performance of ML algorithms. Concurrently, the exploration of systematic and automated approaches for designing high-performance quantum circuit architectures for QML tasks has gained prominence, as these methods empower researchers outside the quantum computing domain to effectively utilize quantum-enhanced tools. This tutorial will provide an in-depth overview of recent breakthroughs in both areas, highlighting their potential to expand the application landscape of QML across diverse fields.

We present a new Python package that uses the established notion of geometric quantum complexity to numerically compute the difficulty associated with preparing a given unitary transformation on a quantum computer. The numerical procedure we implement is presented and discussed. Analyzed quantum circuits include: the quantum fourier transform for up to four qubits, a random circuit with depth 100, and a circuit for analyzing the evolution of a fermionic chain with several lattice sites. This package can be found for download at https://github.com/JAGDiaz/quantum-geodesics

We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.

The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment. Here, we show that retrodiction, employing both prior and posterior knowledge, gives rise to conditional probabilities for measurements on a single system, that can witness if it is part of a larger composite system. The degree of certainty with which one can retrodict the outcomes of multiple measurements on a system can witness both the existence and the quantitative nature of its entanglement with the environment.

The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation are based on agent-specific restrictions on the space of observables or states and do not explain how a single macroscopic quantum system achieves equilibrium dynamically. We instead argue that quantum theory is an effective theory and requires corrections to accurately describe systems approaching the thermodynamic limit. We construct a minimal extension of quantum theory which is practically identical to quantum mechanics for microscopic systems, yet allows isolated, macroscopic systems to thermalize, with an objective notion of thermalization. A fluctuation-dissipation relation guarantees physicality constraints including norm preservation, energy conservation, no superluminal signalling and the emergence of microcanonical equilibrium statistics. We further discuss the inclusion of objective collapse, thereby realizing a falsifiable theory of spontaneous universal irreversibility which describes the quantum to classical crossover dynamics of macroscopic quantum systems. This model admits spontaneous symmetry breaking, quantum state reduction and objective quantum thermalization for individual systems while realizing an emergent hybrid, Born-Maxwell-Boltzmann-Gibbs-microcanonical distribution for ensembles.

Non-equilibrium Rydberg gases exhibit exotic many-body phases stabilized by the interplay of coherent interactions and dissipation. Strong Rydberg interactions drive sustained limit cycle oscillations, whose robustness, long-range temporal order, and spontaneous time-translation symmetry breaking establish a dissipative time crystal (DTC). Collective self-entrainment in driven ensembles leads to global synchronization and a dominant oscillation frequency. Here, injection locking of a Rydberg DTC is demonstrated using a radio-frequency (RF) electric field that gradually pulls the intrinsic oscillation toward the injected frequency. Above a critical threshold, full synchronization occurs, with the locking bandwidth scaling linearly with RF amplitude. This includes synchronization of higher-order harmonics, revealing entrainment of the system nonlinear temporal dynamics. The phenomenon parallels injection locking in classical nonlinear systems, but emerges here in a strongly interacting quantum medium. This approach establishes a new method for stabilizing and controlling quantum temporal order, with applications in precision sensing, quantum metrology, and timekeeping.

We propose a formal framework for understanding and unifying the concept of observers across physics, computer science, philosophy, and related fields. Building on cybernetic feedback models, we introduce an operational definition of minimal observers, explore their role in shaping foundational concepts, and identify what remains unspecified in their absence. Drawing upon insights from quantum gravity, digital physics, second-order cybernetics, and recent ruliological and pregeometric approaches, we argue that observers serve as indispensable reference points for measurement, reference frames, and the emergence of meaning. We show how this formalism sheds new light on debates related to consciousness, quantum measurement, and computational boundaries; by way of theorems on observer equivalences and complexity measures. This perspective opens new avenues for investigating how complexity and structure arise in both natural and artificial systems.

We investigate theoretically the improvement of the entanglement between the indirectly coupled two magnon modes in a magnomechanical system with magnon squeezing. We quantify the degree of entanglement via logarithmic negativity between two magnon modes. We show a significant enhancement of entanglement via magnon squeezing. Additionally, the entanglement of two magnons decreases monotonically under thermal effects. We demonstrate that with an increasing photon tunneling rate, entanglement is robust and resistant to thermal effects. We use purity as a witness to the mixing between the two magnon modes. We show that synchronization and purity are very robust against thermal effects rather than entanglement. We examine the relationship between quantum entanglement, purity, and quantum synchronization in both steady and dynamic states. According to our results, this scheme could be a promising platform for studying macroscopic quantum phenomena.

In quantum information theory, maximally entangled states, specifically locally maximally entangled (LME) states, are essential for quantum protocols. While many focus on bipartite entanglement, applications such as quantum error correction and multiparty secret sharing rely on multipartite entanglement. These LME states naturally appear in the invariant subspaces of tensor products of irreducible representations of the symmetric group $S_n$, called Kronecker subspaces, whose dimensions are the Kronecker coefficients. A Kronecker subspace is a space of multipartite LME states that entangle high-dimensional Hilbert spaces. Although these states can be derived from Clebsch-Gordan coefficients of $S_n$, known methods are inefficient even for small $n$. A quantum-information-based alternative comes from entanglement concentration protocols, where Kronecker subspaces arise in the isotypic decomposition of multiple copies of entangled states. Closed forms have been found for the multiqubit $W$-class states, but not in general. This thesis extends that approach to any multiqubit system. We first propose a graphical construction called W-state Stitching, where multiqubit entangled states are represented as tensor networks built from $W$ states. By analyzing the isotypic decomposition of copies of these graph states, corresponding graph Kronecker states can be constructed. In particular, graph states of generic multiqubit systems can generate any Kronecker subspace. We explicitly construct bases for three- and four-qubit systems and show that the W-stitching technique also serves as a valuable tool for multiqubit entanglement classification. These results may open new directions in multipartite entanglement resource theories, with bipartite and tripartite $W$ states as foundational elements, and asymptotic analysis based on Kronecker states.

