Papers

The resolution of the identity is typically utilized as a passive representation tool in standard quantum mechanics textbooks. In this paper, we reinterpret this traditional perspective by introducing the resolution of the identity associated with Glauber coherent states as a direct generator of exact complex Gaussian integral identities. By systematically projecting the continuous coherent-state completeness relation onto the discrete Fock basis, highly generalized Gaussian integral relations emerge naturally as a direct consequence of state preservation, rather than being introduced as independent mathematical postulates. We demonstrate that this overarching formal structure simultaneously dictates both discrete (Kronecker delta) and continuous (Dirac delta) localization kernels under appropriate basis projections, providing a sharp conceptual contrast between the structural features of overcomplete and strictly orthogonal representations. Crucially, we highlight an intriguing non-commuting behavior in the parameter limits of the master identity. Requiring only the elementary properties of coherent states and the Dirac formalism, this approach offers a transparent and visually intuitive illustration of how Hilbert-space completeness inherently encodes vast libraries of exact, solvable mathematical relations – providing a unifying perspective suitable for advanced undergraduate and graduate instruction.

This study investigates the use of quantum annealing for particle track reconstruction in strip-type gaseous detectors. In such detectors, ghost hits and multiple hit combinations can turn pattern recognition into a combinatorial optimization problem. We formulate two reconstruction subproblems as quadratic unconstrained binary optimization problems. The first subproblem selects detector hits associated with a single photon track inside a localized candidate region. The second subproblem selects cluster triplets from different detector layers so that multiple track candidates can be handled within a single quantum processing unit(QPU) submission. The proposed formulations are tested using simulated DAMSA detector events. For the single track hit selection task, the QPU based reconstruction gives position and angular resolutions close to those obtained with a Kalman based reconstruction. In the simultaneous association task, valid cluster triplets are first extracted from the QPU samples and then connected using an association rule based on graph connectivity to construct track candidates. The DAMSA event topology studied here has low pileup and is dominated by the two photon signal from axion-like particle(ALP) decay. In this setting, the results show that the QUBO formulations can reproduce local reconstruction decisions. This provides a practical basis for further studies of reconstruction methods that combine quantum and classical computing in more complex tracking environments.

We present a variational quantum framework for finite-horizon quantum control based on hardware-efficient ansätze. The objective is to steer a quantum system from a given initial state to a desired target state over a fixed time horizon by minimizing a terminal cost defined in terms of state fidelity. Instead of explicitly synthesizing time-dependent control fields or enforcing Hamiltonian reachability constraints, the proposed method reformulates the control objective as a variational optimization problem in which a hardware-efficient parameterized quantum circuit provides a surrogate parameterization of the terminal evolution. The circuit consists of alternating layers of single-qubit rotations and entangling gates, whose parameters are optimized using classical routines to minimize the terminal infidelity. This formulation avoids reliance on problem-specific or physics-inspired ansätze, providing a flexible and implementation-friendly approach compatible with near-term quantum devices. Numerical experiments on multi-qubit state-transfer benchmarks demonstrate high-fidelity state transfer while highlighting the trade-off between ansatz expressivity, optimization complexity, and scalability with respect to system size and circuit depth.

Quantum circuit optimization for fault-tolerant computing requires exact functional equivalence while minimizing expensive non-Clifford resources such as T gates. We study this problem using a compact 44.8M-parameter encoder-decoder transformer with structured circuit tokenization, evaluating on parameterized circuits (2-6 qubits) and Clifford+T circuits (3-6 qubits). On parameterized circuits, a hybrid approach – structure from the transformer, angles from classical optimization – achieves median fidelity 1.000 on 3-6 qubit circuits. On Clifford+T circuits, where all gates are discrete and no post-processing is possible, the model learns valid syntax and accurate T-Count statistics, yet exact equivalence degrades sharply with target length – from 88% on circuits with <=9 gates to near zero beyond 26 gates. We trace this failure to autoregressive drift: early-token divergence cascading irrecoverably through left-to-right decoding. Two levers partially mitigate the drift: inference-time strategies that generate multiple candidates and select via equivalence verification raise exact-match rates from 7% to 22.5%, while scaling training data by 2.5x pushes them to 39.5%. Yet the degradation with target length persists – even with more data, exact equivalence drops from 94% on short circuits to under 4% beyond 26 gates. The contrast between settings is our central finding: when approximate outputs can be rescued by post-processing, the transformer succeeds; when exact discrete correctness is required, autoregressive drift limits reliability, with both inference-time search and data scaling as effective levers while training-side fine-tuning and model-level diversification are not.

