Papers

We derive an exact information-geometric inequality valid for both Markovian and non-Markovian mixed-state dynamics. This inequality saturates into a strict equality for single qubits because they belong to the quantum exponential family. This identity enables a non-iterative linear regression approach to continuous-time quantum process tomography, which, provided the full-rank condition is satisfied, yields a unique global solution and avoids local minima traps typical of standard non-linear optimization. Furthermore, as the formulation is inherently unconstrained, negative dissipation rates provide direct evidence of non-Markovianity. Numerical simulations of the unital diagonal Bloch generator derived from the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation demonstrate the validity of this geometric estimator and highlight the necessity of error mitigation near the pure-state boundary where the inverse metric becomes singular.

Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own right. A substantial source of difficulty in working with quantum graphs compared to classical graphs stems from the fact that they are no longer discrete objects. This makes it generally difficult to construct insightful, non-trivial examples. We present a collection of non-trivial quantum graphs that can be thought of in discrete terms, and that can be expressed in the diagrammatic formalism introduced by Musto, Reutter, and Verdon. The examples arise as the quantum graphs acted on by increasingly smaller classical matrix groups, and are parametrised by triples of matrices $(A, B, C)$. The parametrisation reveals a clean decomposition of quantum graph structure into classical and genuinely quantum components: $A$ and $C$ are described by a classical weighted graph called the strange graph, while $B$ provides a purely quantum contribution with no classical analogue. Based on this model, we give exact formulas or establish bounds for quantum graph parameters, such as the number of connected components, the chromatic number, the independence number, and the clique number. Our results provide the first large, parametric families of quantum graphs for which standard graph parameters can be computed analytically.

We present a comprehensive and self-contained framework for the efficient classical simulation of Clifford circuits acting on $d$-dimensional qudits, including realistic Pauli/Weyl noise via stochastic simulation. Our approach uses the stabilizer tableau formalism for qudits of arbitrary dimension and tracks both stabilizer and destabilizer generators under Clifford updates. The classical simulation remains efficient with simple algebraic Clifford update rules over $\mathbb{Z}_d$. Computational basis measurements in prime dimensions are handled by a generalized Aaronson-Gottesman (CHP) procedure. In composite dimensions, $\mathbb{Z}_d$ is not a field and the standard tableau reduction fails, so we employ an exact Smith normal form decomposition to enable efficient sampling. Noise is modelled as probabilistic mixtures of Weyl operators that act only on the tableau's phase column. For fast simulation of noisy circuits, we support Pauli frames, respectively generalized Weyl frames, and introduce a noise-pushing technique that allows all noise processes to be consolidated into a single phase update at the end of the circuit. Using this representation, circuit fidelity can be determined entirely by the single accumulated phase-shift parameter $\Delta \tau$, reducing fidelity estimation to a simple phase check per shot. Our codebase supports tableau simulation and conventional state-vector and density-matrix backends for qudits, and also includes circuit and tableau visualisations. Additionally, we provide tests and Jupyter notebooks for validation and illustration. This framework forms the basis for a scalable, open-source strong+weak stabilizer simulator including noise and can be found publicly available at https://github.com/QUICK-JKU/QuickQudits.

Fluxonium superconducting qubits have demonstrated long coherence times and high single- and two-qubit gate fidelities, making them a favorable building block for superconducting quantum processors. We investigate the dominant limitations to fluxonium qubit energy relaxation time $T_1$ using a set of eight planar, aluminum-on-silicon qubits. We find that a circuit-based model for capacitive dielectric loss best captures the frequency dependence of $T_1$, which we analyze within both a two-level and a six-level energy relaxation model. We convert the measured $T_1$ into an effective capacitive quality factor $Q_\mathrm{C}^{\mathrm{eff}}$ to compare qubits on equal footing, accounting for independently estimated contributions from $1/f$ flux noise and radiative loss to the control and readout circuitry. We apply this methodology to compare qubits from two fabrication processes: a baseline process and one that applies a fluorine-based wet treatment prior to Josephson junction deposition. We resolve a small improvement of (13.8 $\pm$ 8.4$)\%$ in the process mean $Q_\mathrm{C}^{\mathrm{eff}}$, indicating that the fluorine treatment may have reduced loss from the metal-substrate interface, but did not address the primary source of loss in these fluxonium qubits.