Rare events are essential for understanding the behavior of non-equilibrium and industrial systems. It is of ongoing interest to develop methods for effectively searching for rare events. With the advent of quantum computing and its potential advantages over classical computing for applications like sampling certain probability distributions, the question arises whether quantum computers could also provide an advantage or inspire new methods for sampling the statistics of rare events. In this work, we propose a quantum reinforcement learning (QRL) method for studying rare dynamics, and we investigate their benefits over classical approaches based on neural networks. As a proof-of-concept example, we demonstrate that our QRL agents can learn and generate the rare dynamics of random walks, and we are able to explain this success as well as the different contributing factors to it via the intrinsic Fourier features of the parameterized quantum circuit. Furthermore, we show better learning behavior with fewer parameters compared to classical approaches. This is the first investigation of QRL applied to generating rare events and suggests that QRL is a promising method to study their dynamics and statistics.

We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia (Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems. Our analysis relies on a novel generalization of a result by Hayashi (Hayashi, J. Phys. A: Math. Gen. 34, 3413, 2001) concerning the asymptotics of quantum relative entropy, which we establish for the infinite-dimensional setting. This enables us to prove that the QUSUM strategy retains its asymptotic optimality, characterized by the relationship between the expected detection delay and the average false alarm time for any pair of states with finite relative entropy. Consequently, our findings apply broadly, including continuous-variable systems (e.g., Gaussian states), facilitating the development of optimal change-point detection schemes in quantum optics and other physical platforms, and rendering experimental verification feasible.

We present a quantum sensing protocol for the simultaneous estimation of the difference in the localization parameters of two single-photon sources, paving the way to single-photon 3D imaging and 3D nanoscopy beyond the diffraction limit. This is achieved by exploiting two-photon interference of the two emitted photons at a beam splitter via sampling measurements in the frequency and transverse momenta at the output. We prove theoretically that this technique reaches the ultimate sensitivity in the 3D relative localization of two emitters, already with a number of sampling measurements of 1000 and a bias in the three localization parameters below 1%. These results are independent of the values of the localization parameters to estimate.

Classically simulating quantum systems is challenging, as even noiseless $n$-qubit quantum states scale as $2^n$. The complexity of noisy quantum systems is even greater, requiring $2^n \times 2^n$-dimensional density matrices. Various approximations reduce density matrix overhead, including quantum trajectory-based methods, which instead use an ensemble of $m \ll 2^n$ noisy states. While this method is dramatically more efficient, current implementations use unoptimized sampling, redundant state preparation, and single-shot data collection. In this manuscript, we present the Pre-Trajectory Sampling technique, increasing the efficiency and utility of trajectory simulations by tailoring error types, batching sampling without redundant computation, and collecting error information. We demonstrate the effectiveness of our method with both a mature statevector simulation of a 35-qubit quantum error-correction code and a preliminary tensor network simulation of 85 qubits, yielding speedups of up to $10^6$x and $16$x, as well as generating massive datasets of one trillion and one million shots, respectively.

Recent advances in quantum hardware and quantum error correction (QEC) have set the stage for early demonstrations of fault-tolerant quantum computing (FTQC). A key near-term goal is to build a system capable of executing millions of logical operations reliably -- referred to as a megaquop quantum computer (MQC). In this work, we propose a novel system architecture targeting MQC on trapped-ion quantum computers (TIQC), leveraging their ultra-high-fidelity single-qubit gates (1Q) and efficient two-qubit (2Q) logical CNOT gates enabled by the quantum charge-coupled device (QCCD) architecture with the ion shuttling feature. We propose Flexion, a hybrid encoding scheme that uses bare qubits for 1Q gates and QEC-encoded logical qubits for 2Q gates. This approach avoids fully encoding all qubits, eliminating the overhead of gate synthesis, teleportation, and magic state distillation for non-Clifford gates. To support this, we design (1) a low-noise conversion protocol between bare and logical qubits, (2) a bare-logical hybrid instruction set architecture tailored for 2D grid-based TIQC, and (3) a compiler that minimizes conversion cost and optimizes the scheduling efficiency. We evaluate our approach on VQA and small-scale FTQC benchmarks, showing that it achieves superior performance improvements with significantly reduced resource overhead, offering a practical path toward early FTQC on TIQC.

The emergence of classical behavior from quantum mechanics as Planck's constant $\hbar$ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly learn the dynamical mapping from initial quantum state parameters (for Gaussian wave packets of the one-dimensional harmonic oscillator) and $\hbar$ to the parameters of the time-evolved Wigner function in phase space [4-6]. A comprehensive dataset of analytically derived time-evolved Wigner functions was generated, and a deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of ~ 0.0390. The network demonstrates a significant and previously unrealized ability to accurately capture the underlying mapping of the Wigner function dynamics. This allows for a direct emulation of the quantum-classical transition by predicting the evolution of phase-space distributions as $\hbar$ is systematically varied. The implications of these findings for providing a new computational lens on the emergence of classicality are discussed, highlighting the potential of this direct phase-space learning approach for studying fundamental aspects of quantum mechanics. This work presents a significant advancement beyond previous efforts that focused on learning observable mappings [7], offering a direct route via the phase-space representation.

