Papers

Nuclear quantum effects are rigorously captured by imaginary-time path integrals, which map the quantum Boltzmann distribution onto a ring polymer of classical replicas. Yet the nuclear masses, the coupling to the environment, and the boundary conditions of the path remain hard-wired in the simulation or the trained model, even though this quantum context enters the path measure only through a quadratic action known in closed form. Here we show that a denoiser trained on classical Boltzmann statistics alone, composed at sampling time with an analytic Gaussian component carrying the entire quantum context, yields the quantum Boltzmann distribution of the nuclei. Such a composition exists and is exact whenever the training noise does not exceed the intrinsic quantum uncertainty of the target ensemble, and it is invariant across all quantum contexts admitted by this bound. We show exact transfer across temperature, isotopic mass, dissipation strength, and the boundary conditions of the path in theory and in numerical experiments, without retraining. The last yields the end-to-end displacement and momentum distributions of a tagged nucleus from open imaginary-time paths. The same invariance extends in principle to the permuted boundary conditions of bosonic exchange, with the identical denoiser. In this view, the noise of generative modeling and the quantum fluctuations of the nuclei are two faces of the same quadratic structure.

We establish the global well-posedness of the Cauchy problem for the reverse space-time nonlocal Fokas-Lenells equation with the weighted Sobolev initial data $q_0(x)\in H^{3}(\mathbb{R}) \cap H^{2,1}(\mathbb{R})$ on the line. We develop the inverse scattering transform formulated via the associated Riemann-Hilbert problems to study this issue. A spectral uniformization transform is introduced to resolve the singular behavior inherent in the KN-type negative flow spectral problem. Owing to the reverse space-time reduction, reflection coefficients no longer satisfy the usual Hermitian conjugation symmetry, and the coercivity of the jump matrix is therefore not available a priori. The quantitative smallness condition on the initial data yields uniform bounds on the reflection coefficients and ensures the uniform positive definiteness of the Hermitian part of the associated jump matrix. The resulting coercivity allows us to establish the bounded invertibility of the associated singular integral operator through a Fredholm and vanishing-lemma argument. Under this condition, we prove an $L^{2}$-Sobolev bijective correspondence between the potential and scattering data, exclude spectral singularities on continuous spectra, and obtain the global existence and uniqueness of solutions. Moreover, the associated solution map is Lipschitz continuous on the admissible initial-data class.

Coherence-generating power (CGP) tells how much coherence a quantum process produces on average from incoherent inputs, but an average can hide where that coherence comes from. We introduce the coherence-generating power deviation (CGPD), the standard deviation of the generated Hilbert–Schmidt coherence over the uniform simplex of incoherent states. CGPD turns coherence generation into a landscape: a small value signals robust production across input populations, whereas a large value reveals selective conversion of particular population imbalances. By representing unitary coherence generation as a quadratic response on population space, we obtain exact first and second moments in arbitrary finite dimension. We prove that every nontrivial unitary generator must fluctuate, and we separate this unavoidable isotropic fluctuation from excess anisotropy. The resulting distinction between average strength and input selectivity has direct consequences for benchmarking, reliability guarantees, input-ensemble susceptibility, and four-copy measurement protocols; it also extends naturally to unital quantum channels. Matched quantum-walk and quasiperiodic-transport examples show that topology and localization can leave CGP unchanged while substantially changing CGPD, revealing structure invisible to the mean alone.

We present the quantum effective fragment molecular orbital (Q-EFMO) method, a hybrid framework that evaluates selected molecular-fragment correlation energies with the variational quantum eigensolver and assembles them through the size-consistent EFMO energy expression. A Hartree-Fock EFMO calculation supplies monomer references, many-body polarization, and distant-pair EFP interactions; independent VQE/UCCSD calculations provide correlation increments for monomers and selected near-field dimers. Consequently, the maximum quantum register is determined by the largest active fragment or fragment pair rather than by total system size. For a three-layer LiH benchmark in STO-3G, a full 2.5 to 3.5 Angstrom separation scan shows that two orbital-reduction schemes approach the full CCSD reference monotonically. The more aggressive scheme remains below 1 kcal/mol for separations of 2.6 Angstrom and greater and reaches 0.10 kcal/mol at 3.5 Angstrom, using 6 qubits for monomers and 12 for the largest dimers, compared with 14 qubits for the frozen-core dimer baseline. An implementation-specific cost proxy decreases from 1000 to 40, a factor of 25. These noise-free results establish the equations, software path, and resource scaling; broader chemical validation, larger bases, and hardware tests remain necessary.

