Papers

Quantum machine learning (QML) could have the potential to leverage advantages of quantum over classical computing but still lacks strong evidence of actual improvements and scalability, partly due to phenomena such as barren plateaus. In this paper, we employ a hybrid quantum neural network (QNN) on a dataset on cloud microphysics, containing processes for phase transitions of water in the atmosphere and its related temperature changes, which are highly relevant for accurate climate predictions and projections. To reach optimal performance of our QNNs, we employ a rich and trainable frequency spectrum together with expressivity enhancing classical postprocessing. We find that our QNNs strongly benefit from extensive hyperparameter optimization and thereby demonstrate the feasibility of applying QNNs to complex physical systems. At the same time, the QNNs are outperformed by classical baselines in the form of simple fully-connected neural networks. We discuss identified bottlenecks of this class of quantum models to learn the full complexity of the cloud microphysics dataset to show that there is a need to further understand and improve variational quantum models for machine learning such that they might fill the gap where classical models fail or are inefficient.

Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.

Based on Geroch's process of dropping a system into a black hole from the vicinity of the horizon, we investigate in this paper the influence of deformation on the Bekenstein entropy bound both for (3+1) and (2+1) dimensions in the context of a generalized uncertainty principle (GUP). While providing a coherent framework that sets an upper limit on the entropy across dimensions we show, within a semiclassical treatment, that while a negative GUP deformation yields a universal relaxation of the bound, a positive deformation tightens it. Our results may be interpreted as a response to Planck-scale modifications of the near-horizon redshift.

In this paper we argue that, in addition to the statistical structure of quantum theory, another structure, referred to here as the “Noether structure," is necessary to describe the composition of systems and to define completely positive operations. A Noether structure reflects the dual role of Hermitian operators as observables on the one hand and as generators of symmetry transformations on the other. This idea has been expressed in a similar form in the works of Alfsen and Shultz, who investigated the conditions under which the Jordan product can be extended to an associative product of operator algebras. Our investigations into the Noether structure and the composition of systems are limited to the finite-dimensional case and establish a connection to completely positive operations. In the case of pure operations, the latter can be characterized as orientation-preserving maps.

Photonic cluster states are a key resource for photonic quantum information processing. So far, deterministic generation of these states has been limited to the near-infrared wavelength range. To achieve quantum advantage in communication while maintaining compatibility with silicon photonics, operation in the telecom wavelength range is required. In this work, we demonstrate deterministic cluster state generation directly in the telecom C-band. This is achieved through repetitive excitation of a hole spin confined in an indium-arsenide quantum dot subjected to an external magnetic field. We characterize the quantum process that generates the cluster state by measuring its process map, obtaining a fidelity of $\mathrm{F} = 0.71 \pm 0.01$ to the ideal case. As part of this characterization, we observe spin–photon polarization entanglement with a negativity of $\mathrm{N} = 0.27 \pm 0.02$. The emitted photons exhibit indistinguishability of at least 83%, demonstrating the potential for future fusion gates necessary for photonic cluster state generation beyond linear connectivity.

In advanced complementary metal-oxide-semiconductor (CMOS) quantum chips, compact gate stacks make it difficult to connect lithographic geometry, electrostatic confinement and many-electron spin filling in one transparent model. This connection is central to design-technology co-optimization (DTCO). Here we develop a reduced-order analytical framework for asymmetric multigate silicon quantum-dot devices. Its electrostatic core, the Poisson-kernel coupled-interface Green-function (PK-GF) model, agrees with an independent finite-volume solution at the millivolt scale for the matched two-dimensional problem, without fitting to that solution. We then pass the gate-derived confinement, rather than a harmonic or fitted potential, to a spin-valley many-body calculation for a jellybean quantum dot with N = 2-17 electrons at B = 5 T. The unrestricted Hartree-Fock (UHF) solution supports occupation-dependent, Wigner-molecule-like charge localization but likely overestimates spin polarization. Complete active-space configuration interaction (CASCI) supports a low-spin branch within the tested active spaces, which aligns with the experiments. The workflow therefore connects CMOS layout, device electrostatics, and potential-determined quantum observables, providing an auditable modelling layer for CMOS-based qubit design and DTCO.

