Papers

Nonlinear photonic time crystals (PTCs) can support solitons inside momentum k gaps, where the amplification of k gap modes is saturated by Kerr nonlinearity, forming spatially homogeneous but temporally localized excitations. Yet their quantum nature remains unclear. Here we quantize nonlinear k gap dynamics of PTCs and show that k gap solitons are represented by biphoton Fock ladder states. K gap amplification drives two-mode squeezing of the biphoton, while Kerr nonlinearity generates an anharmonic potential along the biphoton Fock ladder that balances this squeezing process, creating a finite biphoton number turning point and giving rise to quantum collapse and revival dynamics and nonclassical phase space interference. We further analyze how photon loss and dephasing reshape the biphoton statistics of quantized k gap solitons. Our results establish a biphoton Fock space description of k gap soliton quantization and provide a framework for studying quantum nonlinear excitations and entangled light generation in photonic time crystals.

We report on the first experimental verification of mode-independent entanglement. Commonly, the entanglement of a state is firmly based on pre-defined parties that are correlated, and the state might be disentangled when the definition of the parties is changed. Exceeding this party-dependent concept, we realize a type of quantum entanglement that persists even if the parties, in our case modes, are transformed. This safeguards the performance of entanglement in real-world applications, such as quantum communication settings involving noise and untrusted parties. For the state generation, we present an experimental scheme based on a fully reconfigurable temporally multiplexed interferometer with measurement-induced nonlinearities, which generates heralded two-photon states in two modes that are entangled for all choices of orthonormal mode basis. For the certification process, we utilize a tailored quantum-state tomography, achieving fidelities that validate the presence of mode-independent entanglement as a resilient and operationally advantageous quantum correlation.

Stable readout statistics are often taken as evidence for a well-defined physical response, but stability alone need not identify which state quantity has changed. We analyze this issue for finite collections of qubit states measured by binary readouts, focusing on changes in computational-basis population. The central question is when reproducible response data certify the sign or range of an underlying population change. We show that the answer is controlled by the calibrated measurement directions, not by loop consistency alone. For a fully calibrated finite readout family, we derive an exact closed-form interval of all compatible population changes. We also construct a same-record, jointly measurable example in which identical probabilities and accepted loop checks admit positive, zero, and negative population interpretations. When only a diagonal readout gain and a bound on coherence sensitivity are trusted, we obtain the sharp minimax interval and the necessary-and-sufficient sign condition $g>2\chi$. These results separate implementation stability from population identifiability and provide analytic benchmarks for qubit readout calibration.

We provide a re-formulation of the light-matter interaction of trapped-atom systems in terms of classical modulation theory. We introduce commuting “mean” quadrature operators together with “deviation” operators that describe the quantum fluctuations resulting from the uncertainty principle. From the “mean” position operator stems an accurate approximate expression for the internal transition coupling strengths in terms of Bessel functions which matches that of classical modulation theory. The error of the approximation is a direct result of quantum fluctuations. We also show that this result can also be obtained with WKB theory. The validity of our approach is numerically verified and supported by an expansion of the exact expression using a recurrence relation between orthogonal polynomials. Compared to the exact solution, our result is analytically more tractable, numerically more stable, and admits a transparent physical interpretation which connects the classical and quantum pictures.

Quantum entanglement is one of the most intriguing features of quantum mechanics. To investigate the entanglement between two excitons in a biexciton, an experimental technique called density matrix spectroscopy (DMS) has recently been developed. DMS combines stimulated emission tomography and pump-probe techniques to obtain a time-resolved density matrix of the polarization state of a photon pair emitted from the biexciton. The reconstructed density matrix is expected to encode information about the biexciton state and its entanglement dynamics, but the precise nature of this connection has remained unclear. In this paper, we derive an analytical relationship between the density matrix obtained by DMS and the biexciton state. In addition, we perform numerical simulations to compare the entanglement dynamics obtained by DMS with the biexciton's entanglement dynamics in a two-dimensional electron-hole system using an extended ionic Hubbard model. We find that DMS can partially capture the entanglement in the biexciton, in particular, the dynamics of the difference $S_{\mathrm{bi}} - S_k$, where $S_{\mathrm{bi}}$ is the entanglement entropy of the biexciton and $S_k$ is the entanglement in terms of the wavevectors of the excitons that constitute the biexciton. These results demonstrate the validity of DMS for obtaining information about the entanglement dynamics of the biexciton.

