Papers

A quantum cascade laser based on a metal-insulator-metal structure is proposed, the heterostructure of which consists of diamond and metal films. The profile of the quantum potential in a quasi-periodic MIM heterostructure and the structure of metastable levels in quantum wells are investigated. A number of CCL configurations have been proposed. The possibility of generating radiation from the UV to THz range is theoretically shown.

We present AlchemQ v0.5, a proof-of-concept system that couples an untrusted beam-search optimizer with a machine-checkable per-result certification layer and a versioned certificate protocol (0.2.0), so that every optimized circuit ships with a verifiable artifact rather than a bare claim. The certifier proves equivalence up to global phase by ZX-calculus full reduction, with a numeric-tensor fallback based on the optimal Hilbert-Schmidt overlap. Certificates are self-contained and tamper-evident: canonical gate-canon-v1 hashes, measured residuals, tri-state verdicts (certified/rejected/inconclusive), and versioned phase-note schemas for cross-platform reproducibility. The agent aggregates three fuzzy t-norms, cannot return an uncertified circuit, and since v0.4 guarantees no componentwise regression against the original. On a benchmark of 100 circuits, all 400 optimizations terminate without error, every returned circuit is certified, every mutation is detected, and a 2998-test suite passes on two platforms. The PyZX baseline is strong (21.4% mean T-count reduction over 82 circuits) and the agent is strictly better on 9/100; the three t-norms return identical circuits on all 100 standard instances, diverging only on 4/38 of an adversarial suite. Two case studies are new: a false negative root-caused to a pivot-normalization bug in PyZX's compare_tensors (pivot 4.7e-9; the optimal-overlap residual is 7.4e-11), and eight certificates rejected on macOS due to BLAS-dependent floats in phase_note. Both were fixed; all artifact sets validate 400/400 on both platforms. A pilot run on IBM Heron r2 gives a certified circuit 78% shallower with 65% fewer two-qubit gates; output quality favors it on all three metrics but is not significant at 1024 shots. We release the certificate specification and a standalone reference verifier (Apache-2.0) with data and scripts; the engine is proprietary.

In fault-tolerant quantum computing, lattice surgery (LS) is one of the leading ways to realize logical operations, and the Pauli product measurement (PPM) is the basic instruction of LS-based computing. Compilers that work on the PPM sequence, however, stay at the logical level rather than the physical circuit level. This is because lowering PPMs from the logical level to physical circuits is complicated. CircLS is a full-stack lattice surgery compiler: it compiles a quantum program through its PPM sequence to a Stim circuit, lowering every PPM through linear-time stabilizer construction rules. On this basis, we develop a compiler that allocates data patches dynamically: each patch is allocated at its first use and freed at its last use, and the freed tiles can be reused as ancilla paths. Against the two baselines, CircLS reduces the allocated spacetime volume by 34% and 27% and the logical error rate (LER) by 40% and 48%, and it compiles programs that they cannot. CircLS is open source at https://github.com/John-YuehanZhang/CircLS

We develop a general procedure for constructing time-dependent integrable chiral field theories from autonomous unitary difference-form $S$-matrices satisfying the Yang-Baxter equation. Spectral parameters are transported along the free right- and left-moving characteristics, defining a map from physical spacetime to spectral space on which the two-body scattering data are evaluated. Requiring spatially homogeneous right-left scattering forces the characteristic map to be affine. The inverse Cayley transform then determines the local contact interaction, while evaluation along the affine spectral trajectory fixes its time dependence. Thus, the nonautonomous interaction is determined by the autonomous scattering data together with chiral kinematics and spatial homogeneity, rather than being introduced independently. The Yang–Baxter equation supplies the factorized many-body transport, and on a spatial circle periodicity leads to quantum Knizhnik–Zamolodchikov (qKZ) equations whose compatibility defines a flat discrete transport in spectral space. Pulling the corresponding spectral-space amplitudes back to physical coordinates gives the time-dependent many-body wavefunctions. Rational $SU(N)$, trigonometric $U_q(\widehat{\mathfrak{sl}}_2)$, and rational $O(N)$ scattering illustrate how the same mechanism generates distinct nonautonomous interactions. The resulting framework gives a geometric route from autonomous factorized scattering data to time-dependent integrable field theories.