Quantum simulation of chemistry in realistic environments is constrained by the orbital cost of explicit solvent, ions, and other surroundings. We present the quantum-classical effective fragment potential (Q-EFP) method, in which a chemically active region is treated with a quantum algorithm and the environment is represented by the effective fragment potential (EFP) in GAMESS. Coulomb and polarization potentials enter the active-region one-electron Hamiltonian, while EFP-EFP and short-range environment contributions are assembled classically. Statevector UCCSD/STO-3G benchmarks for LiH in a mixed water/methanol environment, H2O in a five-water environment, and BeH2 in an ammonium/nitrate environment differ from matched classical CCSD/EFP calculations by 0.03, 0.38, and 0.01 kcal/mol, respectively. The active calculations require 4 to 8 qubits, compared with estimated full-system counts of approximately 84 to 246 qubits, corresponding to register reductions of about 10-fold to 35-fold. These proof-of-concept results validate the embedded Hamiltonian and Q-GAMESS workflow while separating environmental size from quantum-register size. Q-EFP is complementary to real-space Q-EFMO fragmentation and virtual-orbital Q-FVO reduction, enabling a layered route to larger solvated systems.

We show that, for a metric graph equipped with the Laplacian operator $\Delta=-\frac{d^2}{dx^2}$, the graph trace formula admits a new interpretation in terms of quantum probability and curvature. Our approach is based on a notion of graph curvature inspired by Wilson-lines and holonomy, together with von-Neumann's ergodic theorem.

The work presents analytical solutions to the Schrodinger equation for the Killingbeck potential, a Hybrid model combining harmonic, linear and Coulomb terms, and which is also an approximate model of Yukawa-type potentials. The radial Schrodinger equation is solved by means of the series expansion method, thus yielding the exact expressions of both bound-states solutions and eigen-functions for the systems; these systems include quarkonium and confined hydrogen-like atoms in plasma environments. Furthermore, we offer a constructive commentary on the work of Obu et al. (East Eur. J. Phys. 3, 146-157, 2023), with the aim of clarifying a mathematical misstatement used in their analytical treatment of analogous systems.

We present a recipe for simulating one-dimensional quantum systems for low and high energies with $L$ qubits within the framework of first quantisation. Assuming a minimum grid spacing $\Delta L$ in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ \Delta L \ll \hbar$. However, for finite $\Delta L \neq 0$, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit $\Delta L = 0$. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.

We conduct a non-relativistic study of plasma screening effects on hydrogen-like atomic systems using the Screened Coulomb Potential (SCP i.e. Yukawa potential). The radial Schrödinger equation is first reduced to a bi-confluent Heun (BCH) equation for the Killingbeck potential which is the truncated version of the SCP, and we write the exact BCH eigenfunctions and eigenenergies. We then study the limitations of these BCH solutions and obtain an analytic description valid for weak to moderate screening using the BCH functional form. The corrected eigenfunctions are constructed order by order up to O(k^3); they are expressed in terms of the Laguerre polynomials and reduces exactly to Coulomb eigenfunctions when k=0. Using these Functions, the energy spectrum is computed via two analytic methods: (i) direct evaluation of the full Yukawa Hamiltonian expectation value, and (ii) the Hellmann-Feynman theorem, yielding integral representation. All methods presented here provide explicit analytical formulas for both wavefunctions and eigenenergies valid for different ranges of the screening. These methods establish a powerful analytic framework for studying confined quantum systems. The thermodynamic properties are also derived using the BCH formulation.