Over the past decades, the operations research community has developed numerous effective optimization algorithms, yet quantum computing is emerging as a new computational paradigm with the potential to approach optimization problems more efficiently. Grover's algorithm offers a provable speedup for combinatorial optimization, but its circuit depth places it beyond current noisy intermediate-scale quantum (NISQ) devices. A more accessible alternative is to reformulate the optimization problem as a quadratic unconstrained binary optimization (QUBO) problem and apply quantum annealing; however, practical problem instances remain out of reach for existing hardware. We introduce AtomTreeSearch, a hybrid classical-quantum algorithm that integrates a quantum subroutine natively implementable on neutral-atom quantum computers within a Monte Carlo Tree Search framework. At each expansion step, a maximal weighted independent set of candidate actions provided by the quantum processor is selected, and these collective actions are performed to obtain a child node. We benchmark our method on the Traveling Salesman Problem, with instances of up to 60 cities on random Euclidean instances and up to 100 cities on TSPLIB instances. Our hybrid algorithm generally matches or outperforms both OR-Tools and simulated annealing on these instances, and we find that the quantum subroutine produces more diverse and higher-quality branches compared to classical alternate subroutines. These results suggest that carefully scoped quantum subroutines embedded in classical search frameworks represent a promising path toward near-term quantum utility in combinatorial optimization.

Molten salts such as FLiBe (2LiF–BeF$_2$) are leading blanket materials for breeding and recovering tritium in fusion reactors. Predicting tritium speciation requires accurate electronic ground-state energies for representative molten-salt clusters, a demanding task for correlated electronic-structure methods. Here we report the first application of heterogeneous quantum–classical computing to tritium binding in FLiBe. Clusters drawn from ab initio molecular dynamics are partitioned by an embedded-wavefunction (EWF) method into atom-centered fragments, and the largest fragments are solved on IBM quantum hardware using extended sample-based quantum diagonalization (ext-SQD). Across nine clusters, the heterogeneous quantum–classical workflow reproduces fragment ground-state energies with agreement to full configuration interaction within 0.7~kcal/mol and a mean absolute deviation of 0.3~kcal/mol. In contrast, fragmented and unfragmented conformational energy differences and tritium binding energies differ by 12~kcal/mol and 110~kcal/mol on average, respectively, identifying fragment construction rather than fragment solution as the dominant source of algorithmic bias. To the best of our knowledge, this is the first such demonstration for a charged ionic system and in particular an inorganic molten salt, where electrostatic and polarization effects make the accurate treatment of electronic correlation particularly challenging. These results also identify areas of future research towards an accurate and scalable quantum–classical workflow to compute free-energy estimates of tritium speciation in fusion blankets.

The universal scaling of critical behavior in phase transitions is a cornerstone of physics. Dynamical quantum phase transitions (DQPTs) are their nonequilibrium analogues: abrupt nonanalyticities that emerge as a quantum system evolves in time. Yet the hardness and cost of detecting this phenomenon remain largely unexplored. We prove that estimating DQPT to a certain precision is intractable even for quantum computers, whereas deciding a subsystem variant of DQPT is as hard as simulating generic quantum circuits, implying a provable exponential quantum advantage. Furthermore, to search for critical times of local DQPTs, we show a quadratically faster quantum algorithm that estimates observables of Hamiltonian dynamics at multiple time points with Heisenberg-limited precision and sublinear scaling in the number of time points. Moreover, through encoding classical evolution into quantum dynamics, our framework enables broader quantum speedups for detecting anomalous phenomena in classical systems.