The probabilistic nature of quantum measurement provides a direct window into the structure and complexity of many-body wave functions. When only part of a system is measured, the remaining degrees of freedom form an ensemble of post-measurement states whose statistical structure can reveal a stronger form of thermalization, known as deep thermalization. Recent numerical evidence suggests that this phenomenon is characterized by convergence of the projected ensemble to the Scrooge ensemble, a maximally random ensemble compatible with a given density matrix. In this Letter, we use the solvable Sachdev-Ye-Kitaev (SYK) model to unveil the mechanism by which the Scrooge ensemble emerges in many-body systems. By formulating measurement probabilities and post-measurement states in terms of path integrals, we analytically characterize all moments of the projected ensemble and show that they exactly match those of the Scrooge ensemble, even at short evolution times. We further connect this result to the saddle-point structure of the measurement path integral, which naturally generates the replica permutations underlying Scrooge statistics. Our results establish the solvable SYK model as a tractable setting for exploring universal statistics of quantum measurements in chaotic many-body dynamics.

Significant effort has been devoted over the past decade to understanding whether quantum resources can provide advantages in distributed computing, and in particular whether they can help overcome locality constraints in networks, typically in Linial's LOCAL model. Recently, Coiteux-Roy~et~al.~(STOC 2024) showed that quantum resources do not help for 3-coloring unrooted trees: in particular, their lower bound holds in the stronger non-signaling model, which formalizes the principle of physical causality in distributed computing. The case of rooted trees, however, was left open by their work. For rooted trees, the deterministic Cole-Vishkin algorithm 3-colors $n$-node trees in $O(\log^\star n)$ rounds, matching Linial's classical $\Omega(\log^\star n)$ lower bound (FOCS 1987). In this paper, we show that any algorithm in quantum-LOCAL (without pre-shared entanglement) that properly 3-colors $n$-node rooted trees with probability at least ${1-O(1/\log n)}$ must perform $\Omega(\log^\star n)$ rounds. That is, quantum resources provide no advantage for 3-coloring rooted trees. To get this result, we show a lower bound of $\Omega(\log^\star \Delta)$ for 3-coloring any $\Delta$-ary tree with success probability at least $1-1/\Delta$. The proof uses a color lifting technique that bears similarity to Linial's original argument. We also show, as a separate result, that 2-coloring even-length $n$-node cycles with probability $1-O(1/n)$ requires $n/2-1$ rounds in the quantum-LOCAL model, even with pre-shared entangled states. This improves the previously known $\lceil (n-2)/4 \rceil$ lower bound of Gavoille, Kosowski, and Markiewicz (DISC 2009) by a factor of two, and shows that quantum algorithms cannot save even a single round over classical deterministic algorithms for 2-coloring even-length cycles.

Quantum architecture search for molecular ground-state estimation is commonly evaluated through energy accuracy, which does not describe circuit cost or the physical properties of the prepared state. We introduce HamQASBench, a structure-aware benchmark comprising eleven molecular Hamiltonians of up to fourteen qubits, selected using Hamiltonian and target-state properties and supplied with exact references. Its evaluation protocol combines energy accuracy and success rates with reference-relative circuit cost, local entropy profiles for non-degenerate targets, and state identification within degenerate ground subspaces. Experiments with five methods spanning four search paradigms reveal differences hidden by energy-only comparisons. On a near-product instance under the shallow search budget, the best outputs of all five methods reach chemical accuracy while using between two and sixty-two gates. Equal-energy outputs on a degenerate instance occupy distinct spin components. Local entropy profiles distinguish inaccurate outputs and show that entangling-gate counts need not reflect realized entanglement. Across the molecular instance ladder, product-state outputs can meet or miss chemical accuracy, motivating interpretation of success alongside target-state properties. These results support retaining energy as the task-success criterion while using circuit-cost and state diagnostics for more informative comparisons. The benchmark instances, references, evaluation implementation, and per-run data are released for reuse.