We investigate Bell-CHSH correlations for a chiral massless Majorana field localized in a double cone. The conformal modular flow of the associated light-ray interval is converted into translations by a rapidity-like coordinate, and the one-particle scalar product is derived in modular momentum space. Particular attention is paid to the fact that this scalar product carries a Fermi-Dirac weight. Requiring the modular conjugation to be antiunitary with respect to that weighted scalar product fixes the Fourier-space realization of the modular objects. The resulting Tomita-Takesaki operator and its adjoint generate Alice and twisted-dual Bob directions for which all four crossed CAR orthogonality relations follow automatically from modular localization. The Bell problem then reduces to a simple one-function functional. For a Gaussian modular-momentum profile $h_\sigma(k)=\exp[-k^2/(2\sigma^2)]$ the Bell parameter is larger than the classical bound for a broad range of widths and approaches the Tsirelson value analytically, \[ \lim_{\sigma\to 0^+}{\it B}(\sigma)=2\sqrt2 \] Thus near-maximal Bell violation is obtained from an explicit sequence of smooth rapidly decreasing profiles concentrated around zero modular momentum, corresponding to the modular spectral value $\lambda=1$.

Macroscopic quantum coherence, such as in laser, Bose-Einstein condensates, superfluids, and superconductors, is important to fundamental physics and useful for quantum technologies. Superradiance provides a mechanism to produce coherence among a large number of particles and photons. Its implementation, however, has been limited to gaseous systems, solids at very low temperature, or short pulses. Here we demonstrate a solid-state superradiant maser under ambient conditions, which establishes long-lived coherence among about $10^{14}$ nitrogen-vacancy center spins in diamond and about $10^9$ photons in a microwave cavity. By varying the system parameters to access the above-threshold, well-above-threshold, and deep-above-threshold regimes, we observed continuous-wave masing, periodic amplitude modulation, and sequences of superradiant bursts, which are attributed, correspondingly, to macroscopic spin coherence synchronized at a fixed frequency, a coherent time crystal of large spins, and unsynchronized superradiant transients. This work demonstrates that macroscopic quantum coherence can be spontaneously generated and maintained in solids under ambient conditions and provides a solid-state platform for exploring bright quantum lights with many-body correlations.

We report the observation of electron spin interactions between Rydberg atoms, which are driven by spin-orbit coupling through second-order dipole perturbation and exhibit a spatial anisotropy governed by the atomic configuration. Specifically, we observe coherent electron spin exchange dynamics, with the measured coupling strength agreeing well with both numerical calculations and theoretical models. Furthermore, we show that global microwave dressing enables active engineering and dynamical freezing of the spin exchange by introducing a differential AC Stark shift between the participating states. Additionally, we achieve tunability of the interaction by applying a stronger magnetic field, which effectively modifies the energy contributions of the underlying spin-orbit coupling channels. Finally, measuring spin dynamics in one-dimensional multi-atom chains aligned parallel or perpendicular to the magnetic field provides a self-consistent validation of the anisotropic XXZ framework. This electron spin interaction natively features spin-position coupling and enables a natural mapping onto the Heisenberg-Kitaev model. Our findings reveal a new class of electron spin-spin interactions among Rydberg atoms, expanding the scope of quantum simulation with Rydberg atom arrays.