Fault-tolerant quantum computing requires architectures that simultaneously address scalability, connectivity, and error correction under realistic noise constraints. We present a compound photonic-atomic quantum computing platform that uses cavity QED to realize near-deterministic entangling operations between flying photonic qubits and stationary atomic qubits. Photons provide long-range connectivity and scalability via measurement-based quantum computing (MBQC), while atoms supply reusable, near-deterministic resources for photon generation and entanglement, overcoming the inefficiency of purely photonic platforms. The core primitive is a symmetrized Duan-Kimble photon-atom controlled-phase (CZ) gate, robust to experimental imperfections and high-fidelity. Using single $^{87}$Rb atoms coupled to optical cavities, we give protocols for state preparation, measurement, photon generation, and entangling gates on tens-of-nanosecond timescales, and show how large-scale cluster states with effectively unrestricted connectivity and reduced overhead can be generated through atomic reuse. We analyze fault tolerance on the Raussendorf-Harrington-Goyal (RHG) lattice with a hardware-aware noise model capturing asymmetric loss and correlated photonic-atomic errors. Logical memory simulations yield a photon-loss threshold near $2.6\%$ per physical gate ($\sim$15% total per trajectory). The full Clifford set – Hadamard, phase, CNOT – is implementable transversally or fold-transversally at thresholds matching the identity channel, and we propose two non-Clifford resource-state routes (code teleportation and magic state cultivation) within the foliated cluster-state architecture.

We design an algorithm for learning the coefficients of an $n$-qubit constant-local Lindbladian to $\varepsilon$ error with $O(g d^2 \log(n) / \varepsilon^2)$ total evolution time, where $g$ is the single-site energy and $d$ is the (approximate) degree of the interaction graph. Though Lindbladians present new challenges not present in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms: (1) it uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a time resolution of only $\Theta(1/g)$; (2) it works without knowledge of the structure of the unknown Lindbladian; (3) it depends on a smooth form of degree, thereby supporting the learning of quasi-local and power-law Lindbladians. Moreover, we prove a lower bound showing that our algorithm is optimal in each parameter up to logarithmic factors. Our algorithm is a simple iterative method, where the objective function consists of Fourier coefficients of the Lindbladian restricted to few-site regions. Its analysis identifies the difficulty unique to open systems, which we call "confusing" terms. For settings where the "confusion" is limited, the performance of the algorithm improves. We demonstrate this for the case of structure learning of Hamiltonians from access to real-time evolution, where we obtain a new algorithm that is significantly simpler than previous work. In addition, using the same iterative method, we design the first efficient algorithm for structure learning Hamiltonians from high-temperature Gibbs states.

Interleaved randomized benchmarking (IRB) provides a scalable estimate of a gate's error rate, but its standard guarantees require the interleaved gate to be Clifford~\cite{Magesan2012Interleaved,magesan2012characterizing}. In superconducting processors, many non-Clifford phase gates in compiled circuits are implemented virtually as software-defined frame updates rather than as additional control pulses~\cite{mckay2017efficient}. This raises the question of whether inserting or removing such virtual phases measurably changes IRB error estimates. We introduce phase-altered interleaved randomized benchmarking (PA-IRB), a paired-IRB diagnostic protocol comparing phase-stripped and phase-dressed Clifford interleaving gates derived from the same compiled implementation. PA-IRB reports $\Delta r=r_d-r_s$ with combined uncertainty to test whether virtual phase gates affect the extracted IRB decay beyond statistical error. As a case study, we apply PA-IRB to a compiled Toffoli gate executed on IBM superconducting processors, where the constituent $T/T^\dagger$ gates are implemented as virtual $Z$ rotations. Across tested calibration runs, $\Delta r$ is consistent with zero within uncertainty, indicating that virtual phase addition or removal does not measurably alter the IRB-derived error estimate under the employed compilation and execution stack. More generally, PA-IRB provides a lightweight, abstraction-aware diagnostic for benchmarking workflows involving software-defined phase operations. The same paired comparison can also be used to place operational bounds on the contribution of non-Clifford components to the compiled gate error, even when those components are physically executed rather than implemented virtually.