Quantum computing has the potential to improve our ability to solve certain optimization problems that are computationally difficult for classical computers, by offering new algorithmic approaches that may provide speedups under specific conditions. In this work, we introduce QAOA-GPT, a generative framework that leverages Generative Pretrained Transformers (GPT) to directly synthesize quantum circuits for solving quadratic unconstrained binary optimization problems, and demonstrate it on the MaxCut problem on graphs. To diversify the training circuits and ensure their quality, we have generated a synthetic dataset using the adaptive QAOA approach, a method that incrementally builds and optimizes problem-specific circuits. The experiments conducted on a curated set of graph instances demonstrate that QAOA-GPT, generates high quality quantum circuits for new problem instances unseen in the training as well as successfully parametrizes QAOA. Our results show that using QAOA-GPT to generate quantum circuits will significantly decrease both the computational overhead of classical QAOA and adaptive approaches that often use gradient evaluation to generate the circuit and the classical optimization of the circuit parameters. Our work shows that generative AI could be a promising avenue to generate compact quantum circuits in a scalable way.

We propose a quantum machine learning task that is provably easy for quantum computers and arguably hard for classical ones. The task involves predicting quantities of the form $\mathrm{Tr}[f(H)\rho]$, where $f$ is an unknown function, given descriptions of $H$ and $\rho$. Using a Fourier-based feature map of Hamiltonians and linear regression, we theoretically establish the learnability of the task and implement it on a superconducting device using up to 40 qubits. This work provides a machine learning task with practical relevance, provable quantum easiness, and near-term feasibility.

Efficient generation of large-scale multipartite entangled states is a critical but challenging task in quantum information processing. Although generation of multipartite entanglement within a small set of individual qubits has been demonstrated, further scale-up in system size requires the connection of smaller entangled states into a larger state in a scalable and modular manner. Here we achieve this goal by implementing memory-enhanced fusion of two multipartite entangled states via photonic interconnects. Through asynchronous preparation of two tripartite W-state entanglements in two spatially-separated modules of atomic quantum memories and on-demand fusion via single-photon interference, we demonstrate the creation of a four-partite W-state entanglement shared by two remote quantum memory modules in a heralded way. We further transfer the W state from the memory qubits to the photonic qubits, and confirm the genuine four-partite entanglement through witness measurements. We then demonstrate memory-enhanced scaling in efficiencies in the entanglement fusion. The demonstrated scalable generation and fusion of multipartite entangled states pave the way towards realization of large-scale distributed quantum information processing in the future.

Quantum fire was recently formalized by Bostanci, Nehoran and Zhandry (STOC 25). This notion considers a distribution of quantum states that can be efficiently cloned, but cannot be converted into a classical string. Previously, work of Nehoran and Zhandry (ITCS 24) showed how to construct quantum fire relative to an inefficient unitary oracle. Later, the work of Bostanci, Nehoran, Zhandry gave a candidate construction based on group action assumptions, and proved the correctness of their scheme; however, even in the classical oracle model they only conjectured the security, and no security proof was given. In this work, we give the first construction of public-key quantum fire relative to a classical oracle, and prove its security unconditionally. This gives the first classical oracle seperation between the two fundamental principles of quantum mechanics that are equivalent in the information-theoretic setting: no-cloning and no-telegraphing. Going further, we introduce a stronger notion called quantum key-fire where the clonable fire states can be used to run a functionality (such as a signing or decryption key), and prove a secure construction relative to a classical oracle. As an application of this notion, we get the first public-key encryption scheme whose secret key is clonable but satisfies unbounded leakage-resilience (Cakan, Goyal, Liu-Zhang, Ribeiro [TCC 24]), relative to a classical oracle. Unbounded leakage-resilience is closely related to, and can be seen as a generalization of the notion of no-telegraphing. For all of our constructions, the oracles can be made efficient (i.e. polynomial time), assuming the existence of post-quantum one-way functions.

We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description, offering a natural interpretation of standard quantum gates on the Riemann sphere that is examined through their Mobius action on holomorphic wavefunction. These wavefunctions emerge via a quantization process, with the Riemann sphere serving as the classical phase space of qubit geometry. We quantize this space using canonical group quantization with holomorphic polarization, yielding holomorphic wavefunctions and spin angular momentum operators that recover the standard $SU(2)$ algebra with interesting geometric properties. Such properties reveal how geometric transformations induce quantum logic gates on the Riemann sphere, providing a novel perspective in quantum information processing. This result provides a new direction for exploring quantum computation through Isham's canonical group quantization and its holomorphic polarization method.

Woodhead [Phys. Rev. A \textbf{88}, 012331 (2013)] derived the lower bound of the secret key rate for a Bennett-Brassard (BB84) like quantum key distribution protocol under collective attacks. However, this lower bound does not always assure the generation of the secret key and thus the protocol may have to be aborted sometimes. Thus, we modify the Woodhead's lower bound of the secret key rate in such a way that the secret key is always generated in a BB84 like quantum key distribution protocol. Exploiting the obtained modified lower bound of the secret key rate, we analyze two state dependent quantum cloning machines such as (i) Wootters-Zurek QCM and (ii) Modified Buzek-Hillery QCM constructed by fixing the cloning machine parameters of Buzek Hillery quantum cloning machine (QCM), which may be used by the eavesdropper to extract information from the intercepted state. We, thereafter, show that it is possible for the communicating parties to distill a secret key, even in the presence of an eavesdropper. Moreover, we also discuss the effect of the efficiency of the QCM on the generation of the secret key for a successful key distribution protocol.