Learning a quantum system's Hamiltonian is crucial for understanding and controlling its dynamics and has recently become a topic of widespread interest. To understand the learning protocol's error tolerances, i.e. its stability in the presence of inevitable errors, this work utilizes tensor network techniques to emulate Hamiltonian learning workflows at scale and with noise. Specifically, we employed a Hamiltonian learning technique based on approximate stationary states which are constructed using matrix product tools. We provide analytic bounds on the Hamiltonian learning estimation errors and perform numerical simulations that highlight learning error's stability under two families of errors. Using our workflow, we are able to scale up the protocol and learn mixed-field Ising model Hamiltonians of an $N=300$ site spin chain. By simulating the protocol at large scale, and empirically studying its practical limitations, our analysis of how errors affect the Hamiltonian learning process provides valuable lessons for future experiments. We conclude by discussing the avenues our work opens as well as future work that can support Hamiltonian learning experiments.

Understanding a composite system through its constituents is a fundamental practice in physics. In the context of quantum reference frames (QRFs), however, combining the usual quantum-theoretic notion of composition with QRF perspectives gives rise to subtle issues, such as the 'paradox of the third particle'. Here we study in depth how to compose subsystems in QRF perspectives, building on a recent formalism for QRFs [E$.$Castro-Ruiz and O$.$Oreshkov, 2025]. We first show how the frames of external observers can be internalised and treated within the framework. This establishes a consistent hierarchy of QRF perspectives, which we use to define the adding and removing of subsystems. We then explain how, owing to the so-called 'extra-particle' degrees of freedom, the formalism gives a consistent treatment of subsystems, avoiding any paradoxes by construction. Consistency then implies that composing subsystems in a QRF perspective differs from, and generalises, the standard quantum-theoretic case. In particular, not every state can be appended in tensor-product form relative to a QRF, and we characterise the set of compatible states. Finally, we introduce 'classicalisation', a procedure that recovers a classical-like perspective from a general QRF. This procedure circumvents the aforementioned state restrictions but carries a different operational meaning, which we study through a concrete example.

Strong interactions between $s$-orbital Rydberg atoms underpin atom-array-based quantum computation and quantum simulation. Typically, the spin dependence of these interactions is negligible and plays no practical role. In this Letter, we uncover that a strong electron-spin-dependent Rydberg interaction can emerge when the principal quantum numbers of the two $s$-orbital atoms differ by a sweet-spot value. This interaction originates from the fine-structure splitting of nearby $p$ orbitals, which endows it with distinct symmetry properties such that the electron spins are coupled to the relative position of the two atoms, featuring a spatially defined anisotropy. We further demonstrate that this interaction admits a universal form, independent of the principal quantum numbers, and highlight its fundamental distinction from conventional magnetic dipolar interactions, establishing it as a new type of native magnetic interaction in nature. Our findings introduce a new element to the Rydberg quantum simulation toolbox. As a concrete application, we propose a native realization of the Kitaev-Heisenberg model, which hosts an unusual stripe phase as a quantum many-body manifestation of spin-space locking.

Fast, precise, and quantum-non-demolition (QND) readout of superconducting qubits is a fundamental component of high-fidelity quantum sensing and computation. Conventional approaches typically operate in the dispersive regime, where the qubit-resonator coupling $g$ is weak compared to the detuning $\Delta$. While exhibiting good QND properties, the readout rate is limited to $\sim g^2\sqrt{N}/\Delta\ll g$, where $N$ is the number of photons in the resonator. QND readout in the nondispersive regime, where the readout rate reaches its full potential $\sim g$, relies on parameter sweeps that may encounter resonances, leading to measurement-induced state transitions (MIST). In this work, we study a nondispersive readout protocol that replaces these sweeps by sudden quenches of the coupling constant, using a resonator that is preloaded with photons. We call this protocol bang-bang readout, and show that it realizes single-shot projective measurements. The fidelity and QNDness of the qubit post-measurement are remarkably high, with an error that decreases like $1/N$. We show that the protocol can also be implemented without preloading the resonator by instead strongly driving the qubit, e.g., with a classical flux drive.