We introduce the method of “intelligent qubits,” which replace live observers in Wigner's friend and Frauchiger–Renner thought experiments, in order to expose the source of the paradoxes: tacit substitution of Boolean hidden variables for non-commuting quantum propositions. The fallacy traces back to London and Bauer's attempt (1939) to legitimize a self-referential interpretation of observers' “introspection,” and thus intertwines the measurement and mind-body problems. We cut the Gordian knot by abandoning reductionism, and describe an alternative which fits, we argue, equally naturally with both physics and anthropology takes on the problems.

Continuous measurement is commonly associated with decoherence and the loss of symmetry. Here, we show that weak continuous measurements can instead act selectively: depending on the measured observable, they may either preserve or remove a dynamical relation between initially mirrored states. Using tunneling between the $|+1\rangle$ and $|-1\rangle$ states of a spin-1 system, we demonstrate that measurements of $S_x$ and $S_y$ break the symmetry of the tunneling dynamics in the presence of a longitudinal bias, whereas measurement of $S_z$ leaves it intact. We formulate this behavior within the Lindblad framework, support it with numerical simulations, and reproduce the dissipative dynamics in a two-qubit quantum circuit using Trotterized evolution and stochastic collective rotations. Our results establish continuous measurement as a selective tool for controlling dynamical symmetry in open quantum systems.

Quantum state tomography estimates an unknown density operator from measurement data. Dense reconstruction however, can be impractical for many-qubit systems because the Hilbert-space dimension grows exponentially. This contribution develops a rank-adaptive matrix-free approach to low-rank quantum state tomography based on rank-one atomic coordinates. The density operator is represented as a convex combination of pure-state atoms, which preserves positivity and unit trace while avoiding dense density, measurement, and gradient matrices. The resultant algorithm combines atom updates, simplex-constrained coefficient reweighting, and periodic spectral refactorization using only predicted probability vectors, atom vectors, and descriptor-level measurement actions. These computations decompose across measurement outcomes, and admit a master–worker implementation with the measurements partitioned across workers. A rank penalty adapts the representation size during optimization. Provable feasibility, prediction consistency, monotone descent of the penalized objective, and an exact spectral proximal characterization of the refactorization step are established. Simulations with Pauli measurements show favorable accuracy–runtime–memory tradeoffs relative to competing alternatives.

We introduce an adaptive simulated annealing algorithm to search for moderately-sized quantum error-correcting codes with high encoding rates and large distances. Our search targets two classes of stabilizer codes: (1) CSS codes, and (2) a subclass of CSS codes that we call “self-dual with equivalent logicals” (SWEL) codes, the latter of which which admit transversal implementations of logical Hadamard and phase gates that can be leveraged to construct fault-tolerant gate sets. The search is guided by an energy function that acts as a surrogate for the logical error rate in a code-capacity noise model, combining code distance with a count of minimum-weight logical operators to resolve the discrete plateaux that impede naïve distance optimization. For block lengths of up to $50$ physical qubits, our search finds state-of-the-art CSS and SWEL codes whose distances frequently meet or exceed the variants of the quantum Gilbert-Varshamov bound. In addition to providing favorable seed codes for fault-tolerant architectures based on code concatenation, the codes found in this work are promising candidates for high-rate code demonstrations on near-term quantum computing hardware.

Quantum error correction can be enhanced by post-selecting out runs that are likely to produce a logical failure, but the most accurate measures for that require costly decoder-level information. We introduce a practical, decoder-agnostic post-selection method that learns directly from syndrome data. The method trains a supervised classifier to distinguish between syndromes from low- and high-noise regimes, and then uses the classifier's output as an abort score for new runs, without requiring logical-error labels, correction operators, or code-specific likelihood calculations. We validate the approach in three complementary settings: circuit-level simulations of the Gross bivariate-bicycle code, code-capacity simulations of the surface code, and experimental logical magic-state distillation data from the QuEra neutral-atom processor. In the Gross and surface codes, learned syndrome post-selection reduces the conditional logical error rate at a fixed acceptance rate, with performance comparable to syndrome-weight filtering. For the surface code, the learned classifier reveals a post-selection transition distinct from the conventional decoding threshold. In the experimental data, the machine-learning score outperforms syndrome-weight post-selection and, when combined with logical-gap filtering, improves the output fidelity beyond using the logical gap alone. These results show that syndrome-only learning provides a scalable and hardware-compatible route to improving the reliability of quantum error correction.