Quantum algorithms rely on quantum computers for implementation, but the physical connectivity constraints of modern quantum processors impede the efficient realization of quantum algorithms. Qubit mapping, a critical technology for practical quantum computing applications, directly determines the execution efficiency and feasibility of algorithms on superconducting quantum processors. Existing mapping methods overlook intractable quantum hardware fidelity characteristics, reducing circuit execution quality. They also exhibit prolonged solving times or even failure to complete when handling large-scale quantum architectures, compromising efficiency. To address these challenges, we propose a novel qubit mapping method HAQA. HAQA first introduces a community-based iterative region identification strategy leveraging hardware connection topology, achieving effective dimensionality reduction of mapping space. This strategy avoids global search procedures, with complexity analysis demonstrating quadratic polynomial-level acceleration. Furthermore, HAQA implements a hardware-characteristic-based region evaluation mechanism, enabling quantitative selection of mapping regions based on fidelity metrics. This approach effectively integrates hardware fidelity information into the mapping process, enabling fidelity-aware qubit allocation. Experimental results demonstrate that HAQA significantly improves solving speed and fidelity while ensuring solution quality. When applied to state-of-the-art quantum mapping techniques Qsynth-v2 and TB-OLSQ2, HAQA achieves acceleration ratios of 632.76 and 286.87 respectively, while improving fidelity by up to 52.69% and 238.28%

Certifying Kochen-Specker (KS) set is a task of certifying a set of uncharacterized projectors as desired KS set. This work demonstrates an improved scheme that enables this certification using only a maximally mixed state, rather than traversing over all states, making it experimental feasible. In this scheme, outcomes obtained from sequential measurements are used for the evaluation of the worst result and its certification threshold, based on the characteristics of maximally mixed state and a semi-definite program. Experimentally, a group of projectors closely approximating the KS set Peres-24 is certified in an optical system, highlighting the feasibility of this scheme in certifying KS set. Furthermore, a quantitative analysis is presented by manually adding errors to the optical system, demonstrating a strict level of experimental imperfection in achieving successful certification. These results offer a new perspective on characterizing measurements from quantum devices.

The strength of quantum contextuality is closely related to quantum computation power. Yu-Oh set is the minimal quantum system with state-independent contextuality(SIC). However, its strength of the contextuality has not been taken into account. In this paper, we present a general method to determine whether there is a quantum state with strong contextuality in the quantum system composed of rank-one projectors. Based on this method, we conclude that Yu-Oh set does not have quantum states with strong contextuality. This indicates that strong contextuality and SIC are mutually independent.

Measurement-device-independent quantum key distribution (MDI-QKD), enhances quantum cryptography by mitigating detector-side vulnerabilities. This study analyzes MDI-QKD performance in thermal-loss and phase noise channels, modeled as depolarizing and dephasing channels to capture thermal and phase noise effects. Based on this channel framework, we derive analytical expressions for Bell state measurement probabilities, quantum bit error rates (QBER), and secret key rates (SKR) of MDI-QKD. Our simulations reveal that SKR decreases exponentially with transmission distance, with performance further degraded by increasing thermal noise and phase noise, particularly under high thermal noise conditions. These findings offer insights into enhancing MDI-QKD's noise resilience, supporting secure key generation in practical, noisy environments.

Optically addressable spin systems, such as nitrogen-vacancy (NV) centers in diamond, have been widely studied for quantum sensing applications. In this work, we demonstrate that flavin-based cryptochrome proteins, which generate radical pairs upon optical excitation, also exhibit optically detected magnetic resonance. We further show that this optical spin interface is tunable by the protein structure. These findings establish radical pairs in proteins as a novel platform for optically addressable spin systems and magnetic field sensors. Additionally, the ability to control spin transitions introduces a new class of biophysical tools that hold promise for enabling multiplexed fluorescence microscopy. Importantly, due to the spin-selective nature of radical pair chemistry, the results lay the groundwork for radiofrequency-based manipulation of biological systems.

We investigate the scattering of two distinguishable particles with unequal masses and a mutual short-range interaction with the aim of quantifying the impact of a tunneling ``projectile'' particle on the quantum mechanical state of the ``barrier'' particle. We find that the states of the barrier particle after the tunneling or reflection of the projectile are displaced by a finite distance that is given by the derivative of the phase of the transmission or reflection amplitudes multiplied by factors dependent on particles' masses, respectively. We demonstrate these results on a numerical example with a resonant interaction between a projectile and barrier. Our work demonstrates physical implication of the concept of phase time delay in the form of finite displacements of particles that are, in principle, experimentally measurable.

The paper addresses the optimization of dynamic circuits in quantum computing, with a focus on reducing the cost of mid-circuit measurements and resets. We extend the probabilistic circuit model (PCM) and implement an optimization framework that targets both mid-circuit measurements and resets. To overcome the limitation of the prior PCM-based pass, where optimizations are only possible on pure single-qubit states, we incorporate circuit synthesis to enable optimizations on multi-qubit states. With a parameter $n_{pcm}$, our framework balances optimization level against resource usage.We evaluate our framework using a large dataset of randomly generated dynamic circuits. Experimental results demonstrate that our method is highly effective in reducing mid-circuit measurements and resets. In our demonstrative example, when applying our optimization framework to the Bernstein-Vazirani algorithm after employing qubit reuse, we significantly reduce its runtime overhead by removing all of the resets.