An agent monitors a complex environment, receiving one observation at each time step and eventually deciding how to label the resulting sequence. Does the sequence indicate an anomaly, and if so, of what type? Does it signal market instability, and to what degree? This is the setting of online multi-class classification: the input arrives sequentially, the full history is never available at once, and the agent must retain any past information relevant to the eventual decision. As the environment becomes more complex, the memory needed to track this information can grow rapidly without bound. Here, we introduce families of such multi-class classification games and show that any exact classical agent requires memory that grows without bound, whereas exact quantum agents can solve all tasks in the family with bounded memory. This separation is sharp: any classical agent using less than the required memory, under suitable input distributions, performs arbitrarily close to random guessing. Moreover, our quantum constructions are provably memory minimal, allowing us to derive the exact classical and quantum memory complexities to perform such tasks. In doing so, we establish an unbounded separation between classical and quantum memory cost for online multi-class classification.

We show that cavity quantum electrodynamics (QED) devices can realize dissipative Sachdev-Ye-Kitaev (SYK) universality, a paradigmatic setting for quantum chaos in open many-body systems. Ultracold fermions with disordered, all-to-all cavity-mediated interactions provide two complementary routes: atomic spontaneous emission in a single-mode cavity and photon leakage from a multimode cavity. Strikingly, both converge to the same non-Hermitian random-matrix universality despite originating from integrable and chaotic closed-system limits, respectively. In the single-mode cavity, dissipation creates quantum chaos from an integrable Hamiltonian. We trace this convergence to a tunable growth in dissipative rank, controlled, respectively, by the Lamb-Dicke parameter and the cavity-mode spacing. The integrability-to-chaos crossover is accompanied by a dynamical crossover from long-lived prethermal memory to rapid thermalization, visible in single-atom-resolved densities.

We study a one-dimensional scalar model for an effective-mass quasiparticle field coupled to a continuum of two-level atoms with at most one excitation present. We prove a general theorem on the existence of bound states under sign-definite spatially localized perturbations of constant atomic density and analyze the bound states for several exactly solvable examples.

Extreme-ultraviolet (XUV) spectroscopy represents an important new direction in precision physics, with potential applications ranging from the metrology of fundamental constants to tests of physics beyond the Standard Model. However, the application of quantum control methods for precision spectroscopy remains an open challenge in the XUV range. Here we present a novel quantum logic (QL) spectroscopy method for precision spectroscopy of weak XUV transitions, and numerically validate its feasibility for the $1S-2S$ transition at 40.81\,eV in singly-ionized helium (He$^{+}$). We propose a scheme based on a single He$^{+}$ ion co-trapped with a Be$^{+}$ ion in a Paul trap, and He$^{+}$ excitation with pairs of frequency-comb (FC) laser pulses upconverted to the XUV via High-Harmonic Generation (HHG). We investigate a nondestructive QL scheme to detect $1S-2S$ excitation, and compare its performance with a destructive readout based on state-selective ionization. Phase coherence of the XUV light is modelled and an optical cavity is used to filter the FC pulses prior to HHG. We model the motional excitation dynamics of trapped ions outside the Lamb-Dicke regime, and numerically validate a scheme we proposed in \cite{Grundeman} to cancel the first-order Doppler broadening and the recoil shift by synchronizing the ion's secular period with the time delay between the two excitation pulses. We show that precision spectroscopy of the $1S-2S$ transition in He$^{+}$ at the 10 kHz level is feasible, for improved tests of quantum electrodynamics (QED), a measurement of the Rydberg constant $R_{\infty}$ independent of hydrogen measurements, or an improved determination of the alpha particle and helion charge radii. The proposed method may also be applied to XUV spectroscopy of other ions outside the Lamb-Dicke regime.