A subwavelength quantum-photonic circuit element should simultaneously generate nonclassical light, suppress plasmonic loss, and remain dynamically tunable. We show that an orthogonal plasmonic nanorod dimer can satisfy all three requirements. A phase-locked control polarization induces plasmonic refractive-index enhancement, driving the probe response toward a near-zero-extinction regime while simultaneously tuning the local second-harmonic parametric interaction. The resulting nonlinear plasmonic source operates in an absorption-suppressed regime and enables all-optical control of quantum correlations. We demonstrate switchable logarithmic negativity and single-mode nonclassicality, establishing a route toward actively tunable quantum-plasmonic circuit elements operating well below the diffraction limit.

Superconducting transmon systems are promising platforms for nanoscale thermometry due to their high sensitivity to environmental fluctuations. Their intrinsic anharmonicity, which is essential for qubit operations, gives rise to a non-equidistant energy spectrum that significantly affects the thermal populations and, consequently, the thermometric sensitivity. In this work, we investigate the ultimate quantum limits of temperature estimation with a transmon beyond the two-level approximation. We compare the thermometric performance of three complementary models: the qubit, a harmonic oscillator and a weakly anharmonic Duffing oscillator, evaluating their corresponding quantum Fisher information (QFI) as a function of the temperature. We show that the multilevel anharmonic structure of the transmon affects its thermometric precision. Indeed, including higher excited states enhances the maximum amount of information that can be extracted about the system temperature, compared to a qubit probe. Furthermore, we address a fundamental limitation of the standard quartic truncation, which yields a potential that is unbounded from below and supports only spurious metastable states. By introducing bounded anharmonic models, namely a confined quartic potential and a sextic correction term, we assess the robustness of the thermometric precision beyond the Duffing regime. Our results provide practical guidelines for transmon-based nanoscale thermometry and clarify the role of the anharmonic multilevel spectrum in quantum temperature estimation.

We demonstrate that light propagation in reciprocal chiral photonic media admits a unified description in terms of an emergent Dirac structure in helicity space. Starting from Maxwell's equations, we reformulate the electromagnetic field as a four-component spinor governed by an effective non-Hermitian optical Dirac equation. In this representation, the magnetoelectric response of the chiral medium appears as a helicity-dependent background that modifies the spectrum and eigenmodes, while the breaking of the spin-degenerate condition generates the intrinsic spin-orbit coupling between helicity and orbital degrees of freedom. After projection onto the positive-frequency sector, the theory reduces to an exact two-level helicity-orbital model. This model is found to have an analytical solution and describes coherent Rabi-like oscillations between spin-orbit-coupled vector modes. Chirality controls the helicity splitting and detuning, whereas the electromagnetic mismatch of the medium determines the coupling strength responsible for oscillatory spin-orbit conversion. The resulting dynamics is constrained by exact conservation of the total angular momentum, leading to reversible conversion between spin and orbital angular momentum with well-defined selection rules. Our work establishes an optical Dirac framework for structured light in chiral media, and provides experimentally accessible predictions for chirality-controlled oscillations, polarization dynamics, and orbital angular momentum conversion in structured optical fields.