Real-world optimization problems must undergo a series of transformations before becoming solvable on current quantum hardware. Even for a fixed problem, the number of possible transformation paths -- from industry-relevant formulations through binary constrained linear programs (BILPs), to quadratic unconstrained binary optimization (QUBO), and finally to a hardware-executable representation -- is remarkably large. Each step introduces free parameters, such as Lagrange multipliers, encoding strategies, slack variables, rounding schemes or algorithmic choices -- making brute-force exploration of all paths intractable. In this work, we benchmark a representative subset of these transformation paths using a real-world industrial production planning problem with industry data: the optimization of work allocation in a press shop producing vehicle parts. We focus on QUBO reformulations and algorithmic parameters for both quantum annealing (QA) and the Linear Ramp Quantum Approximate Optimization Algorithm (LR-QAOA). Our goal is to identify a reduced set of effective configurations applicable to similar industrial settings. Our results show that QA on D-Wave hardware consistently produces near-optimal solutions, whereas LR-QAOA on IBM quantum devices struggles to reach comparable performance. Hence, the choice of hardware and solver strategy significantly impacts performance. The problem formulation and especially the penalization strategy determine the solution quality. Most importantly, mathematically-defined penalization strategies are equally successful as hand-picked penalty factors, paving the way for automated QUBO formulation. Moreover, we observe a strong correlation between simulated and quantum annealing performance metrics, offering a scalable proxy for predicting QA behavior on larger problem instances.

The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick decision (down to a single iteration) based on the correspondence between the data and the desired result, with a probability proportionate to this correspondence. Our approach allows one to calibrate the circuit to control specified proportions.

Frequency-modulation schemes have recently emerged as alternatives to standard Rabi pulses for realizing robust quantum operations. In this work, we investigate short-duration population transfer between the ground and first excited states of a ladder-type qutrit, with the goal of minimizing leakage into the second excited state. Our multiobjective approach seeks to reduce the maximum transient second-state population and maximize detuning robustness. Inspired by two-state models, such as the Allen-Eberly and Hioe-Carroll models, we extend these concepts to our system, exploring a range of pulse families, including those with super-Gaussian envelopes and polynomial detuning functions. We identify Pareto fronts for pulse models constructed from one of two envelope functions paired with one of four detuning functions. We then analyze how each Pareto-optimal pulse parameter influences the two Pareto objectives and amplitude robustness.

There exist several types of configurations of marked vertices, referred to as the exceptional configurations, on one- and two-dimensional periodic lattices with additional long-range edges of the HN4 network, which are challenging to find using discrete-time quantum walk algorithms. In this article, we conduct a comparative analysis of the discrete-time quantum walk algorithm utilizing various coin operators to search for these exceptional configurations. First, we study the emergence of several new exceptional configurations/vertices due to the additional long-range edges of the HN4 network on both one- and two-dimensional lattices. Second, our study shows that the diagonal configuration on a two-dimensional lattice, which is exceptional in the case without long-range edges, no longer remains an exceptional configuration. Third, it is also shown that a recently proposed modified coin can search all these configurations, including any other configurations in one- and two-dimensional lattices with very high success probability. Additionally, we construct stationary states for the exceptional configurations caused by the additional long-range edges, which explains why the standard and lackadaisical quantum walks with the Grover coin cannot search these configurations.

Josephson junctions (JJs) are the key element of many devices operating at cryogenic temperatures. Development of time-efficient wafer-scale JJ characterization for process optimization and control of JJ fabrication is essential. Such statistical characterization has to rely on room temperature techniques since cryogenic measurements typically used for JJs are too time consuming and unsuitable for wafer-scale characterization. In this work, we show that from room temperature capacitance and current-voltage measurements, with proper data analysis, we can independently obtain useful parameters of the JJs on wafer-scale, like oxide thickness, tunnel coefficient, and interfacial defect densities. Moreover, based on detailed analysis of current vs voltage characteristics, different charge transport mechanisms across the junctions can be distinguished. We exemplary demonstrate the worth of these methods by studying junctions fabricated on 200 mm wafers with an industrially scale-able concept based on subtractive processing using only CMOS compatible tools. From these studies, we find that our subtractive fabrication approach yields junctions with quite homogeneous average oxide thickness across the full wafers, with a spread of less then 3$\,$%. The analysis also revealed a variation of the tunnel coefficient with oxide thickness, pointing to a stoichiometry gradient across the junctions' oxide width. Moreover, we estimated relatively low interfacial defect densities in the range of 70 - 5000$\,$defects/cm$^2$ for our junctions and established that the density increased with decreasing oxide thickness, indicating that the wet etching process applied in the JJs fabrication for oxide thickness control leads to formation of interfacial trap state

Quantum secret sharing (QSS) enables secure distribution of information among multiple parties but remains vulnerable to noise. We analyze the effects of bit-flip, phase-flip, and amplitude damping noise on the multiparty QSS for classical message (QSSCM) and secret sharing of quantum information (SSQI) protocols proposed by Zhang et al. (Phys. Rev. A, 71:044301, 2005). To scale down these effects, we introduce an efficient quantum error correction (QEC) scheme based on a simplified version of Shor's code. Leveraging the specific structure of the QSS protocols, we reduce the qubit overhead from the standard 9 of Shor's code to as few as 3 while still achieving lower average error rates than existing QEC methods. Thus, our approach can also be adopted for other single-qubit-based quantum protocols. Simulations demonstrate that our approach significantly enhances the protocols' resilience, improving their practicality for real-world deployment.

Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical simulation of quantum circuits is vital not only for validating and benchmarking quantum hardware but also for gaining deeper insights into the behavior of quantum algorithms. A promising framework for classical simulation is provided by tensor networks. Recently, the Density-Matrix Renormalization Group (DMRG) algorithm was developed for simulating quantum circuits using matrix product states (MPS). Although MPS is efficient for representing quantum states with one-dimensional correlation structures, the fixed linear geometry restricts the expressive power of the MPS. In this work, we extend the DMRG algorithm for simulating quantum circuits to tree tensor networks (TTNs). To benchmark the method, we simulate random and QAOA circuits with various two-qubit gate connectivities. For the random circuits, we devise tree-like gate layouts that are suitable for TTN and show that TTN requires less memory than MPS for the simulations. For the QAOA circuits, a TTN construction that exploits graph structure significantly improves the simulation fidelities. Our findings show that TTNs provide a promising framework for simulating quantum circuits, particularly when gate connectivities exhibit clustering or a hierarchical structure.

Spin defects in semiconductors are widely investigated for various applications in quantum sensing. Conventional host materials such as diamond and hexagonal boron nitride (hBN) provide bulk or low-dimensional platforms for optically addressable spin systems, but often lack the structural properties needed for chemical sensing. Here, we introduce a new class of quantum sensors based on naturally occurring spin defects in boron nitride nanotubes (BNNTs), which combine high surface area with omnidirectional spin control, key features for enhanced sensing performance. First, we present strong evidence that these defects are carbon-related, akin to recently identified centers in hBN, and demonstrate coherent spin control over ensembles embedded within dense, microscale BNNTs networks. Using dynamical decoupling, we enhance spin coherence times by a factor exceeding 300x and implement high-resolution detection of radiofrequency signals. By integrating the BNNT mesh sensor into a microfluidic platform we demonstrate chemical sensing of paramagnetic ions in solution, with detectable concentrations reaching levels nearly 1000 times lower than previously demonstrated using comparable hBN-based systems. This highly porous and flexible architecture positions BNNTs as a powerful new host material for quantum sensing.

Quantum error correction (QEC) is essential for practical quantum computing, as it protects fragile quantum information from errors by encoding it in high-dimensional Hilbert spaces. Conventional QEC protocols typically require repeated syndrome measurements, real-time feedback, and the use of multiple physical qubits for encoding. Such implementations pose significant technical complexities, particularly for trapped-ion systems, with high demands on precision and scalability. Here, we realize autonomous QEC with a logical qubit encoded in multiple internal spin states of a single trapped ion, surpassing the break-even point for qubit lifetime. Our approach leverages engineered spin-motion couplings to transfer error-induced entropy into motional modes, which are subsequently dissipated through sympathetic cooling with an ancilla ion, fully eliminating the need for measurement and feedback. By repetitively applying this autonomous QEC protocol under injected low-frequency noise, we extend the logical qubit lifetime to approximately 11.6 ms, substantially outperforming lifetime for both the physical qubit ($\simeq$0.9 ms) and the uncorrected logical qubit ($\simeq$0.8 ms), thereby beating the break-even point with autonomous protection of quantum information without measurement or post-selection. This work presents an efficient approach to fault-tolerant quantum computing that harnesses the intrinsic multi-level structure of trapped ions, providing a distinctive path toward scalable architectures and robust quantum memories with reduced overhead.

In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex Hilbert spaces. However, the necessity of complex numbers--as opposed to their mere convenience--remains a subject of debate. Several alternative formulations of quantum mechanics using real numbers have been proposed. In this paper, we demonstrate that standard quantum mechanics, formulated in a complex Hilbert space, admits an equivalent reformulation in a real Kahler space. By establishing a natural isomorphism between the operator theories of the complex Hilbert space and the real Kahler space, we prove the equivalence of the two formulations including composite system. This Kahler-space framework preserves all essential features of quantum mechanics while offering a key advantage: it inherently incorporates a Hamiltonian symplectic structure analogous to classical mechanics. This structural alignment provides a unified geometric perspective for both classical and quantum dynamics. Additionally, we show that the ergodicity of finite-dimensional quantum systems becomes manifest in this framework, resolving interpretational ambiguities present in conventional complex formulations.

Motivated by recent proposals for quantum proof of work protocols, we investigate approaches for simulating linear optical interferometers using digital quantum circuits. We focus on a second quantisation approach, where the quantum computer's registers represent optical modes. We can then use standard quantum optical techniques to decompose the unitary matrix describing an interferometer into an array of $2\times 2$ unitaries, which are subsequently synthesised into quantum circuits and stitched together to complete the circuit. For an $m$ mode interferometer with $n$ identical photons, this method requires approximately $\mathcal{O}(m \log(n))$ qubits and a circuit depth of $\mathcal{O}(m n^4 \log_2(n) \: \textrm{polylog}(n^4 / \epsilon))$. We present a software package Aquinas (A QUantum INterferometer ASsembler) that uses this approach to generate such quantum circuits. For reference, an arbitrary five mode interferometer with two identical photons is compiled to a 10 qubit quantum circuit with a depth of 1972.