Superconducting quantum circuit design is reliant on accurately mapping design parameters to a quantum Hamiltonian. Designers typically rely on computationally intensive finite-element electromagnetic simulations. However, effective circuit-level models can in principle capture much of the relevant physics for these systems, reducing the need for finite-element simulations. A barrier to implementing these simpler models has been the prevalence of distributed elements such as coplanar waveguides resonators in device designs. Techniques for modeling these distributed elements have been developed, but may be difficult to scale, reduce intuition, and give inaccurate results under strong coupling. In this work we describe a simple effective circuit-level model that faithfully reproduces the scattering parameters, and subsequently can predict certain Hamiltonian parameters, for a coupled, distributed element within a broader two-port network even up to strong coupling. Our approach does not explicitly require an electromagnetic simulation. Our model, along with other common lumped models used in black box quantization, is publicly available to researchers via an open-source code package, $\texttt{simpleLOMs}$.

Superoscillations, band-limited signals that locally oscillate faster than their highest Fourier component, have recently enabled superspectroscopy and super-sensing. Previous experiments [Phys. Rev. Lett. 131, 153803 (2023), https://doi.org/10.1103/PhysRevLett.131.153803 and APL Photonics 10, 086107 (2025), https://doi.org/10.1063/5.0271556] relied on combining four quasi-sinusoidal harmonics to generate temporal superoscillations. Here, we show that just two harmonics are sufficient to produce superoscillations of comparable quality, as quantified by the local frequency. By reanalyzing prior experimental data with two harmonics (0.5 and 0.6 THz) and performing new experiments with 0.9 and 1 THz harmonics, we demonstrate a twofold enhancement in local frequency relative to the highest frequency component – matching the enhancement previously achieved with four harmonics. We provide a simple analytical explanation for the bichromatic superoscillations based on near-complete destructive interference, and identify an optimal frequency separation of approximately 10% that balances the superoscillatory frequency enhancement against signal amplitude. This simplification substantially lowers the experimental barrier to implementing superoscillation-based technology.

Entangling distant spins via a shared magnonic bus typically faces a tradeoff: stronger spin-magnon coupling increases the entanglement fidelity, but also the spin decay rate. We propose a protocol that breaks this tradeoff. The magnons couple only to a transition outside the computational basis, in which the Bell state is created. Our protocol is probabilistic, and weak coupling reduces the success probability but not the fidelity. We analyze a setup where the spins are two nitrogen-vacancy (NV) centers near a magnetic wire. In the absence of NV dephasing, the protocol reaches unit fidelity with a maximally entangled state, for arbitrarily weak coupling. In our simulations via the Monte-Carlo wavefunction approach, the NV-magnon coupling is taken to be one-third of the magnon linewidth. Considering finite NV dephasing, we predict a fidelity of >0.99 for a state-of-the-art rate, and an optimal fidelity of 0.91 for a moderate rate, both at 0.6% success probability.

Quantum reservoir computing (QRC) uses fixed quantum dynamics as a high-dimensional temporal feature map and trains only a lightweight classical readout. QRC is attractive for near-term quantum machine learning, but its performance depends strongly on architecture choices such as input encoding, reservoir depth, entanglement topology, measurement features, state-reset policy, feature construction, and readout regularization. We introduce \method, a simulator-based benchmark that formulates QRC design as constrained black-box architecture search and evaluates whether large language models can act as proposal controllers for this search problem. The benchmark compares five policies under identical evaluation budgets: random search, evolutionary search, Bayesian/TPE optimization, a feedback-based LLM agent, and \hybrid, which combines LLM proposals with memory, mutation, crossover, duplicate avoidance, and exploration. On NARMA10, Mackey-Glass forecasting, and temporal parity, \hybrid{} is the most consistent policy: it ranks first on NARMA10 and temporal parity and second on Mackey-Glass, narrowly behind evolutionary search. Under a 25-evaluation budget and three seeds, \hybrid{} improves over random search on all tasks, including a 23.6% relative reduction in Mackey-Glass error. The results do not show that LLMs are universal QRC optimizers; rather, they show that generative models can be useful high-level controllers when embedded inside validated, reproducible hybrid search loops.