State cloning and state transposition are fundamental transformations that, despite being desirable, cannot be perfectly realised as a consequence of two distinct requirements of quantum theory: cloning is forbidden by linearity, while transposition is ruled out by complete positivity. In this work, we show that, in spite of these disparate conceptual restrictions, the best physically allowed realisation of both transformations arises from a single physical process described by an isometry, which simultaneously implements their best possible approximations. This complementary relation allows us to determine the exact quantum and private classical capacities of the universal symmetric $N\to N+K$ cloning channel in the fully general multicopy qudit setting, thereby closing the remaining gap in the quantum capacity problem for universal cloning. We provide an explicit circuit that simultaneously implements optimal pure-state $N\to K$ transposition and optimal $N\to N+K$ symmetric cloning, both attaining the same fidelity. Additionally, we prove that the optimal $N\to K$ pure-state transposition channel is unique and realised by an estimation strategy. We also obtain the optimal mixed-state $N\to 1$ transposition, and discuss its differences from its pure-state analogue.

Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles – the Rosenzweig-Porter model and the ultrametric model – fall within the same universality class of ergodicity breaking when embedded in a many-body Hilbert space of spins-1/2. By calibrating the parameters of both models via their Thouless times, we demonstrate that the matrix elements of local observables display similar statistical properties, allowing us to identify the fractal phase of the Rosenzweig-Porter model with the fading-ergodicity regime. This correspondence is further supported through the analyses of quantum-quench dynamics of local observables, their temporal fluctuations and power spectra, and survival probabilities. Our findings reveal that local observables thermalize within the fading-ergodicity regime on timescales shorter than the Heisenberg time, thus providing a unified framework for understanding ergodicity breaking across these distinct models.

A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.

Solid-state spin defects are promising qubits for quantum network nodes. A key challenge towards larger networks is creating defects with high yield into nanophotonic devices, while maintaining good optical and spin properties. Here, we demonstrate the creation of V2 centers in nanopillars fabricated from commercial bulk-grown 4H-silicon carbide using a pulsed above-bandgap (UV) laser. We observe an eleven-fold increase in the V2 center occurrence after UV laser illumination. These laser-induced V2 centers exhibit narrow optical linewidths and spectral diffusion rates comparable to naturally occurring V2 centers in nanopillars of the same material. Furthermore, we measure a spin coherence time of $T_{2}^{\mathrm{DD}} = 3.6 \pm 0.3~\text{ms}$ under dynamical decoupling, consistent with dephasing by the nuclear-spin bath. This demonstration of the in-situ, post-fabrication generation of coherent V2 centers in nanostructures in widely available bulk-grown 4H-SiC, shows the potential for above-bandgap laser illumination for scalable defect creation in integrated photonic devices.

Although quantum annealing is usually considered as a method for locating the ground states of difficult spin-glass and optimization problems, its use in approximate optimization – finding low- but not zero-energy states in a reasonably short amount of time – is no less important. Here we investigate the behavior of quantum annealing at approximate optimization in the canonical mean-field spin-glass models, the spherical $p$-spin models, and find that it performs surprisingly well. Whereas it had long been assumed that infinite-range spin glasses have a unique “threshold” energy at which all quench and annealing dynamics become trapped until exponential timescales, recent work has shown that two-stage quenches can in fact reach states below the naive threshold in more generic situations. We demonstrate that quantum annealing is also capable of exploiting this effect to locate sub-threshold states in $O(1)$ time. Not only can it attain energies as far below the threshold as classical annealing algorithms, but it can do so significantly faster: for an annealing schedule taking time $\tau$, the residual energy under quantum annealing decays as $\tau^{-\alpha}$ with an exponent up to twice as large as that of simulated annealing in the cases considered. Importantly, by deriving and numerically solving closed integro-differential equations that hold in the thermodynamic limit, our results are free from finite-size effects and hold for annealing times that are unambiguously independent of system size.