A central challenge in quantum algorithms and cryptography is reasoning about algorithms with oracle access to a random group element (e.g. a random function, permutation, or unitary). Can we efficiently simulate such algorithms? Can we determine what they know after t queries? A classical tool for this is lazy sampling: the oracle does not commit to the full group element upfront, but rather samples partial information about it on the fly. We study a quantum analog of lazy sampling: compressed oracles (or recording oracles). These are quantum data structures that allow on-the-fly simulation for quantum queries, originally introduced by Zhandry (CRYPTO '19) for random functions, and generalized to unitaries by Ma-Huang (STOC '25) and permutations by Carolan (STOC '26), and used to great effect in security proofs and lower bounds due to their interpretability. We define and analyze a general-purpose and interpretable path-recording oracle, derived from first principles, that perfectly simulates random elements of any closed subgroup of $U(N)$. Our oracle stores, in superposition, t input-output pairs, with updates described in terms of the commutant of the group's tensor power representation. This transparently records the information the algorithm has learned. Our oracle builds on recent work of Grinko-Yoshida (QIP '26), who gave a different general-purpose compressed oracle without clear interpretability. One interesting application of our path-recording is allowing direct comparisons between compressed oracles of different groups, giving a new technique for proving pseudorandomness results. For example, comparing $S_N$ and $U(N)$ yields what is arguably the simplest construction to date of pseudorandom unitaries: the product PC of a pseudorandom permutation and a random Clifford, improving on the prior PFC construction (Metger-Poremba-Sinha-Yuen, FOCS '24; Ma-Huang, STOC '25).

In this paper, we study interacting bosons at zero temperature in a random and higher-dimensional continuum model introduced by Kac and Luttinger. For weak interactions we prove that there is condensation in the lowest eigenstate of the one-particle Hamiltonian (type-I BEC). For strong interactions, however, we show that condensation in a localized state cannot occur. We also prove generalized condensation, where a family of eigenstates of the one-particle Hamiltonian is macroscopically occupied as a whole. Combining these results yields a scenario where there is generalized condensation into a family of eigenstates of the one-particle Hamiltonian, but none of them is macroscopically occupied itself (type-III BEC). This proves a transition in the type of condensation. To the best of our knowledge, this is the first rigorous result in this direction for a random continuum model in higher dimensions.

The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.

Teaching quantum mechanics is challenging, not least because the theory often conflicts with our classical worldview. Quantum correlations in particular are notoriously counter-intuitive. Their non-classical behavior is typically revealed through Bell-type inequalities. Among these, Wigner's Inequality constitutes a particularly accessible test, as it relies on minimal set-theoretic assumptions. In this pedagogical paper, we derive Wigner's Inequality, describe a quantum-optical setup to experimentally violate it, and provide access to the raw data, enabling students and instructors to perform their own analyses. Our measured data shows clear violations of Wigner's Inequality, directly illustrating the non-classical nature of quantum correlations. By connecting theory, experiment, and data analysis, this paper equips educators with a resource for engaging students in authentic scientific practice and developing a deeper understanding of quantum systems.

We investigate the nonlinear optical response of a two-dimensional mesoscopic quantum ring subjected to a spiral dislocation, with emphasis on third-harmonic generation (THG). The topological defect is modeled through a torsion-induced deformation of space, which modifies the effective metric without introducing curvature. By combining the minimal-coupling prescription in curved space with a radial ring confinement and a perpendicular magnetic field, we derive the effective radial Schrödinger problem, obtain the bound states, and evaluate the nonlinear susceptibilities within the electric-dipole approximation. We show that the axial symmetry of the topologically deformed ring preserves the dipole selection rule $\Delta m=\pm 1$ and therefore suppresses second-harmonic generation, while THG remains allowed through multistep transition chains. The study is further expanded through three complementary analyses that can be implemented without changing the Hamiltonian: a dephasing-controlled study of spectral resolution, three-dimensional waterfall spectra showing the dependence on $\beta$ and $B$, and a channel-resolved decomposition of the THG amplitude. Together, these results establish the spiral dislocation as a robust geometric knob for tuning nonlinear optical activity in mesoscopic ring-shaped nanostructures.