Anomalous bunching is a paradoxical quantum interferometric phenomenon in which partially distinguishable photons exhibit a higher probability of bunching into two or more modes than fully indistinguishable photons [Nat. Photonics 17, 702 (2023)]. While this effect is directly linked to violations of certain conjectures on matrix permanents, the mechanism underlying the anomaly is not yet fully understood. Here, we show that boson bunching is governed not by internal indistinguishability alone, but by the total indistinguishability of the postselected output state. Total indistinguishability combines the internal degrees of freedom, such as polarization or arrival time, with the spatial degrees of freedom of their wave functions restricted to the measured output modes of the interferometer. This reformulation preserves the expected connection between boson bunching and total indistinguishability, while clarifying how anomalous bunching can arise. It also reveals several additional facets of the same phenomenon, which are captured within a unified framework. In particular, we exhibit situations in which adding an independent source of distinguishability, either internal or spatial, can enhance multimode or even single-mode bunching probabilities, offering new insights into the subtle role of distinguishability in multiphoton interference.

Quantum resonance arising whenever the ratio of the intrinsic system frequency to the driving frequency becomes a rational number has been demonstrated to generate super-linear entanglement, enhance transport, quantum metrology performance and communication. Here, we demonstrate that quantum resonance can also serve as a powerful resource for quantum batteries. We model the batteries as free rotors charged via a kicked protocol. When the individual batteries are at resonance, we show both analytically and numerically that charging power increases linearly with time while efficiency (defined as the fraction of stored energy that can be extracted) remains near unity despite strong entanglement generation. Furthermore, we demonstrate that this enhanced performance persists at higher-order resonances. Demonstrating the universality of this mechanism, we show that similar enhancements arise in the interacting kicked top model, and briefly note the feasibility of its experimental realization. In a broader context, resonant charging holds significant implications for energy storage, quantum computational resources, and quantum thermodynamics.

We analyze confinement and screening in single-flavor quantum electrodynamics (QED$_2$) on two-dimensional anti-de Sitter space (AdS$_2$), with and without a Schwarzschild black hole, both in the continuum and on the lattice. The theory is formulated in two frames adapted to distinct choices of a preferred time coordinate: the Schwarzschild frame, associated with the Boulware vacuum, and the global AdS$_2$ frame, associated with the $\mathrm{SL}(2,\mathbb{R})$-invariant vacuum. In the massless limit, the static potential between an external charge-anticharge pair is obtained in closed form by bosonization, at both zero and finite temperature. After subtraction of the position-dependent probe self-energies, which, unlike in flat space, are not constant, the potential remains finite as the geodesic separation is taken to infinity, establishing that the theory is screened. This is consistent with the explicit breaking of the $\mathrm{U}(1)$ electric one-form symmetry by the dynamical fermions, and resolves a confining/screening ambiguity in earlier treatments that identify the static potential with the unsubtracted ground-state energy. To validate the continuum analysis, we propose a covariant discretization scheme for placing fermions in curved spacetime on the lattice while ensuring that the continuum properties of the spin and gauge connections are restored in the continuum limit. This construction resolves ambiguities in the existing literature on lattice fermions in curved backgrounds and provides the foundation for our tensor-network simulations. Using a matrix product state ansatz, we confirm our analytical predictions for the phase diagram in AdS$_2$. We perform extensive numerical simulations of the static potential and the electric flux-tube profile for varying fermion masses, which we match to the continuum prediction.

Quantum error-correction experiments increasingly require a verified interface between measured syndrome bits and decoder-native correction requests. We report a four-branch syndrome-to-decoder mapping audit spanning a five-data-qubit repetition code, a distance-five surface Z-check interface, a compact Steane CSS benchmark, and a digitized-GKP proxy. For the surface interface, an independent noiseless interpreter verifies 40/40 single-X syndrome columns and data-bit round trips, while a reversed-register negative control fails for all 40 targets. Sampled hardware and local-noise streams are then analyzed with exact binary minimum-weight representatives to separate mapping validity from noisy localization. The results establish a narrow interface-conformance claim, not a decoder benchmark, threshold estimate, or logical-QEC demonstration.

