Papers

Despite having an unnatural definition, $\mathsf{StoqMA}$ plays a central role in Hamiltonian complexity, e.g., in the classification theorem of the complexity of Hamiltonians by Cubitt and Montanaro (SICOMP 2016). Moreover, it lies between the two randomized extensions of $\mathsf{NP}$, $\mathsf{MA}$ and $\mathsf{AM}$. Therefore, understanding the exact power of $\mathsf{StoqMA}$ (and hopefully collapsing it with more natural complexity classes) is of great interest for different reasons. In this work, we take a step further in understanding this complexity class by showing that the Stoquastic Sparse Hamiltonians problem ($\mathsf{StoqSH}$) is in $\mathsf{StoqMA}$. Since Stoquastic Local Hamiltonians are $\mathsf{StoqMA}$-hard, this implies that $\mathsf{StoqSH}$ is $\mathsf{StoqMA}$-complete. We complement this result by showing that the separable version of $\mathsf{StoqSH}$ is $\mathsf{StoqMA}(2)$-complete, where $\mathsf{StoqMA}(2)$ is the version of $\mathsf{StoqMA}$ that receives two unentangled proofs.

This is a book-length treatment of the subject of non-local quantum computation (NLQC). NLQC is a method for implementing quantum operations that interact two systems without directly bringing the systems together. Instead, a single round of communication and shared entanglement is used. NLQC has appeared in the context of quantum cryptography, computational complexity, communication complexity, quantum gravity, and other applications. The understanding of entanglement cost in NLQC is closely tied to questions in all of these areas. We review upper and lower bounds on entanglement cost, as well as some of the applications of NLQC and its connections to other subjects.

We present an experimental study of energy-to-solution (ETS) of hybrid quantum-classical applications, enabled by direct instrumentation of power consumption of a Forte Enterprise trapped-ion quantum processor. We apply this methodology to a hybrid quantum-classical pipeline for quantum fine-tuning of foundational AI models, and validate the approach end-to-end on quantum hardware. Despite noise and limited qubit counts, the resulting models achieve accuracy competitive with and exceeding classical baselines such as logistic regression and support vector classifiers. Our results show that QPU energy consumption scales approximately linearly with qubit number for shallow circuits, while classical simulation exhibits exponential scaling, indicating a break-even for ETS around 34 qubits. The classification error improvement of the best quantum fine-tuned model over the best classical fine-tuned model considered in this study is around 24%. We further contextualize these findings with comparisons to tensor network methods. This work establishes energy-to-solution as a measurable and scalable metric for evaluating quantum applications and provides experimental evidence of favorable energy-accuracy trade-offs.

The AMPS paradox assumes a globally associative tensor-product stage for the early radiation, the exterior Hawking mode, and the interior partner. We study a retained attractor sector of octonionic magical supergravity whose horizon symbols form the Albert algebra J3(O). This induces an Albertian algebraic-quantum description: states are positive normalized functionals, events are Jordan idempotents, reversible motions are algebra automorphisms, and ordinary quantum mechanics is recovered on associative readout blocks. Peirce theory then splits the horizon data into a hidden exceptional complement, an interface relay, and a two-helicity exterior detector. Eliminating the relay gives a source-fixed Volterra memory law on a neutral-source fixed-charge Reissner–Nordstrom evaporation trajectory. In real time, the leading one-time occupation follows the sourced evaporation clock, while the retained-memory imprint appears as a spectral-overlap connected two-time coherence of windowed helicity/Stokes observables in the emitted history. In Euclidean time, the Peirce–Volterra kernel becomes a transfer kernel with two branchwise superstatistical limits: a regular-opening Tsallis/Lomax onset and a near-extremal shifted-Levy residence branch. The lower admissible envelope of the endpoint actions then reconstructs the Page-curve envelope. The result is an ordinary emitted readout with exceptional memory, not a restored AMPS tensor factorization.