Accurate knowledge of the microwave power delivered to a cryogenic device under test (DUT) is essential for the characterization and operation of superconducting quantum circuits. However, this information is difficult to obtain inside dilution refrigerators because of distributed attenuation, impedance mismatch, switch-path repeatability, and temperature-dependent microwave components. This paper presents an in situ measurement method for RF power at the cryogenic device plane. The method uses a custom variable temperature stage (VTS) as a cryogenic thermal-transfer element. The TVS is alternately heated by a four-wire DC heater and by microwave power dissipated in a 20 dB pass-through attenuator. By fitting the thermal transients and comparing the corresponding steady-state temperatures, the absorbed microwave power is inferred from a directly measured DC electrical power through an AC/DC substitution procedure. The finite reflection and transmission of the attenuator are then accounted for by cryogenic two-port scattering-parameter measurements based on a switch-assisted Short–Open–Load–Reciprocal calibration, so that the result is referred to the DUT reference plane. The system is demonstrated in a dilution refrigerator with powers between -43 and -58 dBm at the DUT input plane. The demonstrated relative standard uncertainty ranges from about 2% at -43.9 dBm to about 40% at -57.6 dBm. The proposed approach combines thermal RF power transfer, cryogenic S-parameter correction, and uncertainty evaluation in a measurement architecture compatible with quantum-device experiments, providing a practical route toward traceable microwave-power calibration at millikelvin stages.

Restart of a quantum process is typically modeled as a global reinitialization that erases the system's entire history. Here we introduce subspace restart, a protocol that periodically resets only the internal degrees of freedom while preserving the spatial distribution, as a tunable knob for the quantum-to-classical crossover. Using the discrete-time quantum walk as an example, we show that this selective reset drives the walker into an engineered drifted-diffusion regime. This phenomenon can be understood by a Huygens-Fresnel mechanism, where each restart fragments the wave function into a set of independent secondary sources to screen long-range correlations and isolate a robust classical backbone, whose drift and diffusivity are set by the geometric orientation of the initial coin and the restart period. Residual quantum interference, confined to effective light cones, survives only as a short-range correction that renormalizes these coefficients and imprints periodic modulations on the cumulants. Our results establish subspace restart as a route to controlling the quantum-to-classical crossover in synthetic lattices.

Heating usually destroys quantum entanglement. We show that thermalization constrained to a non-Abelian strong-symmetry sector can instead generate a distillable resource that diverges with system size. In an exactly solvable local dimer chain, entanglement across an equal bipartition is exactly zero at $T=0$, whereas every fixed $T>0$ yields $E_D=\frac12\log_2 N+C(T)+o(1)$. Measurements of the two half-chain representation labels convert thermally populated non-Abelian sectors into standard ebits. More generally, for global-singlet thermal states of finite-range, uniformly bounded, locally $SU(2)$-invariant chains, there is a nonzero high-temperature interval in which the protocol yield satisfies $Y_N=\frac12\log_2 N+O_\beta(1)$ and $E_D\geq Y_N$. For the dimer chain, the full finite-size onset is governed by a universal Bessel-function crossover with $T_*(N)=\Delta/[\ln N+O(1)]$. Exact diagonalization of a frustrated $J_1$-$J_2$ chain shows the expected finite-size signatures. Thus thermal fluctuations can create entanglement across a macroscopic cut and convert it into an unbounded operational quantum resource.