Transport networks often lose functionality through gradual degradation in link operating conditions before topological disconnection occurs. Link-centred and binary percolation measures identify important facilities or connectivity failures, but they provide limited information on which spatial areas cause the largest loss of network-wide propagation capability. This paper develops a Dynamic Propagation Connectivity (DPC) metric based on quantum percolation for critical-area identification in transport networks. Time-varying link travel times are converted into continuous propagation strengths, which define a Hermitian propagation operator at each observation time. Candidate regions are then evaluated by a regional degradation experiment that measures the resulting loss of DPC. The method is applied to a benchmark Sioux Falls network and six Florida road networks during the post-Hurricane Irma disruption and recovery period, using 1,281 five-minute observation times. The benchmark confirms that the regional DPC score identifies a predefined structurally critical corridor. In the Florida networks, the identified critical areas differ from regions selected by link count, local degradation, edge betweenness, algebraic connectivity, and classical percolation. In Networks 1 to 4, DPC and classical percolation rankings have negative Spearman correlations, showing that continuous propagation degradation and binary fragmentation reveal different vulnerability patterns. Robustness tests under alternative travel time scaling, degradation strength, and grid size show stable results, with mean rank agreement between 0.84 and 0.96. The findings extend transport resilience analysis based on percolation from binary connectivity loss to continuous propagation degradation and provide a spatial diagnostic tool for regional monitoring, emergency planning, and recovery prioritisation.

Quantum fields exhibit a rich entanglement structure which is still not fully understood. In this work, we study the entanglement structure of the vacuum state of a massless scalar field in (1+1)-dimensions – a paradigmatic case for both high energy and condensed matter physics. We fully characterize the entanglement negativity between two arbitrary compact spacelike-separated regions of the field by calculating the logarithmic negativity along with the modes carrying it, called negativity cores. We achieve this using a framework based on the Kähler structure of Gaussian states, wherein we calculate the diagonalization of the operator associated with the partially-transposed restricted linear complex structure. In doing so, we extend the methods of this framework by proposing a basis-independent definition of the transpose operation. The explicit diagonalization we perform is enabled by a reformulation of the eigenvalue problem as a boundary value problem in the complex plane. Our results also suggest extensions to higher dimensions and fermionic fields.

We investigate three-flavor neutrino oscillations within the framework of quantum estimation theory using the quantum Fisher information matrix (QFIM). We analyze all six independent elements of the QFIM for the parameters $\theta_{23}$, $\delta_{\mathrm{CP}}$, and $\Delta m^2_{31}$, together with the corresponding quantum Cramér–Rao bounds and normalized parameter correlations. To connect the intrinsic quantum sensitivity of the neutrino state with experimentally accessible information, we further compare the QFI with the classical Fisher information (CFI) associated with flavor-probability measurements. We find that the difference between the quantum and classical information bounds is strongly dependent on the oscillation parameter and $L/E$, demonstrating that the efficiency with which the available quantum information is accessed depends on the measurement. We also investigate probability-degenerate solutions in the $(\theta_{23},\delta_{\mathrm{CP}})$ parameter space. Although different parameter sets can produce identical $\nu_\mu\rightarrow\nu_e$ appearance probabilities at specific $L/E$ values, their corresponding quantum states can remain distinct, as demonstrated by the quantum fidelity. The QFIM differences further reveal distinct local quantum-information geometries for these probability-degenerate solutions, while the corresponding CFIM differences show a parameter and $L/E$ dependent degree of distinguishability accessible through the flavor-probability measurement. Our results demonstrate that QFI and CFI provide complementary information for neutrino parameter estimation, with the QFIM serving as a measurement-independent quantum benchmark and the CFI characterizing the information accessible through a specified measurement.