Axions are promising candidates for the role of Dark matter particles. In this paper, the question of the suitability of the RaOH molecule for the experimental detection of electron-electron interactions through the exchange of axions is studied. To take into account an impact of the rotations and vibrations a computation must be performed for a large number of molecular configurations. In this work we study this problem using a combination of the Generalized relativistic effective core potential and One-center restoration technique of the correct four-component spinors.

While out-of-time-order correlators establish a causal light cone for operator spreading, they do not guarantee that the parameter sensitivity carried by the operator remains locally recoverable. We examine the distinction between operator spreading and metrological recoverability for a parameter encoded in a single site of an XX spin chain subjected to a $U(1)$-breaking transverse field. We evaluate three levels of local metrological accessibility: the bare single-site quantum Fisher information (QFI), the QFI recovered by a variational sweep decoder acting on a finite spatial block, and the exact block QFI. In the integrable limit, the sensitivity propagates as a one-magnon wave packet, and a single-qubit decoder recovers the full block QFI. Breaking magnon-number conservation couples the parameter tangent state to multi-magnon sectors. We analytically demonstrate that the local QFI has no first-order correction in field strength; the leading depletion enters at $\mathcal{O}(h^2)$ through two-magnon scattering. As the field strength increases, the decoded QFI falls below the exact block QFI – a gap reflecting a generic finite-dimensional compression limitation, as a single output qubit generically cannot capture the full QFI of a block state whose parameter dependence spans more than an effective two-dimensional subspace. The block QFI itself falls below the conserved global value, confirming that the sensitivity has spread beyond the block into non-local correlations. This operational hierarchy provides a precise quantitative distinction between the arrival of operator support and the local accessibility of metrological information.

The Sachdev-Ye-Kitaev (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties can be derived heuristically using a combination of the replica method and path integration techniques. Analyzing it mathematically rigorously, however, turned out to be notoriously difficult, even for basic questions such as computing the annealed free energy. In this paper we rigorously compute the free energy limit (annealed and quenched) for this model at high enough but constant temperature. Our results are in numerical agreement with the results derived by physics methods. Remarkably, though, our method of proof is novel and is different from the physics approach. It is based on (a) the theory of the component structure of sparse random graphs and (b) a variant of the cavity method, used widely in prior rigorous and heuristic treatments of classical spin glasses.

Material defects give rise to parasitic two-level systems (TLS) which present a major source of decoherence in superconducting qubits. Here, we study a strongly coupled TLS that resides in the tunnel barrier of transmon qubit. We use multi-photon spectroscopy and TLS strain tuning to explore the rich spectrum of the interacting three-partite system consisting of TLS, qubit, and its readout resonator. This reveals a strong effective resonant coupling between the TLS and the qubit's readout resonator which dresses the resonator states and results in a resonance frequency shift that spoils the readout signal. Our finding presents yet another way how material defects can interfere with qubit operation and hinder the realization of solid-state quantum processors.

We demonstrate a delay-programmable two-color femtosecond source based on a chirped-seed noncollinear optical parametric amplifier. Introducing controlled dispersion into the seed enables spectral selection through pump-seed delay, allowing flexible generation of two independently tunable pulse components with adjustable relative timing at high repetition rate. The temporal and spectral properties are characterized using nonlinear optical cross-correlation and dispersion-scan measurements. As a benchmark application, the source is employed in a COLTRIMS-based multiphoton ionization experiment on trapped Li atoms, revealing delay-dependent ionization pathways and demonstrating its suitability for bichromatic ultrafast spectroscopy.

We consider the one-dimensional Dirac equation with the most general relativistic contact interaction supported on two points symmetrically located with respect to the origin. In order to determine the shape of the interaction, we use a distributional method, which in the present case is equivalent to the standard method of defining contact interactions by self-adjoint extensions of symmetric operators. The interaction on each of these two points depends on four parameters, each one having a clear physical meaning. We are interested in the scattering and confining properties of this model. We focus our attention on even or odd interactions under parity transformations and investigate the existence of critical and supercritical states, bound states, confinement and scattering resonances for some particular interactions of special interest.