Quantum PDE solvers are difficult to evaluate in practice because published studies use different discretizations, output models, reconstruction rules, and hardware assumptions. We present a reproducible, application-driven benchmark for the 1-D Dirichlet heat equation that compares eleven kernels under the same problem instances and readout contract. The benchmark covers coherent linear solvers (HHL, QSVT, and QLS-Fourier), VQLS, imaginary-time methods (QITE, var-QITE, and AVQDS), real-time Hamiltonian simulation and unitary dilations (Hamiltonian simulation, Schade-Hamiltonian, and Schr"odingerisation), and the spectral quantum simulation method (QSM). We use three initial conditions, four grid sizes from $n=4$ to $7$ qubits ($N=16$ to $128$), a CFL-like ratio $r\approx0.4$, and final time $T=1$. Statevector, ideal-shot ($10^5$ shots per step), and noisy Aer backends separate algorithmic, sampling, and device-noise errors. On statevector, QSM and Schade-Hamiltonian reproduce the semi-discrete reference to floating-point precision, Schr"odingerisation reaches approximately $10^{-4}$ error, and QITE is the strongest non-transform method for smooth data. Under the fixed-shot setting, HHL degrades to approximately $0.79$ relative $\ell_2$ error, while several low-depth or postselected methods become readout-limited. A norm-mismatch ablation attributes 23–29% of the $n=7$ smooth-initial-condition error of Hamiltonian simulation, AVQDS, and QLS-Fourier to reconstruction normalization. Compact observables, including total thermal energy and individual Fourier-mode weights, require 1–3 orders of magnitude fewer shots than full-field reconstruction. The resulting public benchmark provides a practical guide for selecting quantum PDE solvers.

Inelastic light scattering is a central tool for sample characterization and label-free imaging across the physical and life sciences. Recent work has suggested that scattered light can also exhibit nonclassical correlations. Here, we develop a microscopic theory of Raman scattering that connects naturally to established descriptions of entangled-photon generation in three- and four-wave mixing, while capturing essential differences arising from the resonant, dissipative character of Raman scattering. Using a cumulant-expansion approach, we analyze the entanglement structure of the scattered sidebands and identify signatures that distinguish Raman-mediated correlations from those generated in conventional off-resonant nonlinear wave mixing. In particular, we show that Raman scattering induces chiral couplings between Stokes and anti-Stokes sidebands, leading to nonreciprocal amplification of coherent seed fields. These results establish a theoretical framework for Raman-based quantum photonic protocols and suggest routes toward quantum-enhanced Raman spectroscopy and imaging.

The Swing-UP of quantum EmitteR population (SUPER) scheme has recently been proposed as a deterministic method for the preparation of collective radiative states in two strongly dipole-coupled quantum emitters (Phys. Rev. Res. 8, 013179 (2026)). Here, we apply this approach to an equilateral subwavelength triangular trimer of dipole-coupled two-level quantum emitters (QEs), loosely inspired by biological light-harvesting ring geometries, and demonstrate that tailored, time-overlapping, red-detuned ultrashort SUPER pulses can selectively prepare collective states in a $C_3$-symmetric system, including energetically degenerate eigenstates that are resolved through site-dependent optical phases. We find that both the state selectivity and the preparation efficiency depend strongly on the inter-emitter spacing. In particular, at deep-subwavelength separations, the symmetric collective state can be deterministically prepared with near-unity efficiency (approximately $94\%$), whereas the inversion efficiency and state selectivity are significantly lower at larger inter-emitter separations. Furthermore, this state preparation technique inherits a certain degree of robustness against reasonable static position imperfections and on-site frequency inhomogeneities of the individual QEs. Our results demonstrate that deep-subwavelength triangular trimers and, more broadly, highly compact ring geometries are excellent candidates for the deterministic preparation of collective radiative states via SUPER excitation. These predictions could be realized with solid-state emitters and molecules. Our findings offer a route toward the direct probing of the `pure' electromagnetic layer of interaction in biological and bio-inspired synthetic nanophotonic ring configurations, with possible relevance in photonics, quantum information processing, and metrology.