We present a contract-preserving, family-aware comparison of decoder behavior across four syndrome-generation stacks (PennyLane, Qiskit, Cirq, and a LiDMaS+ reference) under a fixed replay interface. Request streams from repeated-round surface-code and digitized-GKP circuits are replayed through BP, MWPM, and UF with matched controls. The unified matrix spans 24 cells and achieves line-level integrity: $24\,000$ request lines, $24\,000$ response lines, response ratio $=1.0$ in every cell, zero parse failures, and zero decoder-name mismatches. Fifteen warning-no-syndrome events occur only in GKP-Cirq rows. Within-family ordering is stable in both families ($\mathrm{BP}<\mathrm{MWPM}<\mathrm{UF}$); source-averaged flip counts are 2.435, 4.768, and 5.870 for surface and 1.595, 2.908, and 3.681 for GKP. Relative to MWPM, BP reduces mean intervention volume by $48.9\%$ in surface and $45.1\%$ in GKP. Source-vs-reference effects are family dependent, with larger coherent shifts in GKP. Source-bootstrap ranks remain unchanged, and hidden-truth sidecars add an outer-code logical-parity error-rate check in which UF has the largest source-mean rate in both families. The comparison is stack-aware, contract-verified, and avoids raw cross-family threshold-equivalence claims.

Natural and engineered classical systems are replete with examples of synchronization, understood as the adjustment of rhythms of physical systems. Such synchronization is at the heart of the stability of several classical technologies, such as mechanical bridges and electrical networks. Given the advent of quantum simulation and computation technologies, it is natural to study a quantum analogue of synchronization and explore novel applications. This review surveys synchronization in few and many-body quantum systems, measures that quantify them, and their applications to quantum technologies.

Many well-motivated dark matter models predict meV-scale energy deposits in interactions with terrestrial experiments, but this regime is challenging to probe due to a lack of mature single-quantum detectors. Here we report results from QUALIPHIDE (QUAntum LImited PHotons In the Dark Experiment), a cryogenic dark matter search using a $41$-pixel array of energy-resolving microwave kinetic inductance detectors with a $13$ meV threshold, simultaneously used to look for both conversion photons from THz wavelength hidden photon dark matter and phonons from particle-like light dark matter interactions. The experimental design, with on- and off-focus pixels for the hidden photon search, allows for a data-driven background model, giving the experiment discovery potential. A blind analysis of $22$ hours of data shows no significant excess, setting the strongest constraints on the hidden photon kinetic mixing parameter $\chi$ over the mass range of $13$-$90$ meV/$c^2$, reaching $1.5\times10^{-12}$ at $50$ meV/$c^2$. These data also yield among the first terrestrial limits on dark matter scattering off nuclei and electrons, down to $5$ MeV/$c^2$ and $20$ keV/$c^2$, respectively. The low threshold also enables future study of the low-energy excess limiting cryogenic detectors and, as we project, will allow for a terahertz-scale QCD axion search with a magnetic field.

The Variational Quantum Eigensolver (VQE) is a leading algorithm for estimating molecular ground-state energies on near-term quantum hardware, with applications spanning quantum chemistry, materials science, and drug discovery. As VQE workloads are increasingly deployed through cloud-based “VQE-as-a-service” pipelines, they become exposed to adversaries such as compromised service components, malicious co-tenants, or insiders in the transpilation stack, any of which can corrupt results before they reach the user. A range of attacks on variational quantum circuits has been proposed, but each has been studied in isolation: some on quantum classifiers with accuracy-based metrics, others on variational quantum algorithms with energy-error metrics. This lack of a common evaluation setup makes their relative severity difficult to compare and leaves the security of VQE poorly characterized. In this work, we present VQE-AdvBench, the first unified red-teaming benchmark for the Variational Quantum Eigensolver, systematizing these attacks under a single evaluation protocol to rigorously assess VQE's adversarial robustness. We organize attacks along a black-, gray-, and white-box access taxonomy, and evaluate seven representative attack scenarios – the QTrojan circuit backdoor, the QDoor parameter backdoor, parameter-space adaptations of FGSM and PGD, and three QNBAD noise-induced variants – over a fixed molecule-ansatz-backend-metric configuration, on H$_2$ and H$_3^+$ across five noise-calibrated IBM backends. Our results reveal a clear severity ordering: noise-induced attacks that manipulate the Zero-Noise Extrapolation (ZNE) pipeline are the most damaging (up to 8.84$\times$ error amplification), followed by the QTrojan circuit-level backdoor (7.52$\times$), while the QDoor parameter-level backdoor is the least effective, yielding only marginal amplification (up to 1.37$\times$).