As distributed quantum architectures begin to emerge, understanding the interaction between quantum circuit optimisation and circuit partitioning becomes increasingly important. In this work, we study how circuit optimisation influences distributed quantum workloads under system-level trade-offs. We compare three compilation strategies (global optimisation, local optimisation, and a hybrid approach) across a large benchmark suite of quantum algorithms. Using telegate-based partitioning, we evaluate the resulting distributed circuits in terms of gate counts, circuit depth, the number of induced non-local gates, and compilation overhead, thereby approximating computational, communication, and classical preprocessing costs. Our results show that circuit optimisation does not uniformly benefit distributed execution. Global optimisation minimises computational resources and achieves the lowest compilation overhead. Local optimisation can reduce communication cost even though it is not explicitly communication-aware. The hybrid strategy can simultaneously reduce both computational and communication overhead, but at the expense of significantly increased compilation time.

Entangled photons are widely used in quantum technologies. Many photonic experiments generate them with probabilistic photon-pair sources that can be modeled as squeeze operators. In practice, these sources are usually treated in the low-gain (perturbative) regime, keeping only the leading single-pair term and neglecting higher-order multi-pair emission events. In pursuit of fidelity, the probability of successful entanglement generation can become extremely small, a tradeoff often ignored. Here we develop an automated design algorithm for quantum experiments to optimize both fidelity and success probability while accounting for higher-order multi-pair emissions. Our discovery algorithm explores different design topologies subject to varying hardware constraints. It optimizes the source parameters to reduce undesired higher-order terms or even benefit from them. The experiments presented outperform previous proposals for widely used states, including heralded Bell states, W states, and NOON states, paving the way for more efficient photonic technologies.

The monitoring of the three independent components of the angular momentum (or spin) of a quantum system by its environment that does not isolate any preferred orientation is modelled in two different ways. One describes the dynamics by the Lindblad equation generated by three independent angular momentum operators. The other uses iterated measurements of the “phase-space” point on the sphere in terms of the positive operator-valued measure generated by SU(2) coherent states. In contrast to the equivalent scenario on a flat phase space, these two models give rise to subtle differences. Specifically, it is shown that the two super-operators corresponding to the two decoherence models for angular momentum systems are commutative, but their eigenvalues are different. Hence although both models give rise to phase-space decoherence, their dynamical behaviours are not equivalent. In either model, we find that the characterisation of classicality as represented by the decay rates of the elements of the density matrix (i.e. decoherence) and that as represented by the positivity of the quasiprobability distribution are not equivalent for angular momentum systems.

This study explores quantum and classical hybrid architectures for financial time-series fore casting, focusing on Quantum Long Short-Term Memory (QLSTM) networks and Quantum Reservoir Computing (QRC), using univariate and multivariate lag structures on real financial data. We assess how lag embeddings affect predictive accuracy and robustness. Data are en coded into quantum states via amplitude encoding, enabling efficient representation of normalized lagged observations under realistic qubit constraints. The recurrent dynamics of QLSTM and the reservoir of QRC are implemented as parameterized quantum circuits, while classical optimizers train the readout and, where applicable, variational circuit parameters. We benchmark quantum models against classical LSTM and reservoir computing using common error like metrics. Our results show that, with suitable lag selection and amplitude encoding, quantum-enhanced archi tectures match classical baselines in univariate settings and can modestly outperform them in multivariate regimes with correlated inputs, where expressive encodings are most beneficial.