Metrology with undetected photons is an emerging technique that leverages quantum effects and photon correlations (entanglement) to retrieve valuable information in a target spectral range (e.g., mid-infrared, mid-IR) using measurements in an easily accessible domain (e.g., visible, near-IR). The underlying quantum process of spontaneous parametric down-conversion (SPDC) is utilized to generate non-degenerate correlated signal and idler photons to serve as detection and probing photons, respectively. Sensing with undetected photons enables important advantages, such as ultra-low probe powers, room-temperature operation, and shot-noise-limited detection. In this contribution, we apply a quantum nonlinear interferometer based on an SPDC source to perform applied mid-IR spectroscopy, mid-IR microscopy, and mid-IR optical coherence tomography (OCT) as among the most promising techniques for quantum-based routine non-destructive testing. Moreover, we characterize the system, benchmark it against classical systems, and provide a prospective outlook for this new technology.

Quantum metrology protocols typically consist of four steps: state preparation, evolution, measurement, and data processing. Often, the first three steps are prioritised when designing a scheme as they contain all the quantum elements. The data analysis is generally considered an add-on with an implicit assumption that this step is well behaved and so standard data techniques can be applied. However, the situation can be more nuanced, such as when the available data are limited. In limited-data quantum metrology the choice of data analysis technique and cost function of the estimator is of great importance, and a reliable prior distribution of the unknown parameters is required for Bayesian analysis. An interesting question is what we should do when no such prior is available. In this work, we consider how the James-Stein estimator can give significant advantages when measuring multiple unknown parameters with limited data and, importantly, does not require any prior distribution. We demonstrate the advantage by applying this methodology to simple quantum metrology schemes.

Recent advances are enabling quantum emitters to interact with photonic crystals, whose electromagnetic modes exhibit complex dispersion relations, spatial mode structure, and polarization textures. However, modeling light-matter behavior in these systems faces a persistent trade-off: electromagnetic approaches based on Maxwell-equation solvers provide realistic vectorial descriptions but are difficult to integrate with quantum many-body and non-perturbative methods, whereas simplified quantum-optical lattice models are tractable but typically rely on scalar and spatially independent light-matter couplings that miss essential features of these structured photonic environments. Here, we introduce a constructive framework to derive quantum-optical lattice descriptions that overcome this trade-off. Combining symmetry-constrained tight-binding constructions with numerically computed photonic band structures and field profiles, our method yields minimal, symmetry-enforced lattice Hamiltonians that reproduce the target photonic dispersion while retaining the mode-resolved (position- and polarization-dependent) structure of the light-matter coupling. We show that these models recover Green's-function-based emitter dynamics in the perturbative regime, while providing access to non-perturbative quantum dynamical simulations beyond emitter-only descriptions. As a proof of principle, we apply the framework to a two-dimensional photonic crystal and show that it captures polarization-dependent directional emission inaccessible to scalar models, while enabling the analysis of non-Markovian light-matter dynamics and entanglement. Our results provide a practical bridge between classical electromagnetic simulation tools and quantum-optical many-body and non-Markovian modeling in photonic crystal settings.

In this work we derive statistical inequalities whose violation is equivalent to the impossibility of describing the data by a genuine joint probability distribution. So they are witnesses of the failure of a common probability space. We examine whether the most significant quantum quasidistributions violate these inequalities. We examine also whether these inequalitites are violated by the joint distributions derived form a noisy joint measurement. As a relevant example we find violations for the maximally mixed state, as well as cases where all system states violate them. This points to the idea that these results are more than a property of the system states, but are instead a property of the statistical structure of quantum mechanics.