Given the recent interest in perspectival quantum reference frames (QRFs), we ask how quantum properties in the perspectival picture relate to their global (non-perspectival) counterparts. Such a connection could allow established quantum information to be understood from the perspective of QRFs. Specifically, we find sufficient conditions under which global entanglement decomposes into a combination of perspectival entanglement and coherence – a phenomenon that we call entanglement transference. We apply this result to non-inertial QRFs, revisiting the problem of acceleration-induced entanglement degradation. We find that entanglement degradation in the perspectival picture can be offset by an increase in coherence resources. This novel insight into (relativistic) quantum resource transformations suggests that QRFs may play a useful role in understanding more general quantum resource and quantum information phenomena.

We propose a quantum sensing protocol for coupled qubit-oscillator systems that enhances the sensitivity by exploiting a geometric phase for dark matter searches. Instead of letting the cavity evolve freely under a weak dark matter background, we combine large coherent displacements and squeezing operations within the evolution protocol, thereby mapping the signal onto an enhanced quantum phase determined by the geometric area enclosed in phase space. Relative to the conventional free-evolution scheme, the protocol enhances the quantum Fisher information and improves the projected sensitivities to cavity-based detection of dark-photon and axion dark matter.

Quantum reference frames provide a relational description of multipartite quantum systems in which physical states and observables are defined relative to quantum observers. Yet different observers can assign different entropies to the same system, raising the question of how such observer-dependence is constrained. We identify a family of frame-independent diagonal Rényi entropies for arbitrary subsystems, yielding a generalized multipartite coherence-entanglement tradeoff. For ideal frames, the observer-dependence of subsystem entropy admits an exact decomposition into a sum of single-frame coherences and inter-frame correlations; for non-ideal frames, it is instead bounded by the dimension of an effective relational Hilbert space determined by the representation structure of the frames. Our results place quantitative limits on how much quantum observers can disagree about subsystem entropy, with potential implications for observer-dependent entropy assignments in gravitational settings.

Agreement theorems are no-go results about rational disagreement: if two agents start from a common prior and their posterior beliefs are common knowledge, they cannot assign different probabilities to the same event. Standard treatments of the result have the agents reason about an underlying state of the world, which has lead some to ask whether the result can extend to quantum or postquantum phenomena, where such a description may no longer be appropriate. We derive an operational version of Aumann's agreement theorem without assuming an objective state of the world and instead focusing only on what is observed. This allows us to establish the theorem's validity in quantum theory and even in situations with indefinite causal order or involving hypothetical postquantum phenomena. We comment on seemingly contradictory results in the literature and point to the one place where the theorem might fail: Wigner's friend-type situations.

We ask under what conditions a finite brickwork circuit of random gates retains local information about the initial state. To answer this question we measure the averaged Frobenius distance between the reduced states obtained by evolving two arbitrary initial states and tracing out a portion of the system. By characterising this distance exactly at all times we find that the information is retained if the environment – the subsystem traced out – is smaller than half of the system and washed away otherwise. We also find that, while the dynamics of the Frobenius distance depends on the specific initial states chosen, this dependence becomes increasingly weak for large scales and eventually the Frobenius distance attains a universal form as a function of time. Finally, we show that by introducing weak enough boundary dissipation, one can observe a phase transition between a memory preserving phase and one where the information is completely lost.

We establish an information-theoretic scaling law for generic autoregressive neural quantum states, determined by the middle-cut mutual information of the wavefunction amplitude. By formalizing the virtual bond as an effective information channel across a sequence bipartition, we rigorously prove that exact autoregressive representation of a quantum state requires the virtual-bond dimension to scale with the amplitude mutual information. For stabilizer-state families, we show that this law yields an explicit, analytical rank formula. Applying this framework across quantum-state tomography, ground-state and finite-temperature learning, our numerical experiments expose precise exponent matching, architecture-dependent scaling differences between recurrent and Transformer neural quantum state, and the critical role of autoregressive basis ordering. These results establish a rigorous physical link between the intrinsic structure of a quantum many-body state and the corresponding neural-network capacity required for its faithful representation.