Although quantum error correction is widely believed to be necessary for impactful applications of quantum computers, the design of quantum error correction codes is largely done by hand, without respect to problem or hardware constraints. In this work, we present a highly general and flexible framework for the computational design of both physics-inspired and hardware-aware quantum codes. To do so, we formulate code design as a Boolean satisfiability (SAT) problem and show how to incorporate all required error correction criteria. We prove that code design is NP-complete, ruling out any efficient algorithm for designing codes in general. Nonetheless, we show that state-of-the-art SAT solvers are able to effectively find solutions for many practical problems. Notably, we are able to design physics-inspired codes with up to 100 physical qubits in minutes, and we design new hardware-aware codes for biased noise which have a lower logical error rate than state-of-the-art surface codes.

Quantum sensors can achieve precision unattainable by classical sensors. However, dissipation coming from interaction with the environment can greatly degrade the performance of quantum sensors. Therefore, it is crucial to attempt harnessing dissipation to our advantage and investigate the sensing performance of driven-dissipative systems to gain practical quantum advantages. In this paper, we study a system of two-level systems driven coherently at a detuned frequency, and importantly, connected to a chiral waveguide that serves both as an interaction mediator and a bath. We show analytically that the steady state of such a system shows enhanced sensitivity to estimate weak detuning strength while the probe preparation time only grows linearly with system size. Therefore, the enhanced sensitivity is sustained even when the preparation time is incorporated. We further establish measurement protocols to achieve such sensitivity that are experimentally implementable. The chirality of the waveguide helps us to control both precision and range of enhanced sensitivity.

Excitation-energy transfer underpins the conversion of light into usable energy in photosynthetic organisms and serves as a paradigm for evolutionary optimized transport in open quantum systems. Although this process is often described as incoherent thermally assisted hopping, such descriptions become inadequate when electronic coupling, vibronic interactions and environmental fluctuations occur on comparable energy scales. Determining how the environment controls transport therefore remains a fundamental challenge. Here, we use temperature-dependent 2DES to investigate energy transfer in the photosynthetic antenna protein allophycocyanin over the range 10 - 296 K. The dominant $\beta \rightarrow \alpha$ transfer step exhibits a pronounced non-monotonic temperature dependence: the transfer time decreases from 400 fs at 10 K to 200 fs near 30- 40 K before increasing again to 400 fs at 296 K. In contrast, the homogeneous optical dephasing time decreases monotonically across the same temperature range. To interpret these observations, we model APC as a vibronically coupled excitonic dimer interacting with a structured environment and solve the dynamics using hierarchical equations of motion. Conventional fixed-bath models, including Drude-Lorentz and explicit intermolecular-mode spectral densities, fail to reproduce the observed turnover. Quantitative agreement is obtained only when the low-frequency sector of the environmental spectral density is allowed to anharmonically evolve strongly with temperature, while the high-frequency bath remains essentially unchanged. More broadly, these findings demonstrate that transport efficiency is controlled not simply by the magnitude of environmental fluctuations, but by the distribution of environmental spectral weight across frequency space, providing new experimental constraints on theories of molecular transport in complex quantum environments.

The usefulness of entanglement as a resource in quantum technologies increases for larger systems, that is, if more particles or higher-dimensional quantum systems are considered. Yet, the interplay between dimensionality and multiparticle entanglement is not well understood. Only for two-particle systems an unambiguous and coherent notion of entanglement dimensionality, based on the Schmidt decomposition, is known. We introduce a concept to characterize the entanglement dimensionality of multiparticle states based on decompositions of pure states into superpositions of states without genuine multiparticle entanglement. We provide constructive methods to characterize the resulting partition rank for pure and mixed states. This allows the identification of novel maximally correlated states as well as a discrete classification of quantum states under stochastic local operations and classical communication. From a mathematical perspective, our approach can be formulated in terms of the slice rank and partition rank of tensors and our results allow to characterize these by connecting them to a generalized injective tensor norm.