In this work, we develop and study the classical Lanczos algorithm allowing us to define Krylov complexity using the symplectic structure of phase space: Poisson brackets take on the role of the quantum commutators and phase-space integrals furnish the inner product needed to define the Lanczos recursion. We show, using general methods of quantum mechanics in phase space, that the $\hbar \to 0$ limit of the usual quantum mechanical Krylov framework smoothly goes over into the classical one. In theories with well-defined semiclassical limits, we show that classical Krylov complexity accurately approximates quantum complexity at early enough times, and thus is a useful characteristic of early-time chaotic dynamics. We define a Krylov-Ehrenfest time, which quantifies the eventual divergence of classical and quantum complexities, corresponding to a characteristic depth of the Krylov chain, $n\sim n_*(\hbar)$, which in the time domain translates to the well-known scale, $t_*\sim\lambda_K^{-1}\log(1/\hbar)$, in generic chaotic systems. We additionally define microcanonical Krylov complexities, both in the classical and quantum setting, which allows one a fine-grained study of complexity, energy shell by energy shell. We apply this framework to the Lipkin-Meshkov-Glick (LMG) and Feingold-Peres (FP) models, which are collective spin systems known to classicalize in the thermodynamic limit. In particular, while the FP model features spectral chaos for some range of coupling values, the LMG model is known to exhibit early-time saddle-dominated scrambling. Our analysis shows that the instability in LMG is resolved by the microcanonical Krylov complexity, which is controlled by the integrable structure of the Hamiltonian in spectral windows away from the instability, both at early and late times.

We show that driven qubit junctions enable programmable control of physical entropy transport, with entropy conductance governed by quantum dynamics rather than by reservoir parameters alone. By comparing two simple quantum architectures – a driven single-qubit junction and a driven two-qubit junction – we find that the two-qubit junction enhances entropy transfer while requiring substantially lower driving power than its single-qubit counterpart. We further reveal two non-intuitive effects in both junctions: a sizable coherent contribution to the entropy current that emerges only under resonant driving, and negative differential entropy conductance, where increasing the thermal bias suppresses entropy flow into the probe reservoir. These results identify quantum logic architectures as programmable devices for entropy transport and suggest routes toward quantum feedback control, reservoir protection and refrigeration in driven quantum circuits.

Thermally charged quantum batteries provide a stable and easy-to-have energy resource, but remain passive and therefore do not allow useful energy extraction on demand via unitary operations. We introduce a time-dependent stirring protocol that activates a thermally charged quantum battery through a time-dependent coupling to an auxiliary activator, thereby generating correlations that drive the battery into an active state. Accounting explicitly for the energetic cost of the stirring process, the entropic cost of correlation generation and the activation time, we derive bounds on the maximal net extractable energy. Incorporating projective measurement on the activator and exploiting the information gained through the measurement further enhances the extractable energy. As an experimentally relevant example, we analyze a waveguide-QED setup where a harmonic-oscillator battery (waveguide) is stirred and monitored by a two-level system. We characterize the performance of the protocol in terms of net extractable energy (net ergotropy) and power output.

Physics-informed neural networks (PINNs) provide a pathway to reunify the simulation and control of quantum systems, in which these two tasks are typically decoupled in traditional strategies. However, most work remains confined to Markovian environments. When applied to non-Markovian systems, standard PINN architectures fail to converge reliably due to multi-objective optimization conflicts arising from the coupled differential equations. To address this fundamental limitation, we extend our previously proposed forked PINN (FPINN) by incorporating a dedicated control branch. By decoupling the optimization objectives at the gradient level via selective gradient flow, our method turns a previously intractable multi-task optimization into a well-conditioned one, allowing simulation and control to be optimized jointly without compromise. Numerical simulations on a two-qubit Heisenberg XXX model confirm that our framework faithfully reproduces the features of non-Markovian dynamics, including decoherence and information backflow. Taking a state-preparation task on the same model as an example, our FPINN achieves higher fidelity than gradient ascent pulse engineering, chopped random basis, and standard PINNs, with the advantage becoming more pronounced as the environment becomes more dissipative and more Markovian. The generated pulses are also noticeably smoother, which is advantageous for experimental implementation. Our framework thus provides a unified, end-to-end differentiable paradigm for simulation and control of open quantum systems, with potential implications for quantum computing, simulation, and control.