While complex-pole hierarchical equations of motion (HEOM) have dramatically expanded the reach of numerically exact quantum dynamics simulations of open quantum systems, they suffer from numerical instabilities rooted in the non-Hermitian structure of their Liouvillian. Yet, the origin of this structure remains obscure. Here, we report a previously unknown gauge freedom in complex-pole HEOM: a continuous family of analytically equivalent Liouvillians, all encoding the same bath correlation function, whose numerical properties vary dramatically. This gauge controls both the eigenspectrum and non-normality of the hierarchy generator, revealing spectral divergence and non-normal error amplification as two distinct instability mechanisms. By optimizing this gauge, we introduce GO–HEOM, which eliminates divergences in strongly coupled Brownian oscillator environments and extends numerically exact simulations of sub-Ohmic dynamics – including through the delocalized-to-localized quantum phase transition – to previously inaccessible coupling strengths. Because this gauge transformation is independent of the bath-correlation decomposition scheme, our GO–HEOM becomes a general, broadly compatible strategy for accessing numerically exact quantum dynamics of open quantum systems over arbitrary coupling and highly non-Markovian regimes.

Finite quantum environments can relax local probes without acting as canonical baths. We study this distinction for a probe qubit coupled to a programmable bath of ($N$) qubits under excitation-number-conserving dynamics. The conserved charge partitions the Hilbert space into sectors. We characterize probe-level bath emergence using the sector-resolved late-time population ($p_e^{(q)}$), the sector-memory variance ($M_N$), and a global Gibbs-fit error ($\Delta_G^{\mathrm{global}}$). Exact simulations with Haar-random pure states in each complete fixed-charge sector yield sector-dependent populations close to the maximally mixed-sector benchmark ($p_e^{(q)}=q/(N+1)$), producing a nonzero Gibbs obstruction. We then construct charge-preserving Floquet circuits using ($R_z$) phases and ($XX+YY$) exchange gates, validate them with ideal and noisy Qiskit simulations, and implement finite-depth experiments on IBM Fez. For ($N=4$) and ($\epsilon=0$), the hardware data give ($M_N \simeq 0.044$), ($\Delta_G^{\mathrm{global}} \simeq 0.558$), and charge preservation near 0.90 after readout mitigation. A paired symmetry-breaking scan using bath ($R_x(\epsilon)$) rotations reduces both diagnostics while increasing charge leakage, but does not erase sector ordering over the accessible depths. These results show that equilibration within constrained sectors is insufficient to produce a single sector-independent Gibbs state for the probe.

We present a theoretical study of spin- and valley-resolved quantum transport in monolayer MoS$_2$ under the combined influence of mechanical strain and an external scalar potential, a combination whose simultaneous unexplored. Within an effective massive Dirac Hamiltonian that incorporates intrinsic spin–orbit coupling, strain induces valley-dependent momentum shifts that lift the degeneracy between the $K$ and $K'$ valleys and strongly modify the transport characteristics. The scalar potential modifies the tunneling spectrum, leading to pronounced changes in resonant transmission, Fabry–Pérot interference, and conductance. We show that the interplay between strain and electrostatic potential enables efficient control of both valley and spin polarization of the transmitted current. In particular, we identify a dual-knob control scheme in which the barrier width governs the frequency of conductance oscillations while strain independently controls their phase and amplitude. Furthermore, we predict electrostatic spin inversion – a sign reversal of spin polarization achievable purely by gate tuning at finite strain, requiring no geometric reconfiguration. Depending on the strain orientation, the transmission probability and conductance can be selectively suppressed or enhanced, resulting in highly tunable valley- and spin-polarized transport. These findings demonstrate that strain and potential engineering provide orthogonal and independently operable mechanisms for controlling conductance as well as spin and valley degrees of freedom in monolayer MoS$_2$, offering promising prospects for spintronic and valleytronic device applications.