Efficient, deterministic, and high-fidelity preparation of large Fock states is essential for scaling bosonic quantum technologies and exploring quantum phenomena at large excitation energies. We introduce a deterministic one-parameter (D1p) protocol that maps Fock-state preparation in an infinite-dimensional Hilbert space onto two-dimensional amplitude amplification. Starting from a coherent state with $|\alpha|\simeq\sqrt{n}$, the initial target-state population scales as $n^{-1/2}$, yielding an iteration count and circuit depth of $\mathcal{O}(n^{1/4})$. Phase matching guarantees unit fidelity in the ideal model; remarkably, preparing $|{10^6}\rangle$ requires only 39 iterations. The protocol uses only displacements and number-selective phase operations, requires no numerical optimization, and further extends to state transfer, general superpositions, finite-dimensional systems, and multipartite entangled states. In the large-amplitude regime, its multi-target form prepares $L$-legged cat states with an iteration count determined only by $L$; cats with up to ten legs require only two iterations, independent of the coherent-state amplitude. This framework provides a broadly applicable route to highly excited bosonic states on platforms supporting these elementary controls.

Owing to their high controllability and connectivity, one-dimensional ion chains are attractive building blocks for near-term quantum computers. However, long ion chains are susceptible to motional heating caused by fluctuating external electric fields. To enable deep computations, this source of noise must be suppressed without inducing qubit decoherence or degrading qubit connectivity. We demonstrate steady-state mid-circuit sympathetic cooling of all computationally-relevant motional modes of a 23-ion chain consisting of \qubit qubit and \coolant coolant ions without using any qubit operations. In a room-temperature system, our cooling scheme preserves the mean phonon occupations of the long-wavelength axial and radial modes near their values following state preparation, while keeping the modes used to implement entangling gates near their ground states throughout a 56-ms circuit. Crucially, we show that our cooling sequence preserves qubit coherence, and evaluate its impact on single- and two-qubit gate operations. Additionally, we demonstrate a parallel qubit reset protocol leveraging the shared radial mode coupling between species. Our sympathetic cooling scheme represents a critical step toward reducing gate errors in individually-addressed long ion chains and establishes a versatile platform for simulating open quantum systems.

Multimode squeezing is a key resource for continuous-variable quantum technologies, but its spatial range in bosonic lattices is usually tied to dispersive propagation. Here we show that parametric pairing can create an exactly flat Bogoliubov band spanned by compact Bogoliubov generators, while producing phase-sensitive anomalous correlations and sub-vacuum collective-mode squeezing that extend far beyond their finite support. Each compact generator mixes annihilation and creation operators, thereby encoding the Bogoliubov squeezing structure, and neighboring translated generators can have nonzero commutator overlap. Enforcing canonical bosonic commutation relations therefore requires spatially extended linear combinations of these translated compact generators, which define the canonical Bogoliubov modes. The squeezing transformation of these modes varies with momentum and is quantified by the squeezing-sector symplectic quantum metric. A complex-momentum singularity of the analytically continued canonical Bogoliubov modes sets both the anomalous-correlation decay length and the momentum-space width of this metric, defining an intrinsic quantum-geometric length scale. This singularity can be tuned continuously while preserving exact flatness, thereby controlling the spatial range of correlations and squeezing. Away from exact flatness, long-distance correlations persist through multiple decay channels, while modes localized by defects and dimerized boundaries provide complementary probes of the underlying quantum geometry. In the weak-damping limit, the same quantum-geometric length scale can be extracted from frequency-filtered two-port correlations. Our results establish the quantum geometry of canonical Bogoliubov modes as a mechanism for spatially extended quantum resources arising from compact Bogoliubov generators.