Density functional theory (DFT) offers an exceptional balance between accuracy and efficiency, but practical density functional approximations face an unavoidable trade-off among simplicity, accuracy, and transferability. Here we present a systematic functional-development protocol that combines constraint enforcement, flexible functional forms, and modern optimization within a predefined application domain and functional class. Applying this strategy to the range-separated hybrid (RSH) meta-GGA framework, we obtain the carefully optimized and appropriately constrained hybrid (COACH) functional. Across broad molecular benchmarks, COACH improves both accuracy and transferability relative to leading RSH meta-GGAs, including \(\omega\)B97M-V, while retaining the computational practicality of its rung. These results suggest that COACH comes closer to the performance limit of traditional hybrid meta-GGA functionals for general molecular ground-state chemistry. Further substantial progress will likely require richer nonlocal or orbital-dependent information than is available from semilocal density ingredients combined with simple exact-exchange mixing.

Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below $1\times10^{-18}$. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of $5.3\times10^{-19}$ and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the $10^{-20}$-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of $0.6926711632159660405(20)$, with a statistical uncertainty of $0.9\times10^{-18}$ and a combined uncertainty of $2.9\times 10^{-18}$. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.

We introduce the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Majorana Propagation Eigensolver (ADAPT-VMPE), a quantum-inspired classical algorithm that exploits Majorana Propagation (MP) to produce circuits for approximating the ground state of molecular Hamiltonians. Equipped with the theoretical guarantees of MP, which provide controllable bounds on the approximation error, ADAPT-VMPE offers an efficient and scalable approach for iterative ansatz construction. A theoretical analysis of the computational complexity demonstrates that it is polynomial in both the number of qubits and the number of iterations. We present an in-depth analysis of circuit construction strategies, analyzing their impact on convergence and provide practical guidance for efficient ansatz generation. Using ADAPT-VMPE, we construct up to 100-qubit ansätze for a strongly correlated photosensitizer currently undergoing human clinical trials for cancer treatment. Our results demonstrate that constant overlap with the ground state across system sizes can be reached in polynomial time with polynomially sized circuits.

Dynamics of open quantum systems with structured reservoirs can often be simulated efficiently with tensor network influence functionals. The standard variants of the time-evolving matrix product operator (TEMPO) method are applicable when the systems is coupled to Gaussian bosonic baths via hermitian coupling operators that mutually commute. In this work we introduce a generalization to cases where the system is coupled to a single reservoir through multiple non-commuting operators, representing the most general form of linear system-bath coupling. We construct a Gaussian influence functional that properly handles Trotter errors arising from a finite evolution time step, thus ensuring convergence for long evolution times. Based on this result, the uniform TEMPO scheme can be employed to obtain a matrix product operator form of the influence functional, enabling efficient simulations of the real-time dynamics of the open system. As a demonstration, we simulate the time evolution of driven two-level emitters coupled to a bosonic lattice at different lattice sites.

Exciton transport in molecular aggregates is a fundamental process governing the performance of organic optoelectronics and light-harvesting systems. While most theoretical studies have emphasized long-time transport behavior, recent advances in ultrafast spectroscopy have brought into focus the short-time regime, in which exciton motion remains ballistic on femtosecond-to-picosecond timescales. In this work, we develop an analytical framework for short-time exciton dynamics in a one-dimensional lattice subject to both on-site energetic (diagonal) disorder and intermolecular coupling (off-diagonal) fluctuations. Utilizing the reciprocal-space analysis, we derive closed-form expressions for the first and second spatial moments considering both localized excitation and moving Gaussian initial conditions. Our analytical and numerical results show that, while the long-time dynamics are influenced by diagonal disorder, the short-time ballistic expansion is governed primarily by off-diagonal disorder. Crucially, we reveal a synergistic interplay between the average intermolecular coupling and the off-diagonal coupling disorder strength, demonstrating that they contribute equivalently to short-time exciton transport. Moreover, we integrate this generic disorder model with a realistic molecular system within the framework of macroscopic quantum electrodynamics, thereby providing a theoretical foundation for characterizing and optimizing ultrafast energy flow of disordered molecular aggregates in complex dielectric media.

Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultra-cold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.