Bound states in the continuum (BICs) are counterintuitive localized states that lie within the continuum of extended states. While extensively realized and utilized in classical wave systems, it is still unclear what a close analog of BICs would be, and how to extract their experimental signature in quantum-optical settings – where the wave field itself is quantized into bosonic excitations. Here, we present a paradigmatic quantum-optical model consisting of a driven multi-level Jaynes-Cummings (JC) system, featuring few quantum degrees of freedom yet capable of hosting a BIC. Using the concept of a Fock-state lattice (FSL), this model can be mapped to an extended structure comprising two semi-infinite inhomogeneous Su-Schrieffer-Heeger (SSH) chains coupled to a common continuum. An appropriate quantum superposition of two topological zero modes from the separate chains forms a BIC that remains perfectly localized in the Fock-state dimension within the continuum spectrum, due to complete decoupling from the common continuum via destructive quantum interference. We further develop a method to extract the spectroscopic signature of the BIC – a discrete peak embedded in a continuous background – by Fourier-transforming the time-dependent dynamics of the system's chiral-symmetry operator. A highly feasible experimental proposal using a single trapped ion is provided. Our work bridges BIC physics with quantum optics, opening a pathway to harnessing such exotic states at the quantum limit.

Strengthening light-matter coupling has become a central challenge in cavity quantum electrodynamics (QED), enabling ultrafast gate operations, qubit protection, and deterministic nonlinear optics. As the coupling increases, even the simplest configuration, a two-level atom interacting with a quantized field, requires careful treatment, as exemplified by the gauge-invariant quantum Rabi model (QRM). Here we propose a magnetic graph model for single-atom cavity QED, which enables the interpretation of quantum dynamics across the ultrastrong coupling regime through graph connectivity. We demonstrate that the generalized QRM maps onto a complex bipartite graph of identical sites under Floquet boundary conditions. This framework captures the crossover from weak to deep-strong coupling via a single metric: the cost of disconnecting a nonmagnetic subgraph. We examine the mechanism underlying this connectivity transition, establishing phase frustration induced by subgraph topology as the primary driver. Scalable to many-body systems, this approach bridges graph theory and cavity QED, revealing highly complex-graph dynamics even in the simplest setting.

Graph-theoretic frameworks have been widely employed in quantum physics to address the high-dimensional complexity of quantum systems. Although open quantum dynamics incorporates system-bath coupling via numerous interacting operators, it has been formulated algebraically with a partial set of jump operators or statistically universal reservoirs, leaving the underlying connectivity structure largely unexplored. Here, we propose a universal graph-theoretic framework for Markovian quantum dynamics. The framework maps open quantum dynamics onto two uniquely defined graphs, where the quantum master equation is rigorously interpreted as the average wave characteristic of operator-valued signals across the graphs. Applying this framework to the open quantum Rabi model, we demonstrate an open-system generalization of Fock-state lattices, characterize graph-topological signatures of dissipation, and classify the weak-to-ultrastrong coupling transition. Building on these representations, graph pruning reveals the backbone of open quantum dynamics, which enables superior graph neural-network learning. Our results bridge graph theory and open quantum dynamics, achieving efficient data-driven analysis of high-dimensional complexity.

Coherent perfect absorption (CPA) extinguishes optical fields through interference and dissipation, but conventional implementations rely on material loss that is largely fixed after fabrication. Here we demonstrate all-optically controllable CPA based on frequency conversion in a periodically poled lithium niobate waveguide resonator. Pump-driven frequency conversion couples a resonant signal field at 1581 nm in the main system to a non-resonant environmental mode at 780 nm, creating a dynamically tunable effective loss channel. The nonlinear cavity acts as a tunable lossy beamsplitter without intrinsic material absorption. Under coherent two-sided signal injection, we observe up to 92 % absorption. We further introduce environment-assisted CPA by injecting an external field into the frequency-converted environmental mode, turning the environment from a passive loss reservoir into an addressable coherent control port. Our results establish a frequency-conversion-based platform for all-optical control of dissipation in CPA, combining pump-tunable loss with environment-assisted coherent control.

Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.

Hamiltonian estimation is an effective approach in studying the structure and dynamical evolution of quantum systems. The difficulty in estimating the Hamiltonian is that an $N$-qubit Hamiltonian has $4^N-1$ unknown parameters, requiring exponentially many equations for information extraction. In this paper we develop a method based on compressed sensing to estimate the Hamiltonian of a multi-qubit system. We identify a problem where as $N$ increases, the common sufficient condition (Restricted Isometry Property) for compressed sensing often fails, obstructing the application of compressed sensing in ($N\geq 3$)-qubit Hamiltonian estimation. To solve this problem, we propose a “scale transformation" technique to restore RIP and ensure a compressive estimation of a $k$-sparse Hamiltonian using only $O(k\log(4^N/k))$ equations. In the numerical examples, we estimate the Hamiltonians of two 6- and 30-qubit systems, demonstrating the effectiveness of the method.