Optimized daemonic ergotropy can make entanglement thermodynamically dispensable in measurement-assisted work extraction: for a fixed system marginal, quantum-classical states can reproduce the maximal work obtainable by optimizing the auxiliary measurement. We show that this equivalence is broken when the auxiliary measurement is randomized. For qudit-qubit quantum-classical states under Haar-random projective measurements, we derive upper bounds on the averaged daemonic gain and prove a gain-fluctuation trade-off, showing that any positive randomized gain necessarily entails measurement-induced fluctuations. In sharp contrast, a family of two-qubit entangled pure states attains the algebraic maximum of the gain allowed by a system marginal while remaining fluctuation-free for every measurement basis, yielding at least twice the gain achievable by any quantum-classical state with the same marginal. We further demonstrate that such conclusion holds when general two-qubit separable states are considered positioning randomized gain as a sufficient criterion for entanglement certification. Finally, we show that the entanglement advantage persists under partially randomized measurements sampled from a polar cap around the optimal basis. These results establish randomized daemonic ergotropy as a thermodynamic probe of entanglement and exhibit the connection between measurement-induced work fluctuations on the type of correlations: quantum entanglement vs classical.

Topological photonics has provided powerful design rules for routing and localizing light through geometry, symmetry and engineered coupling. However, fabricated nanophotonic and plasmonic devices rarely realize only the local or short-range interaction networks assumed in compact topological models. Long-range near-field coupling, retardation, radiation leakage, substrate-assisted hybridization, material dispersion and fabrication disorder can reshape the optical modes that are interpreted as topological. In this Perspective, I argue that nonlocality should be treated as a design parameter rather than as a residual perturbation. This shift requires moving from ideal phase labels toward calibrated interaction models, finite-structure observables, robustness maps and graded confidence measures. I discuss how full-wave simulations, experiments and physics-informed learning can connect geometric design variables to effective electromagnetic interaction networks. Such calibrated workflows can clarify when a topological design rule is reliable, when it fails, and how nonlocal coupling can be exploited for robust nanophotonic devices.

We give a rigorous realization of the dilute instanton picture for a semiclassical Schrödinger operator with a symmetric double-well potential on $\mathbb{R}^n$. Using a localized Feynman–Kac representation, we decompose the heat-kernel trace according to the number of passages made by a Brownian bridge between shrinking neighborhoods of the two wells. We identify the weight of one passage with a hopping coefficient $\rho_\lambda$, $\displaystyle \rho_\lambda = \int_{\partial\Omega} \left( \nabla\overline{\varphi_{\lambda,0}^{\Omega}}\, \varphi_{\lambda,0}^{-\Omega} - \overline{\varphi_{\lambda,0}^{\Omega}}\, \nabla\varphi_{\lambda,0}^{-\Omega} \right)\cdot\nu. $ On the exponentially long time scale $\beta=N/\lvert\rho_\lambda\rvert$, the number of passages converges, for every fixed $N>0$, to a Poisson random variable of mean $N$. We identify $-\frac{1}{\lambda}\log\lvert\rho_\lambda\rvert\to S(d,-d)$ and obtain $\displaystyle E_1(\lambda)-E_0(\lambda) = 2\lvert\rho_\lambda\rvert\left(1+o(1)\right). $ Thus the familiar instanton expansion of the double-well eigenvalue splitting emerges directly from a factorization of the heat-kernel trace.