The sponge is a cryptographic construction that turns a public permutation into a hash function. When instantiated with the Keccak permutation, the sponge forms the NIST SHA-3 standard. SHA-3 is a core component of most post-quantum public-key cryptography schemes slated for worldwide adoption. While one can consider many security properties for the sponge, the ultimate one is indifferentiability from a random oracle, or simply indifferentiability. The sponge was proved indifferentiable against classical adversaries by Bertoni et al. in 2008. Despite significant efforts in the years since, little is known about sponge security against quantum adversaries, even for simple properties like preimage or collision resistance beyond a single round. This is primarily due to the lack of a satisfactory quantum analog of the lazy sampling technique for permutations. In this work, we develop a specialized technique that overcomes this barrier in the case of the sponge. We prove that the sponge is in fact indifferentiable from a random oracle against quantum adversaries. Our result establishes that the domain extension technique behind SHA-3 is secure in the post-quantum setting. Our indifferentiability bound for the sponge is a loose $O(\mathsf{poly}(q) 2^{-\mathsf{min}(r, c)/4})$, but we also give bounds on preimage and collision resistance that are tighter.

An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their vicinity. Here we consider perhaps the simplest quantum model which exhibits an exceptional point and which allows for an analytical treatment. In particular, we re-examine a two-level atom driven by a laser and suffering from losses. The same exceptional point arises in several non-Hermitian matrices which determine various aspects of the dynamics of the system. There are consequences for some important observables, for example the spectrum evolves from being a Lorentzian-like singlet to a Mollow triplet upon passing through the exceptional point. Our analysis supports the perspective that viewing certain quantum systems through the lens of exceptional points offers some desirable explanatory advantages.

The Su-Schrieffer-Heeger (SSH) model, a prime example of a one-dimensional topologically nontrivial insulator, has been extensively studied in flat space-time. In recent times, many studies have been conducted to understand the properties of the low-dimensional quantum matter in curved spacetime, which can mimic the gravitational event horizon and black hole physics. However, the impact of curved spacetime on the topological properties of such systems remains unexplored. Here, we investigate the curved spacetime (CST) version of the SSH model by introducing a position-dependent hopping parameter. We show, using different topological markers, that the CST-SSH model can undergo a topological phase transition. We find that the topologically non-trivial phase can host zero-energy edge modes, but those edge modes are asymmetric, unlike the usual SSH model. Moreover, we find that at the topological transition point, a critical slowdown takes place for zero-energy wave packets near the boundary, indicating the presence of a horizon, and interestingly, if one moves even a slight distance away from the transition point, wave packets start bouncing back and reverse the direction before reaching the horizon. A semiclassical description of the wave packet trajectories also supports these results.

Nowadays, the quest for non-Abelian anyons is attracting tremendous attention. In particular, a Majorana quasiparticle has attracted great interest since the non-Abelian anyon is a key particle for topological quantum computation. Much effort has been paid for the quest of the Majorana state in solids, and some candidate material platforms are reported. Among various materials that can host the Majorana state, chiral p-wave superconductor is one of the suitable materials and the iron-based layered superconductor FeTeSe is one of the promising material platforms because its surface can host effective p-wave superconducting state that is analogous to chiral p-wave superconducting state thanks to its topological surface state. Given that a chiral p-wave superconductor possesses spin polarization, detecting the spin polarization can be evidence for the chiral p-wave trait, which results in the existence of Majorana excitation. Here, we show successful detection of the spin polarization at the surface of FeTe0.6Se0.4 in its superconducting state, where the spin polarization is detected via a potentiometric method. Amplitudes of the spin signal exhibit characteristic dependence for temperature and bias current, suggesting detection of spin polarization of the Bogoliubov quasiparticles. Our achievement opens a new avenue to explore topological superconductivity for fault-tolerant quantum computation.

An incident wave at a temporal interface, created by an abrupt change in system parameters, generates time-refracted and time-reflected waves. We find topological characteristics associated with the temporal interface that separates distinct spatial topologies and report a novel bulk-boundary correspondence for the temporal interface. The vanishing of either time refraction or time reflection records a topological phase transition across the temporal interface, and the difference of bulk band topology predicts nontrivial braiding hidden in the time refraction and time reflection coefficients. These findings, which are insensitive to spatial boundary conditions and robust against disorder, are demonstrated in a synthetic frequency lattice with rich topological phases engendered by long-range couplings. Our work reveals the topological aspect of temporal interface and paves the way for using the time boundary effect to probe topological phase transitions and topological invariants.

Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians $H$ with complex energy eigenvalues $E_n \in {\mathbb C}$ are considered. The method of evaluation of quantities $\sigma_n=\sqrt{E_n^*E_n}$ known as the singular values of $H$ is proposed. Its basic idea is that the quantities $\sigma_n$ can be treated as square roots of eigenvalues of a certain auxiliary self-adjoint operator $\mathbb{H}$. As long as such an operator can be given a block-tridiagonal matrix form, we construct its resolvent as a matrix continued fraction. In an illustrative application of the formalism, a discrete version of conventional Hamiltonian $H=-d^2/dx^2+V(x)$ with complex local $V(x) \neq V^*(x)$ is considered. The numerical convergence of the recipe is found quick, supported also by a fixed-point-based formal proof.

We explore the quantum state transition of photon orbital angular momentum (OAM) in the present of gravitational waves (GWs) and demonstrate the potential of a new photonic single-arm GW detection technique. The interaction is calculated based on the framework of the wave propagation in linearized gravity theory and canonical quantization of the electromagnetic field in curved spacetime. It is demonstrated that when a photon possessing OAM of 1 interacts with GWs, it may relinquish its OAM and produce a central signal that may be detected. The detector provides a high and steady rate of detected photons in the low-frequency range ($<1$ Hz), opens a potential window to identify GWs in the mid-frequency range ($1\sim10$ Hz), which is absent in other contemporary GW detectors, and establishes a selection rule for GW frequencies in the high-frequency range ($>10$ Hz), allowing for the adjustment of detector parameters to focus on specific GW frequencies. Furthermore, the detector is insensitive to seismic noise, and the detectable photon count rate is proportional to the square of the GW amplitude, making it more advantageous for determining the distance of the source compared to current interferometer detectors. This technique not only facilitates the extraction of GW information but also creates a new approach for identifying and selecting GW signals.