Connectivity degradation in transport networks under structural disturbance is a central problem in network resilience research. Existing methods rely mainly on percolation theory and topological connectivity measures. They focus on whether paths exist and whether connected components fragment. These approaches cannot capture functional degradation where network topology remains intact but propagation ability has already declined substantially. This paper introduces quantum percolation theory into transport network connectivity analysis and proposes Dynamic Propagation Connectivity (DPC) as a new measure that characterises network propagation ability under disturbance. By mapping a transport network under disturbance into a propagation operator system, this paper establishes a spectral analysis framework for DPC and defines the time-averaged participation index as its core quantification. This paper provides a series of rigorous theoretical results. DPC remains constant under homogeneous disturbance and degrades under heterogeneous disturbance. This paper establishes a quantitative relationship between the degradation rate, the minimum eigenvalue spacing of the propagation operator, and heterogeneous deviation strength. This paper proves a separation theorem between DPC and algebraic connectivity. It derives an analytical expression for DPC and a second-order perturbation approximation on the ring graph. Numerical experiments on three transport benchmark networks verify all theoretical conclusions and confirm degradation monotonicity, separation from algebraic connectivity, and degradation amplification by network size. This paper provides a theoretical framework for transport network resilience assessment that goes beyond topological connectivity.

Symmetries plays a significant role in understanding the conservation laws in Quantum field theories. Here, we attempted a quadratic type dimensionless gauge transformation to achieve the invariance in QFTs. We have shown the extensive study of invariance of complex scalar, Abelian and Non- Abelian theories and established the conservation laws. We included an explicit graphical analysis to invoke the invariance. This is studied in a physical context, where different field configurations correspond to the same physical state. The necessity of the covariant derivative is studied in detail, highlighting how it ensures consistent transformation under local symmetry operations. The meaning of covariance is clarified as the preservation of the form of physical laws under transformations.

Decoherence is the biggest bottleneck in all quantum technologies. For nitrogen-vacancy (NV) centers in diamond, the loss of coherence is caused by the electron and nuclear spin bath of the diamond lattice. Here, we demonstrate that the spin bath - that typically causes decoherence - entangles the spin states of the NV electron and the host $^{14}$N nucleus. The many-body interaction between the $^{14}$N nucleus - electron - bath spins at an energy level anti-crossing occurring for an applied magnetic field orientation perpendicular to the NV axis is responsible for this effect. This is observed experimentally in NV ensembles via electron spin-echo measurements, where the echo envelope is modulated at the frequency of a $^{14}$N nuclear spin transition. Using numerical simulations, we show that the spin bath coupling to the NV centers is essential for observing this modulation. Due to the zero first-order Zeeman effect at the anti-crossing, the observed oscillations have long spin-echo coherence times, 2–3 times those at the parallel magnetic field orientation. The oscillation frequency is highly stable and robust against environmental fluctuations. These findings provide new opportunities for fundamental studies of many-body physics and quantum sensing.

Variational quantum algorithms (VQAs) have emerged as a promising approach to quantum cryptanalysis on noisy intermediate-scale quantum (NISQ) devices. Although numerous variational attack schemes have been proposed for symmetric cryptosystems, a systematic and modular benchmarking framework to evaluate their performance is still lacking. In this work, we present a comprehensive benchmark study of variational quantum attacks on the Simplified Data Encryption Standard (S-DES), focusing on the modular design choices that determine attack efficiency. We formulate variational quantum attacks within a unified framework consisting of four components: initial state preparation, parameterized circuit (Ansatz) design, cost function construction, and classical optimization. Through numerical simulations, we systematically compare representative design alternatives and evaluate their combinations in terms of convergence behavior, success probability, and effective time complexity. We further introduce standardized metrics for assessing variational quantum attack performance. Our results reveal clear performance hierarchies among different modular configurations and show that carefully optimized designs can significantly outperform naive quantum search. This work establishes a principled benchmark methodology for variational quantum cryptanalysis and positions S-DES as a practical testbed for evaluating quantum attacks on symmetric ciphers in the NISQ era.