The one-way distillable entanglement is a central operational measure of bipartite entanglement, quantifying the optimal rate at which maximally entangled pairs can be extracted by one-way LOCC. Despite its importance, it is notoriously hard to compute, since it is defined by a regularized optimization over many copies and adaptive one-way protocols. At present, single-letter formulas are only known for (conjugate) degradable and PPT states. More generally, it has remained unclear when one-way distillable entanglement can still be additive beyond degradability and PPT settings, and how such additivity relates to additivity questions of quantum capacity of channels. In this paper, we address this gap by identifying three explicit families of non-degradable and non-PPT states whose one-way distillable entanglement is nevertheless single-letter. First, we introduce two weakened degradability-type conditions–regularized less-noisy and informationally degradable–and prove that each guarantees additivity and hence a single-letter formula. Second, we show a stability result for orthogonally flagged mixtures: when one component has orthogonal support on Alice's system and zero one-way distillable entanglement, the mixture remains single-letter, even though degradability is typically lost under such mixing. Finally, we propose a generalized spin-alignment principle for entropy minimization in tensor-product settings, which we establish in several key cases, including a complete Rényi-2 result. As an application, we obtain additivity results for generalized direct-sum channels and their corresponding Choi states.

Generative quantum machine learning models are trained to deduce the probability distribution underlying a given dataset, and to produce new, synthetic samples from it. The majority of such models proposed in the literature, like the Quantum Circuit Born Machine (QCBM), fundamentally work on a binary level. Real-world data, however, is often numeric, requiring the models to translate between binary and continuous representations. We analyze how this transition influences the performance of quantum models and show that it requires the models to learn correlations that are solely an artifact of the way the data is encoded, and not related to the data itself. At the same time, structure of the original data, like continuity, can be obscured in the binary representation, hindering generalization. To mitigate these effects, we propose a strategy based on Gray-codes that can be implemented with essentially no overhead, conserves structures in the data, and avoids artificial correlations in situations in which the standard approach creates them. Considering datasets drawn from various low-dimensional probability distributions, we verify that, in most cases, QCBMs using the reflected Gray code learn faster and more accurately than those with standard binary code. This shows that, as complement to specifically tailored circuit ansätze or data pre-processing, binary encodings can be used to introduce inductive biases into generative machine learning models.

Family-Vicsek (FV) scaling provides an understanding for the growth and finite-size saturation of fluctuations in classical systems. Here, we extend the FV roughness to transferred segment magnetization after quantum quenches in a dissipative XXZ spin chain with homogeneous gain and loss, starting from a nonequilibrium steady state with finite magnetization. In the non-interacting limit, we derive a closed-form expression for the roughness in the presence of dissipation. It displays two-parameter FV scaling and smoothly interpolates between the clean ballistic behavior and the dissipation dominated scalings. For interacting chains, tensor-network simulations show that the non-dissipative ballistic growth at finite magnetization is robust, whereas the full Lindblad evolution is generically controlled by the dissipative relaxation time and exhibits a dissipation-dominated collapse.

We introduce the concept of quantum actuators as mediators for globally controlled quantum computation. Auxiliary quantum systems act as controllable elements that transiently store and release interaction energy, enabling the selective activation of multi-qubit gates within globally driven architectures. During compilation they remain passive and require no fine-grained local control, while during operation they allow for controlled activation of interactions and directional flow of quantum information. We provide a framework for embedding quantum actuators in globally controlled processors, showing how they enhance connectivity, enable long-range entangling operations, and bridge distant regions without increasing local control overhead. We discuss physical implementations and architectural strategies illustrating how these elements extend the capabilities of global-control schemes. A complementary interpretation in terms of quantum batteries naturally emerges, connecting global-control architectures with concepts from quantum thermodynamics while highlighting the distinct operational role of quantum actuators.

Ultralight bosonic dark matter with masses in the meV range, corresponding to terahertz (THz) Compton frequencies, remains largely unexplored due to the difficulty of achieving both efficient signal conversion and single-photon-sensitive detection at THz frequencies. We propose a hybrid detection architecture that integrates a dielectric haloscope, Rydberg-atom transducer, and superconducting nanowire single-photon detection within a unified cryogenic platform operating at $\lesssim 1\,\text{K}$. The dielectric haloscope converts dark matter into THz photons via phase-matched resonant enhancement, achieving form factors $C \sim 0.4$ and loaded quality factors $Q_L \sim 10^4$. A cold $^{87}$Rb ensemble then coherently up-converts the THz signal to the optical domain through six-wave mixing among Rydberg states. The intrinsic directionality and narrow bandwidth ($\Delta\nu_{\mathrm{atomic}} \sim 1\,\text{MHz}$) of this process provide extra suppression of isotropic thermal backgrounds. With 10 days of integration at $0.3\,\text{K}$, we project sensitivity to the axion-photon coupling $g_{a\gamma\gamma} \sim 10^{-13}\,\mathrm{GeV}^{-1}$ at $m_a \sim 0.4\,\text{meV}$, reaching the QCD axion band and opening the THz window for searches of both axion and dark photon dark matter.