The optimization of parametric quantum circuits is technically hindered by three major obstacles: the non-convex nature of the objective function, noisy gradient evaluations, and the presence of barren plateaus. As a result, the selection of classical optimizer becomes a critical factor in assessing and exploiting quantum-classical applications. One promising approach to tackle these challenges involves incorporating curvature information into the parameter update. The most prominent methods in this field are quasi-Newton and quantum natural gradient methods, which can facilitate faster convergence compared to first-order approaches. Second order methods however exhibit a significant trade-off between computational cost and accuracy, as well as heightened sensitivity to noise. This study evaluates the performance of three families of optimizers on synthetically generated MaxCut problems on a shallow QAOA algorithm. To address noise sensitivity and iteration cost, we demonstrate that incorporating secant-penalization in the BFGS update rule (SP-BFGS) yields improved outcomes for QAOA optimization problems, introducing a novel approach to stabilizing BFGS updates against gradient noise.

We propose and implement modern computational methods to enhance catastrophe excess-of-loss reinsurance contracts in practice. The underlying optimization problem involves attachment points, limits, and reinstatement clauses, and the objective is to maximize the expected profit while considering risk measures and regulatory constraints. We study the problem formulation, paving the way for practitioners, for two very different approaches: A local search optimizer using simulated annealing, which handles realistic constraints, and a branch & bound approach exploring the potential of a future speedup via quantum branch & bound. On the one hand, local search effectively generates contract structures within several constraints, proving useful for complex treaties that have multiple local optima. On the other hand, although our branch & bound formulation only confirms that solving the full problem with a future quantum computer would require a stronger, less expensive bound and substantial hardware improvements, we believe that the designed application-specific bound is sufficiently strong to serve as a basis for further works. Concisely, we provide insurance practitioners with a robust numerical framework for contract optimization that handles realistic constraints today, as well as an outlook and initial steps towards an approach which could leverage quantum computers in the future.

By generalizing the construction of genuine multi-entropy ${\rm GM}[\mathtt{q}]$ for genuine multi-partite entanglement proposed in the previous paper arXiv:2504.01625, we give a prescription on how to construct ${\rm GM}[\mathtt{q}]$ systematically for any $\mathtt{q}$. The crucial point is that our construction naturally fits to the partition number $p(\mathtt{a})$ of integer $\mathtt{a}$. For general $\mathtt{q}$, ${\rm GM}[\mathtt{q}]$ contains $N (\mathtt{q}) = p(\mathtt{q})-p(\mathtt{q}-1)-1$ number of free parameters. Furthermore, these give $N (\mathtt{q})+1$ number of new diagnostics for genuine $\mathtt{q}$-partite entanglement. Especially for $\mathtt{q}=4$ case, this reproduces not only the known diagnostics pointed out by arXiv:1406.2663, but also a new diagnostics for quadripartite entanglement. We also study these ${\rm GM}[\mathtt{q}]$ for $\mathtt{q} = 4, 5$ in holography and show that these are of the order of ${\cal{O}}\left(1/G_N \right)$ both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

It is well-known that the momentum spectra of particles confined to finite spatial volumes deviate from the continuous spectra used for unconfined particles. In this article, we consider real scalar particles confined to finite volumes with periodic boundary conditions, such that the particles' spectra are discrete. We directly compute the density matrices describing the decay processes $\phi \to \varphi^2$ and $\phi \to \varphi\chi\nu$, and subsequently derive expressions for the decay probabilities both for confined and unconfined particles. The latter decay process is used as a rough toy model for a neutron decaying into a proton, an electron, and an anti-electron neutrino. We propose that finite volume effects can have an impact on the outcomes of experiments measuring the neutron lifetime. In addition, our findings at the toy model level suggest that taking into account possible initial correlations between neutrons and their daughter particles might be relevant as well.

We investigate the behavior of the quantized Hall conductivity in a two-dimensional quantum system under rotating effects, a uniform magnetic field, and an Aharonov-Bohm (AB) flux tube. By varying the angular velocity and the AB flux, we analyze their impact on the formation, shifting, and structure of quantized Hall plateaus. Our results reveal that rotation modifies the energy spectrum, leading to slight shifts in the plateau positions and variations in their widths. Additionally, we identify Aharonov-Bohm-type oscillations in $\sigma_{\text{Hall}}$, which become more pronounced for lower values of the cyclotron frequency $\omega_c$, indicating enhanced quantum interference effects in the low-field regime. These oscillations are further modulated by $\Omega$, affecting their periodicity and amplitude. The interplay between the confinement frequency $\omega_0$, the cyclotron frequency $\omega_c$, and the rotational effects plays a crucial role in determining the overall behavior of $\sigma_{\text{Hall}}$. Our findings provide insights into the interplay between rotation, magnetic field, and quantum interference effects, which are relevant for experimental investigations of quantum Hall systems in rotating systems.

We investigate the eigenstates, that is, the wavefunctions of Rydberg excitons in cuprous oxide quantum wells and derive expressions relating them to the oscillator strengths of different exciton states. Using the B-spline expansion, we compute the wavefunctions in coordinate space and estimate the oscillator strengths. The symmetry properties of the states and the non-separability of the wavefunctions are illustrated. Wavefunctions associated with resonances above the scattering threshold, in particular those of bound states in the continuum as well as their partner states, are also given.