Large-scale Greenberger-Horne-Zeilinger~(GHZ) state is useful for quantum technologies but difficult to be prepared. Here, we propose fast measurement-based preparation of large-scale GHZ states by a four-qubit quantum phase gate with nuclear-spin qubits of alkaline-earth-like atoms, which is named as quantum ferromagnetic gate~(QFG) due to its analogy to the alignment of molecular magnetic moments in a classical magnet. A high-fidelity Rydberg-mediated QFG can be realized in a time of $6\pi/\Omega_{\text{m}}$ with $\Omega_{\text{m}}$ the maximal Rydberg Rabi frequency. From a product state of three data atom and one ancilla atom, a gluing circuit with one QFG, two single-qubit gates, and a projective measurement of the ancilla can generate a 3-qubit GHZ state, and repetition of this gluing circuit can lead to 9, 27, 81, 243, $\cdots$-qubit GHZ states. Analyses based on currently available techniques show that a 243-qubit GHZ state is realizable, and more qubits can be entangled with higher detection fidelity.

This manuscript investigates the possibility of defining a quantum Hamiltonian that leads to the same mean acceleration high-harmonic generation (HHG) spectra as those predicted by Floquet theory in the regime where the number of infrared (IR) pump photons is much larger than the number of emitted UV photons. The key assumption underlying our derivation is that the intensity of the emitted high harmonics is many orders of magnitude smaller than that of the IR laser, and that the emission of the Nnt harmonic results from the absorption of N IR photons.

This paper establishes a rigorous, unified geometric framework for quantum state spaces by constructing smooth, regular embeddings into higher-order dual number algebras $\mathcal{Q}_N \equiv \mathbb{R}[\varepsilon]/(\varepsilon^{N^2-1})$, wherein every quantum state is faithfully represented as a non-reduced scheme-theoretic point. We show that under this unified family of truncated rings, the non-linear matrix commutators governing the Liouville-von Neumann dynamics map globally onto flat, linear, and rigid algebraic flows, establishing nilpotent dual algebras as a pristine geometric landscape for higher-dimensional quantum kinematics. As $N \to \infty$, this family converges to a Cauchy-complete power series ring $\mathcal{Q}_\infty$, where non-Archimedean completion linearizes the phase space, aligning the Fubini-Study geometry with the classical Fisher-Rao manifold.

Methanol radio lines observed in space provide sensitive probes of whether the proton-to-electron mass ratio has changed over cosmic time, but such tests require laboratory rest frequencies with very high accuracy. Here we determine the frequency of the astrophysically important 12.2 GHz $3_{-1}$E – $2_{0}$E transition of CH$_3$OH by measuring near-infrared rovibrational transitions rather than the microwave line directly. Using wavelength-modulated NICE-OHMS locked to an ultra-stable optical frequency comb and referenced via a fiber link to a hydrogen-maser frequency standard, we measure Lamb-dip frequencies near 1.4 $\mu$m (216 THz) with 10 Hz statistical reproducibility and absolute uncertainties as low as 130 Hz. Pairs of optical transitions sharing common upper levels form a triangulation scheme that yields the ground-state rotational combination difference. We obtain 12 178 596.415(135) kHz, improving on earlier molecular-beam microwave spectroscopy by a factor of 20 and agreeing with a recent free-induction-decay measurement. This result establishes a sub-kHz laboratory benchmark for a key radio-astronomical methanol line and demonstrates that optical triangulation can be extended to non-chiral molecules with internal rotation.