A Cayley graph $\operatorname{Cay}(\Gamma,S)$ over a finite group $\Gamma$ is said to be normal if its connection set $S$ is a union of some conjugacy classes of $\Gamma$. This paper investigates perfect state transfer in Grover walks on normal Cayley graphs. The Grover walk is a widely studied discrete-time quantum walk. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on normal Cayley graphs. As applications, we derive explicit spectral criteria for perfect state transfer on Cayley graphs over abelian groups, dicyclic groups, and dihedral groups. These results yield several infinite families of Cayley graphs exhibiting perfect state transfer. We further obtain simple combinatorial characterizations of the existence of perfect state transfer on Cayley graphs over dihedral and dicyclic groups. Our general characterization also recovers a number of previously known results as special cases. As a further consequence, we obtain a complete characterization of perfect state transfer on unitary Cayley graphs. In particular, we prove that exactly four graphs in the class of unitary Cayley graphs exhibit perfect state transfer.

We show that informational completeness, while sufficient to have a bijection between ideal measurement probabilities and quantum states, does not guarantee statistically stable reconstruction from finite measurement data. To address this problem, we develop a general estimation theory for continuous-variable systems in which stable reconstructibility is characterized by the POVM effects forming a measurement frame. Informational completeness is therefore necessary, but not sufficient, for stable reconstruction. Our framework is based on measurement frames in a $\sigma$-regularized operator geometry, where the reference state $\sigma$ encodes prior information about relevant features of the measured states. For any fixed measurement scheme, observables may be inaccessible, weakly reconstructible only through estimators with divergent variance, or stably reconstructible by finite-variance unbiased estimators. The relevant regime is determined by the range of the POVM synthesis operator. Our framework provides practical methods for constructing estimators and gives an operational interpretation of singular quasiprobability distributions, including the Glauber-Sudarshan $P$ representation: quasiprobabilities act as unbiased estimators for associated observables, and their singularities reflect a pathological feature of the corresponding measurement: its lack of loewr frame bound. We furthermore show how this formalism naturally provides operational regularization procedures tied to prior information. Overall, our framework provides a unified view of continuous-variable tomography, quasiprobability representations, and classical-shadow estimation.

Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-$1/2$ driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.

Gaussian Boson Sampling (GBS) provides a native photonic quantum heuristic for sampling dense subgraphs from adjacency matrices, offering a scalable physical approach to combinatorial graph search problems. Simultaneously, correlation matrix clustering algorithms, such as Spectral and SPONGE, have established robust benchmarks for identifying co-moving assets from correlation matrices in statistical arbitrage (StatArb) strategies. In this work, we map S&P 500 residual correlation data into GBS-compatible adjacency matrices. We benchmark those classical clustering algorithms against two quantum clustering algorithms, GBS Boost and our novel GBS Roots, to construct dynamic, market-neutral portfolios over a rolling one-year window. Simulations across distinct macroeconomic regimes reveal that quantum clustering generates superior alpha within large stock universes during periods of high volatility, effectively isolating structural market idiosyncrasies. Crucially, this economic advantage persists under simulated low-loss conditions and extends into high-loss regimes via the application of coherent displacement to compensate for photon loss. Our findings underscore the efficacy of GBS-derived graph clustering in constructing robust StatArb portfolios, establishing a quantum foundation for broader quantitative finance applications.