Quantum tomography is a cornerstone of quantum information science, enabling the reconstruction of states and channels from experimental data. Here we introduce a new paradigm, temporal state tomography (TST), for reconstructing quantum processes across multiple times. Our approach is based on temporal quasiprobability distributions (TQDs), which, in the informationally complete setting, provide a complete description of multi-time quantum processes and uniquely determine temporal states. We formulate TST as a unified framework for reconstructing both density operators and quantum channels within a single scheme. We show that any TQD can be obtained via classical post-processing of measurement outcomes generated by a fixed set of quantum instruments, thereby establishing a direct operational route to accessing TQDs experimentally. For informationally complete TQDs, the associated temporal state can be reconstructed via a temporal Bloch-type representation. Leveraging this correspondence, we derive the sample complexity of TST, thereby quantifying its statistical efficiency.

Markovian transport is often described by a master equation for the system state. The thermodynamic information measured in transport experiments, however, is carried by reservoir-resolved transfer records, such as particle currents, heat currents, entropy production, and current noise. We identify a thermodynamic incompleteness of state dynamics: a Markovian state generator can fix the occupation probabilities, stationary response, and relaxation without specifying how the underlying transitions are assigned to reservoirs and energy filters. We study a multi-terminal Coulomb-blockaded quantum dot coupled to energy-filtered reservoirs, for which different assignments of reservoir channels can generate the same state master equation. These assignments give identical occupation dynamics, stationary state, and linear response of the dot, but different heat currents, entropy production, and current noise. We formulate a thermodynamic completeness criterion: a transport observable can be reconstructed from state dynamics only when it is invariant under all changes of reservoir-channel assignments that leave the state generator unchanged. The criterion gives a practical diagnostic for Markovian transport models and a measurable prediction: state tomography can be insufficient to predict heat-noise and cross-correlation measurements, even when the full Markovian state dynamics is known. The analysis identifies a concrete limitation of state-only Markovian thermodynamics and shows which additional transport records must be specified to make thermodynamic predictions experimentally complete.

The present work experimentally demonstrates the fabrication of CVD grown monolayer MoS2 ultra thin quantum well based double barrier resonant tunneling device (RTD) architecture well compatible with conventional CMOS fabrication technology. The strongly quantized electronic states from multiple valleys in the momentum space in such ultra 2D sheet along the c-axis sandwiched in between Al2O3 tunneling barriers exhibit multiple resonant tunneling peaks thereby enhancing the FWHM of the NDR region as derived from experimental I-V characteristics as well as theoretical joint invision through Density Functional Theory (DFT) and Non-Equilibrium Greens function (NEGF) visualized via Tunneling Density of States (TDOS). Understanding extended to S-vacancies not only change the bandgap, as evaluated through nanoscale Cathodoluminescence (CL) spectroscopy, but also alters the effective mass hence the mobility as investigated here within the high symmetry path in the k-space. Electrical performances of fabricated RTD, starting from cryogenic to room temperatures, show a significant milestone via exhibiting huge PVR values of 178 at 4K and 24 at RT with more possible improvement in the field of room temperature quantum technology. Momentum conserved and non conserved tunneling from highly n-doped Si through multiple valleys of 1L-MoS2 provides a tremendous opportunity in gate-induced manipulation in Spin-Valley Qubit technology operational at deep cryogenic temperatures (mK).

A recent article by Lohmiller & Slotine (Proc.\ R.\ Soc.\ A 482: 20250413) claims that the Schrödinger equation can be solved exactly using only classical least action and classical fluid density, asserting that this formulation avoids semiclassical approximations. We show that their mathematical derivation contains a foundational error. By neglecting the spatial derivatives of the probability density amplitude, the authors inadvertently omit the quantum potential – the term originally identified by Madelung and later emphasised by Bohm. Consequently, their proposed equivalence is not exact but rather constitutes the standard semiclassical approximation. We further demonstrate that each of the paper's illustrative examples either belongs to a class where the quantum potential vanishes identically due to the geometry of the problem, or recovers the correct quantum result by importing quantum eigenfunctions through the initial conditions, thereby concealing the error.