We investigate phase transitions in the extended Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor hoppings and an imaginary staggered chemical potential. In the presence of small non-Hermiticity, exceptional points emerge in pairs from the gap-closing momenta near the topological phase boundaries of the Hermitian limit. Utilizing the Krylov spread complexity and entanglement entropy, we analyze two dynamical protocols: (i) preparing the non-Hermitian ground state via a unitary transformation, and (ii) evolving the system under the non-Hermitian Hamiltonian. We show that the spread complexity, and long-time spread complexity as well as entanglement entropy can effectively signal phase transitions in the first and second protocols, respectively. To unravel the detailed structure of the transitions, we introduce the momentum-resolved complexity that identifies the characteristic modes and tracks their evolution with the driving parameter. In the regime where the system possesses a purely imaginary spectrum, we further identify dynamical phases based on the saturation behavior of the spread complexity. The entanglement entropy is also found to exhibit similar saturation behavior, thereby providing a more experimentally accessible probe of the dynamical phases.

Quantum networks can exhibit nonclassical correlations that cannot be explained by classical models with independent sources. While the role of entanglement is well understood, the impact of measurement design remains largely unexplored. Here we develop an operational framework for certifying network nonlocality in the bilocal Alice–Bob–Charlie network using ancilla-assisted meters to evaluate the nonlocal observables required for bilocal and fully network nonlocal (FNN) witnesses. The approach successfully reproduces both bilocal and FNN correlations in simulation. On the 156-qubit superconducting processor ibm\_kingston, we observe bilocal nonlocality with $\mathcal{S}_{\rm BLHV}=1.067(6)>1$ after readout-error mitigation, while the FNN witnesses reach $99\%$ and $96\%$ of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.

Expressive parameterized quantum circuits (PQCs) are often designed under a dilemma: the growth of expressibility and entangling power (EP) that improves Hilbert-space coverage is also expected to randomize an ansatz and activate barren-plateau (BP) conditions. We show that this dilemma is not a one-dimensional tradeoff. The usual picture collapses three inequivalent objects – parameter-ensemble coverage, fixed-circuit entangling response, and local gradient moments – into one scalar narrative. For a fixed circuit probed by Haar-product inputs, EP is a global two-copy mean of the output-entanglement distribution, whereas entangling-power deviation (EPD) is a global four-copy fluctuation descriptor. Gradient variance, however, is a local two-copy contraction selected by a parameter light cone and a cost observable. This moment hierarchy yields an analytic separation: equal EP need not imply equal trainability, as witnessed by equal-EP circuits with different EPDs and different gradient variances. These separations turn EP and EPD into a two-dial design rule for PQC ansatzes: EP measures how far the circuit has moved along the coverage dial, while EPD monitors whether input-dependent variability remains. We find that ansatz routes can reach high, Haar-like coverage before EPD and gradient variance collapse, showing that coverage and BP activation are distinct crossover events. The EP/EPD framework thus breaks the apparent one-dimensional expressibility-trainability tradeoff into a practical design rule: search for highly expressive PQCs in the window where coverage is high but BP-like homogenization has not yet erased trainable structure.