Quantum weakest preconditions are a fundamental tool for program verification of quantum programs. Many variations have been reported in the literature. We revisit quantum weakest preconditions from the perspective of expected runtime analysis of quantum programs and introduce a novel pre-expectation framework that enables to reason about the preconditions of quantum programs without the need of an upper bound. This is particularly interesting for quantum programs involving reward statements. The overall goal is to analyze runtime behavior even in the case of programs with potentially infinite expected runtime. This paper presents several ways to do so, e.g., a program transformation such that the expected runtime of a quantum program can be expressed using the weakest pre-expectation calculus with rewards.

Quantum nonlinear optics by Rydberg polaritons can enable single-photon transistor and switch, single-photon source, and deterministic quantum information processing. A major hindrance in this study is the fast motional decoherence. Here, we devise a scheme to significantly enhance the coherence of Rydberg polariton by letting the atoms remember their velocities, or, alternatively, by changing the phase of Rydberg polariton according to its storage time. After the Rydberg polariton is prepared with a Rydberg state $|r_1\rangle$, i.e., during the storage time, two laser fields induce a transition between $|r_1\rangle$ and a nearby Rydberg state $|r_2\rangle$ via a low-lying intermediate state $\lvert f\rangle$ which is largely detuned. In particular, we find that either a $2\pi\mathbb{N}$ protocol, a $\pi$-wait-$\pi$ protocol, or a wait-$\pi$ protocol, along with an appropriate choice of $\lvert f\rangle$ can lead to a phase-coherent Rydberg polariton upon its retrieval. Importantly, the coherent transition between $|r_1\rangle$ and $|r_2\rangle$ ensures that the Rydberg polariton can block the Rydberg excitation of nearby atoms as in usual applications of Rydberg polaritons. Numerics show that the theory can nearly completely eliminate the motional dephasing, leaving Rydberg-state decay as the only fundamental channel of decoherence. This sheds light on a broad application of Rydberg-mediated quantum nonlinear optics.

Many quantum machine learning models employ quantum feature maps to encode classical data into quantum states. While fixed feature maps often lack sufficient expressivity for complex nonlinear classification tasks, trainable quantum feature maps (TQFMs) enable adaptive quantum kernels with enhanced learning capability. Different loss functions can induce distinct optimization dynamics, yet their effects remain poorly understood. In this work, we apply the Log-Likelihood Loss function for TQFMs and provide a systematic comparison with Distance Loss and Measurement Loss. Through extensive numerical experiments, we compare their optimization dynamics, computational costs, and classification performance. Our results show that Log-Likelihood Loss consistently achieves more stable optimization than Measurement Loss while retaining linear computational complexity. The resulting benchmark offers practical guidance for balancing trainability, computational efficiency, and predictive performance in quantum kernel optimization.

Positive but not completely positive maps provide one of the most direct ways to detect entanglement beyond the positive-partial-transpose (PPT) criterion. We introduce and analyze an exactly solvable two-parameter family of sparse bistochastic positive maps on qutrits, in which two coherence channels are independently tuned by parameters $w$ and $z$. The sparse structure makes the full phase diagram analytic: positivity holds exactly on the square $0\le w,z\le2/3$, complete positivity on the smaller square $0\le w,z\le1/3$, and decomposability is lost precisely outside a quarter circle in the corner $w,z\ge1/3$. The indecomposable region is certified by explicit PPT entangled state adapted to the same witness geometry. At the endpoint $W_*=W(2/3,2/3)$ we construct a four-parameter family of PPT edge states of rank type $(5,5)$, derive their analytic detection region, and show that the corresponding rays are exposed faces of the PPT cone. Finally, although $W_*$ is not optimal, we give an explicit optimal refinement whose detection region on this family is strictly larger. The result is an analytically tractable qutrit setting in which positivity, indecomposability, PPT entanglement, optimality, and exposed convex geometry can be studied in a single framework.