Phase-space and quasiprobability methods now play operational roles in quantum technologies, characterizing localization, non-Gaussianity, nonclassical resources, and coarse-graining. We develop an exact, representation-consistent analysis of the lowest quasi-exact ground state of the symmetric double-Morse oscillator. In the double-Morse potential, the dimensionless parameter $A$ controls the separation of the minima and the central barrier, thereby changing the physical ground state. At fixed $A$, the Cahill–Glauber parameter $s$ labels the quasiprobability $W_A^{(s)}(q,p)$: $s=0$, $-1$, and $1$ give the Wigner, Husimi $Q$, and Glauber–Sudarshan $P$ representations, respectively. Although the potential is double-welled for $0<A<1$, the exact ground-state amplitude is single-peaked at the origin and lies above the barrier; as $A$ approaches unity, the merged well remains locally quartic rather than harmonic. Closed analytical expressions are obtained for the Wigner function and Weyl characteristic function. The Wigner function displays the $A$-dependent exchange between position and momentum localization and retains negative regions, certifying nonclassicality and, for this pure state, non-Gaussianity. The Weyl function is its Fourier dual, generates symmetrically ordered moments and cumulants, and yields the full $s$-ordered hierarchy. For $s<0$, isotropic Gaussian smoothing suppresses fine sign-changing structure while preserving the large-scale localization envelope. The Husimi endpoint is nonnegative without implying classicality, whereas the $P$ representation remains distributional. Thus, $A$ controls the physical phase-space geometry, while $s$ controls how the same non-Gaussian and nonclassical state is resolved across complementary representations

Translating observed data into a reliable estimate of the secure key rate is a crucial step for operating a quantum key distribution device. We provide a computational method for this task that only requires eigenvalue computations and is therefore both fast and resource efficient. In contrast, existing approaches rely on semidefinite programming or programming on the entropy cone, whose memory requirements can scale as $d^4$ in the underlying Hilbert-space dimension. Our method reduces this requirement to $d^2$. A minimal implementation of our algorithm takes fewer than 100 lines of Common Lisp. We demonstrate real-time key-rate estimation on a Raspberry Pi with a 1 GB memory and a Cortex-A53 processor. Despite these modest resources, our implementation outperforms existing workstation-based benchmarks by several orders of magnitude. Non-numerical verification can be incorporated with little overhead using rational approximations. These results open the way toward embedding complete numerical security analysis directly into qkd hardware.

We establish a geometric generalization of the Bloch sphere for two-level quantum systems with non-Hermitian Hamiltonians using the Spacetime Algebra (STA) formulation. By lifting the state density operator from the even subalgebra to the full STA, we show that the state space expands from the unit 2-sphere to a future light cone. The non-unitary time evolution generated by a general non-Hermitian Hamiltonian corresponds to proper orthochronous Lorentz transformations on the null vectors. We classify the Hamiltonian dynamics into four distinct geometric classes: spatial rotations (corresponding to $\mathcal{PT}$-symmetric systems), pure boosts (anti-$\mathcal{PT}$-symmetric systems), null rotations (exceptional points), and general mixtures. We also use this formulation to study several results from PT-symmetric quantum mechanics, including the topological features of the exceptional points.

Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been extended beyond the measurement of conventional linear observables. This review summarizes recent progress in adapting QMC to many-body quantum-information, focusing on qubit or spin-$1/2$ systems as a concrete setting while keeping the discussion broadly applicable to qudit and bosonic systems. We present a unified perspective on the extraction of nonlinear diagnostics, including entanglement entropies and entanglement spectra, Rényi negativities for mixed-state entanglement, stabilizer entropies for quantum magic, and decoherence-driven phenomena such as the interplay between imaginary-time evolution and decoherence and strong-to-weak spontaneous symmetry breaking.

We present a variational–adjoint interpretation of quantum mechanics in which the interaction between forward and adjoint wavefunctions defines a general sensitivity kernel of the system. This Fréchet interaction density quantifies how perturbations in the wavefunction (or system parameters) influence a chosen observable. The familiar Born probability density appears as a special case when the adjoint wavefunction is chosen as the complex conjugate of the forward wavefunction, for which the interaction density becomes real and non-negative. Within this framework, probability is a particular positive-definite form of sensitivity described by the Fréchet interaction density. In general, the variational–adjoint interpretation also produces Fréchet sensitivity kernels associated with other quantum observables, including momentum, energy, and spin. This suggests that the Born probability density belongs to a broader class of Fréchet sensitivity kernels associated with quantum observables. The proposed interpretation also provides a connection with time-symmetric interpretations of quantum mechanics and possible future applications in quantum control and quantum metrology.