Quantum compilers play a key role in transforming quantum circuits into lower-cost implementations with improved execution fidelity. This process is commonly guided by circuit-level metrics, such as gate counts and circuit depth. Although compiler pass tuning has been widely studied in classical compilation, directly transferring these techniques to quantum compilers is challenging, because quantum programs are expressed as circuits and exhibit optimization behaviors that are shaped by quantum-specific structures. Prior quantum compiler tuning approaches have begun to use circuit features to guide pass selection, but they remain limited in two aspects: they search only a small portion of the optimization-pass space, and they mainly rely on static features that do not explicitly reflect how a circuit reacts to compiler optimizations. We present QuTuner, a feature-guided quantum compiler pass tuning framework that generalizes across compilers and tuning objectives. QuTuner first builds a large optimization dataset. It then characterizes each circuit from two complementary views: static circuit features that describe circuit structure, and optimization-aware pass embeddings that summarize the circuit's responses to individual optimization passes. Using these representations, QuTuner trains two offline models to retrieve and rank candidate pass sequences for unseen circuits, followed by lightweight refinement. We evaluate QuTuner on Qiskit and PyTKET using two benchmark suites. On Qiskit, QuTuner improves the evaluation-metric reduction by up to 84.85% over the strongest baseline while reducing tuning time by 73.59%. On PyTKET, it improves metric reduction by up to 18.68% with a 64.49% reduction in tuning time. These results show that QuTuner provides an effective approach to adaptive pass tuning for quantum compilers.

With unitary coin operator that is a random matrix drawn from a uniform distribution with respect to the Haar measure, we construct a variant of a discrete quantum random walk using a d-regular undirected connected simple graph. With each step of the walk, the coin operator random matrix is drawn independently from the distribution. The expectation value over the distribution of random unitaries for the associated quantum channel gives a depolarization channel for the coin subspace and resembles the associated classical random walk where the direction a walker steps depends upon the outcome of a fair coin or balanced d-sided dice. Remarkably, despite the fact that the averaged channel depolarizes the coin subspace, measurements in the vertex subspace can be designed that would reveal information about the initial quantum state, even after many iterations of the channel. We illustrate with examples of quantum walks on Cayley graphs of Abelian groups, such as the cycle and hypercube graphs. For Cayley graphs of Abelian groups, the averaged channel is dephasing in the Fourier basis. These quantum walks are examples of bipartite strongly interacting systems, where one subsystem is strongly perturbed, yet information about the initial state in the other subsystem is potentially measurable forever. Due to its decoherence, a quantum random walk with a Haar-random coin would not be useful in search algorithms but could aid in understanding quantum systems with strongly perturbed subsystems.

Conical 2-designs are families of positive operators possessing crucial symmetry properties that allow them to efficiently characterize important quantum measures. However, little is known about their general structures and properties. We propose a construction method of conical 2-designs whose elements are not of equal traces, based on a generalization of equiangular weighted frames to non-projective operators. We provide a detailed analysis of their properties, relations to quantum measurements, and applications, together with examples that go beyond the known classes. This constitutes a major step toward a full characterization of informationally overcomplete quantum measurements.

In 2017, Terry Rudolph introduced an elementary rewriting system that relies on a representation of quantum states as misty states to accurately describe the basics of quantum circuits and quantum computation to high-school and middle-school students. The accessibility and effectiveness of the system are remarkable: every calculation can be done to good-enough accuracy, and perhaps with a small overhead, using just a tiny, universal set of gates chosen to take advantage of a remarkable mathematical result by Yaoyun Shi, leveraging another powerful result by A. Y. Kitaev. The misty formalism greatly simplifies calculations and makes them accessible to first-time learners using only simple arithmetic, and without sacrificing accuracy; it, too, is universal, inasmuch as you can use it to do any quantum calculation with maybe just a small overhead. We don't advocate that we should recast all of quantum theory into this formalism. The misty state picture is a good way of getting people to the heart of some nontrivial quantum theory without having to first absorb a huge amount of (what might initially seem largely) irrelevant math. Our argument is that the misty formalism can effectively be used to facilitate a transition to the full, conventional quantum-mathematical apparatus. To this end, we start by reviewing the original proposal, consider its strengths and limitations, and show it in action via entanglement swapping. We then extend the formalism through a new category of (irreducible) misty states acting as fixed points, and present the GHZ game in this new, general setting and representational semantics.

Tractatus Quanticum (arXiv:2512.06034 [quant-ph]) is described by its authors as 'a re-editing, which takes quantum mechanics into account, of Wittgenstein's famous Tractatus.' The original Tractatus appeared with an introduction by Bertrand Russell. For Tractatus Quanticum, that role fell to us. This is the result.