Topological pumping is conventionally governed by single-particle band topology. Here we show that promoting tunneling to a dynamical, occupation-conditioned variable fundamentally reshapes this paradigm, leading to occupation-selective topological pumping. In a periodically driven one-dimensional superlattice with density-dependent hopping, two-body bound states (doublons) acquire Chern numbers distinct from those of single particles and exhibit quantized transport even when the single-particle pump is trivial, including counter-propagating responses. We identify a dynamical-gauge-field mechanism that induces topological phase transitions in the bound-state sector absent from the single-particle spectrum. Furthermore, the gauge field concentrates Berry curvature into sharply localized resonant regions without compromising adiabatic quantization. A Floquet realization with ultracold atoms is proposed to realize such occupation-selective pumping. Our results reveal a mechanism for occupation-selective topological responses that can persist across higher-occupancy bound states.

The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search space and the large number of constraints required to eliminate subtours. This paper introduces a preprocessing strategy that significantly reduces the size of the optimization model by restricting the set of candidate arcs and retaining only the lowest-cost neighbors for each vertex. Computational experiments on TSPLIB benchmark instances demonstrate that the proposed approach substantially reduces the number of decision variables. The method is evaluated using both classical and quantum optimization techniques, showing improvements in computational time and reductions in optimality gaps. Overall, the results indicate that the proposed preprocessing enhances the scalability of the formulations and makes them more suitable for both classical solvers and emerging quantum optimization frameworks.

To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated computational fluid dynamic algorithms coupled with powerful supercomputers can not find approximate solutions for several design challenges in both adequate time and scale-resolving accuracy. One difficulty arises from solving high dimensional, strongly nonlinear partial differential equations, such as the Navier-Stokes equations, which capture the underlying physics. For nearly all classical algorithms, methods closely related to Newton's method are used to approximate a solution to the problem. Approximately solving the large-scale linear systems of equations occurring in this iterative scheme is generally a main contributor to the total computational complexity. In this paper a new quantum linear system solver supporting Newton's classical method to solve nonlinear partial differential equations is introduced. We present a new variant of the HHL algorithm, requiring less apriori information regarding the eigenvalues of the corresponding matrix. We apply this quantum linear system solver in a hybrid quantum-classical fashion to solve nonlinear partial differential equations. Moreover, a resource estimation for advanced use-cases of practical relevance is provided. Our results demonstrate how quantum computation may improve existing classical methodologies for solving nonlinear partial differential equations. This approach provides another promising application of quantum computers and presents a possible way forward for handling nonlinearities on inherently linear quantum systems.

The disjunction effect in human decision making is often taken to show that the classical law of total probability is violated, motivating quantum-like models. We re-examine this claim for the Prisoner's Dilemma disjunction effect. Under the mental-event reading of the opponent-choice events, the conventional classical decision-process model implicitly builds in a certainty-only premise: its standard partition assumptions leave no room for ambiguity, forcing every participant to be certain that the opponent will defect or will cooperate. We relax this by introducing a new classical model in which each participant carries a continuous expectation parameter representing the anticipated likelihood of opponent defection, and the participant pool is partitioned by expectation level; the resulting ambiguity set is precisely the union of the interior expectation bins. In contrast, under the quantum-like event semantics, ambiguous pure states are generic (dense and of full unitarily invariant measure on the unit sphere), so "certainty states" are mathematically exceptional. We prove that an instance of our classical model can realize any empirically observed triple of defection rates across the three information conditions, including strong disjunction-effect patterns, while strictly obeying the classical law of total probability. We further prove that for any such triple produced by a standard quantum-like model of the same experiment, there exists a classical instance reproducing it exactly. In this sense, classical and quantum-like approaches have the same observable-rate expressiveness; their substantive difference lies in how ambiguity is represented and in their respective event semantics, not in a breakdown of classical probability.