We investigate quantum synchronization in a coupled cavity optomagnonic system which consists of two spatially separated optical whispering-gallery-mode (WGM) resonators and each resonator is also coupled to a yttrium iron garnet (YIG) sphere through the optomagnonic interaction. Phase-dependent single-photon hopping factor couples the two optical resonators and provides an indirect interaction between the two distant magnon modes. We then investigate complete synchronization, {\phi}-synchronization, and quantum phase synchronization using the covariance-matrix formalism as well as also studying the effects of the hopping term on the overall synchronization dynamics of two distant magnon modes. It can be seen that the photon-hopping phase provides an efficient way to control the synchronization dynamics and when it is varied from 0 to {\pi}, the magnon trajectories gradually evolve from weakly correlated motion to a highly synchronized state, which is also accompanied by a significant reduction in the synchronization error. The influence of the photon-hopping strength and thermal fluctuations is also investigated, where it can be seen that stronger photon hopping enhances all synchronization measures, while thermal noise weakens the coherent correlations responsible for synchronized dynamics. Our results demonstrate that the phase of the hopping factor offers a simple and effective approach for controlling synchronization dynamics in WGM based coupled cavity optomagnonic systems and also provide a useful route towards coherent control of collective magnon dynamics in such quantum optomganonic devices.

We propose a framework for the direct generation of flying cat-qubit states from vacuum using time-dependent two-photon drives in nonlinear bosonic systems. We study both Kerr-based and two-photon-dissipation-based generation. By engineering Kerr nonlinearity, two-photon driving, and dissipation, we demonstrate logical control of a cat qubit during its generation and emission, while its quantum information is simultaneously shared between the nonlinear system and the propagating output field. We further analyze the effects of photon loss and pure dephasing, showing that both the state generation and logical control remain robust under realistic noise conditions. These results provide a route toward programmable bosonic quantum networks and future propagating error-correctable encodings.

In the control of dissipative quantum systems, the slow relaxation modes usually set the ultimate manipulation timescale. We show that this bottleneck can be bypassed when dissipation itself is used as the engine of the transfer. For a qubit with non-unital, anisotropic Bloch relaxation characterized by the ratio $\kappa=T_1/T_2>1$, coherent control can only rotate the Bloch vector, whereas the bath alone can change its length. The fastest transfer between two thermal states therefore consists in steering the Bloch vector, at every instant, along the direction in which the bath contracts it most rapidly. This direction is obtained in closed form and lies slightly beyond the equatorial plane. With strong pulses, the resulting minimum transfer time is a fraction of $T_2$, instead of several $T_1$ for passive relaxation. With bounded fields, the Pontryagin maximum principle yields a bang–singular–bang synthesis whose singular arc is precisely this fastest-contraction direction, and the minimum time exceeds its strong-pulse limit by a correction inversely proportional to the field amplitude. We also determine the full time–energy Pareto front: moderate accelerations require little energy, and the time optimum lies at its steep, high-energy end. Off-axis targets are treated within the same framework; their only additional benefit is a shorter final rotation. These results apply directly to magnetic-resonance spins, nitrogen-vacancy centers and superconducting qubits, all of which operate deep in the strong-pulse regime.

Understanding the geometry of quantum Hall systems is a central challenge in modern condensed matter physics. We introduce a framework for probing the geometric structure of quantum Hall droplets by engineering the geometry of a dichroic probe and identifying the onset of "perfect elliptic dichroism", a regime in which the system responds exclusively to an elliptically polarized drive of a given chirality. This phenomenon provides a direct diagnostic of the droplet's intrinsic metric, and we show that it extends naturally to ideal Chern bands, where holomorphicity of the occupied states guarantees the vanishing of one chiral absorption rate with a quantized response for the other. In lattice realizations, such as the Harper-Hofstadter model, finite lattice-spacing corrections break the exact continuum metric description and give rise to a renormalized, emergent Landau-orbit metric; the probe ellipticity at which perfect dichroism is achieved then shifts accordingly, offering a direct spectroscopic window onto this lattice-induced geometric renormalization. Our results illuminate the rich geometric structure of quantum Hall phases and offer concrete pathways for observing these effects in quantum-engineered platforms.