Continuous Ising solvers embed a discrete optimization problem into a continuous dynamical system and recover the spin configuration by sign readout, but dense interaction evaluation gives an $O(N^2)$-per-step cost. We show that this cost is not intrinsic: during late-stage simulated bifurcation the trajectory collapses onto a lower-dimensional active subspace, and saturated coordinates can be eliminated exactly by a variational frozen-set identity whose couplings fold into an induced field on the unresolved subsystem. We prove large-parameter recovery for the external-field quartic model, the hard-box limit of ballistic confinement, and a robust-margin freezing criterion. The resulting algorithm, iSTAR (Ising Stable-set Tail-Aware Reduction), exploits this collapse by detecting stabilized coordinates and continuing only on the active tail. An online certified implementation on the G-set benchmark preserves the same-seed baseline in all runs and removes on average 64.4% of the dense interaction work.

Quantum conference key agreement (QCKA) enables multiple users to establish a common secret key with information-theoretic security and is regarded as a key primitive for secure communication in future quantum networks. However, practical implementations of QCKA typically suffer from higher noise levels than conventional bipartite quantum key distribution (QKD), making the improvement of the tolerable error threshold an important challenge. Gottesman and Lo proposed two preprocessing procedures for QKD with two-way classical communication, known as the B-step and the P-step, which enhance the tolerable error threshold. In this paper, we analyze the asymptotic security of QCKA with tripartite GHZ states and two measurement bases using two-way classical communication, including multiple B-steps and P-steps. We derive the corresponding secure key rate analytically and demonstrate that iterative B-steps can increase the tolerable error threshold beyond 20%, significantly improving upon the approximately 11% threshold achievable without two-way classical communication and the approximately 15% threshold obtained with only a single B-step. Our results show that two-way classical communication can substantially enhance the robustness of practical QCKA protocols.

In this paper, we study the two-dimensional Schrodinger oscillator within a dynamical noncommutative (DNC) space. By leveraging perturbation theory, we derive the energy eigenvalues and eigenvectors and systematically analyze the effects of both dynamical and non-dynamical noncommutative settings. First-order corrections to the eigensystem are obtained, revealing that the energy shift explicitly depends on the DNC parameter tau. Furthermore, we explore the thermal properties of the system by employing the partition function. Numerical results are presented to provide a comprehensive analysis of the system behavior under the considered effects. Notably, in the DNC framework, the commutation relations and the deformation parameter are position-dependent. Using the two-dimensional Bopp-shift, we effectively map the noncommutative problem to its commutative counterpart.

We address the ratio between the trace speed and the Hilbert-Schmidt speed for differentiable finite-dimensional quantum states, $\mathcal R=\|\partial_\phi\rho\|_1/\|\partial_\phi\rho\|_2$. Since the tangent $\partial_\phi\rho$ is Hermitian and traceless, $\mathcal R$ obeys stronger bounds than those for generic operators. For any nonzero tangent of rank $r$, we prove the sharp bounds $\sqrt{2}\le\mathcal R\le\sqrt{r}$ for even $r$ and $\sqrt{2}\le\mathcal R\le\sqrt{r-1/r}$ for odd $r$, characterizing all equality cases. Nonstationary pure-state and qubit families saturate the lower bound $\mathcal R=\sqrt2$. For odd Hilbert-space dimension $d$, we further prove the sharp global maximum $\mathcal R\le\sqrt{d-1/d}$. Interpreting $\mathcal R^2$ as the participation ratio of the singular-value distribution yields an effective-rank picture, $r_{\mathrm{eff}}=\mathcal R^2$. We decompose the effective rank into classical eigenvalue and quantum eigenvector contributions and obtain the bound $r_{\mathrm{eff}}\le r_C+r_Q$, with equality when either component vanishes. Linking the effective rank to the quantum Fisher information $F$ gives $r_{\mathrm{eff}}\ge 8\,\mathrm{TS}^2/F$, showing that a large effective rank is required when this lower bound substantially exceeds the universal minimum value $2$. Finally, a hierarchy of quantum speed limits shows how the effective rank controls the tightness of bounds expressed through the Hilbert-Schmidt speed.