The nitrogen-vacancy (NV) center in diamond can be operated as a microwave-dressed qubit. In the ideal two-level limit, its transition frequency is first-order insensitive to static magnetic fields, providing robustness against magnetic detuning noise. In practical diamond devices, however, residual transverse crystal strain mixes the $\ket{m_{s}=\pm1}$ spin sublevels and modifies the dressed qubit. In this study, we derive an analytical effective two-level model of a strained dressed NV qubit by perturbatively eliminating the far-detuned spectator state from the full three-level dressed Hamiltonian. We obtain closed-form expressions for the dressed-state splitting, the spin-locking mixing angle, and the longitudinal magnetic-field coupling. We show that transverse strain shifts the dressed-state resonance and tilts the spin-locking axis. These two effects restore a finite DC-field response and thereby quantify the loss of magnetic robustness. We demonstrate these features in simulated pulsed electron spin resonance spectra that incorporate rate-equation-based optical readout. We further derive exact validity criteria from the eigenvalues and spectator weights of the full three-level Hamiltonian. For practical use, we reduce these criteria to two controlled guidelines: the spectator-like branch must remain above the nominal upper dressed state, and its branch-specific admixture must remain small. A validity diagram over the axial-field–transverse-strain plane summarizes these approximate conditions and provides practical guidelines for designing dressed-NV sensing experiments.

The unique and non-classical features of quantum networks make their simulation and intuitive understanding inherently difficult. In this work, we present Q2NSViz, an open-source Python-based visualization tool for replaying and inspecting quantum-network simulation traces. Q2NSViz reconstructs the time evolution of the simulated network state, including physical topology, stored and in-flight qubits, classical bits and packets, measurements, and entanglement relationships. In this way, it exposes not only physical connectivity, but also the dynamic entanglement-induced structure produced, consumed, and transformed by protocol execution. Q2NSViz is built around a decoupled JSON/NDJSON trace contract, a Qt-free replay engine, and an interactive PyQt6 interface, making it a standalone companion to Q2NS and reusable by other simulation backends that emit the same trace format. By turning execution traces into navigable and reproducible visual artifacts, Q2NSViz provides a zero-coding tool for researchers and educators, narrowing the gap between abstract protocol logic and concrete execution.

Minimum-leakage continuous-variable quantum key distribution suppresses Eve's Holevo information by engineering the signal ensemble during state preparation. The existing symmetric realization relies on Alice-side heralding. Here we propose an alternative two-mode symmetric realization that is deterministic without heralding. The minimum-leakage condition of the new protocol requires transmitting two phase-conjugated twin beams (PCTB). We show that the PCTB protocol is related to the heralding protocol through a common entanglement-based source but corresponds to a different prepare-and-measure decomposition. The two protocols attain the same secret key rate per transmitted optical mode in the very-large-squeezing limit. For finite squeezing, however, the PCTB protocol requires approximately 3 dB less squeezing to achieve the same performance. We further optimize mode-symmetric Gaussian two-mode entangling-cloner attacks and find that correlated ancillary modes provide only a limited advantage over independent attacks under the minimum-leakage condition. These results establish phase-conjugated twin beams as a deterministic and experimentally appealing route to symmetric minimum-leakage CV-QKD.

Measurement-induced phase transitions (MIPTs) in monitored quantum circuits are usually characterized by preparing steady states at different uniform measurement probabilities. Here we introduce a spatial realization of the MIPT by imposing a deterministic measurement gradient in a single monitored Clifford chain. The resulting steady state contains coexisting volume-law, critical, and area-law regions, with the point $p(x)=p_c$ acting as a spatial critical cut. By scanning entanglement observables across this profile, we show that the transition is organized by a spatial scaling form. Although this structure is analogous to finite-time scaling in temporally driven MIPT, the spatial protocol has no Kibble-Zurek dynamics. Instead, the physical bounds $0\le p\le 1$ impose a finite linear window, producing cutoff-controlled asymptotic regimes whose fitted exponents provide direct access to the correlation-length exponent $\nu$. Our results establish spatially inhomogeneous measurements as a controlled route to engineer and probe measurement-induced criticality within a single steady state.