Quantum conference key agreement (QCKA) protocols utilize GHZ states to establish shared group keys between multiple parties. While previous work has shown that standard Classical Advantage Distillation (CAD) protocols can sometimes benefit QCKA performance, it was unknown if past results were asymptotically tight. In this work, we design a new CAD protocol, "Selective Classical Advantage Distillation (S-CAD)", for QCKA, which generalizes prior QCKA+CAD work and allows the parties to selectively enable or disable CAD. We derive an asymptotic proof of security against general coherent attacks, which outperforms prior work. Finally, we evaluate in a variety of simulated star network topologies, showing when S-CAD can help, and when it is best to disable CAD entirely.

The von Neumann entanglement entropy of exact valence-bond ground states is studied in two frustrated one-dimensional spin chains: the spin-1/2 Majumdar-Ghosh (MG) model and the spin-3/2 J1-J2-J3 chain in its fully dimerized (FD) and partially dimerized (PD) phases. Using matrix-product-state representations, the entropy is computed as a function of system size for three complementary bipartitions - half-chain, single-site, and pairwise - under both open and periodic boundary conditions. In all cases, the entropy saturates to a finite constant in the thermodynamic limit, confirming area-law behavior. The saturation values, extracted via finite-size scaling, are directly related to the underlying virtual-spin bond structure. The MG model and FD phase exhibit similar entanglement behavior, differing primarily in saturation magnitude determined by spin value and bond multiplicity, and both display even-odd oscillations and exponential convergence with system size. In contrast, the PD phase shows qualitatively distinct signatures, including multiple half-chain saturation values depending on the bond type at the cut, asymmetric edge contributions in the single-site entropy, and a multi-band structure in the pairwise entropy reflecting the coexistence of single- and double-singlet bonds. These results establish entanglement entropy as a robust signature of frustrated bond architecture, enabling clear distinction among dimerized phases with different spin magnitude, bond multiplicity, and dimerization patterns.

Stacked quantum memory is an architecture in which multiple layers of qubits are stacked. Quantum rank-metric codes are effective for error correction in stacked quantum memories. However, the previously proposed quantum Gabidulin codes based on the CSS construction had a problem: due to algebraic constraints, the applicable memory layouts were strictly limited to square shapes of odd length. In this paper, we first propose a framework for constructing quantum rank-metric codes from classical linear codes with symplectic self-orthogonality. Building upon this, we propose a new construction method for quantum Gabidulin codes by combining the Hermitian self-orthogonality of classical Gabidulin codes–utilizing the self-dual basis that exists when the extension degree of the finite field is even–with the quantum code construction method using Hermitian orthogonality by Matsumoto and Uyematsu. The proposed method succeeds in approximately doubling the ratio of the minimum rank distance to the number of physical qubits while maintaining the code rate. Furthermore, it eliminates the restriction of the conventional method that requires the number of cells and layers of the stacked memory to be odd, realizing the construction of quantum rank-metric codes applicable to memories with an even number of cells and layers. This construction improves the relative error correction capability of the stacked quantum memory architecture and increases the degree of freedom in design while preserving the code rate.

Recently, sample-based quantum diagonalization (SQD) has emerged as a promising approach to compute ground and excited states of problem Hamiltonians.This method classically diagonalizes a Hamiltonian in a subspace that is spanned by samples obtained from a quantum computer. However, by its nature, SQD suffers from a fundamental sampling problem, as some basis states that are required for a targeted accuracy may only be sampled extremely rarely. To alleviate this limitation, we introduce the SQD-AA algorithm that combines SQD with amplitude amplification (AA). SQD-AA uses AA to sequentially reduce probabilities of already measured bitstrings, thus making the observation of new ones more likely. We observe a reduction in the total query complexity of more than a factor 100 for algebraically and exponentially decaying model distributions, and analytically show a quadratic advantage for the latter. Moreover, we evaluate real molecules in an early fault-tolerant scenario and compare SQD-AA to SQD and iterative quantum phase estimation (iQPE). For all considered examples, we observe the lowest total number of T-gates for SQD-AA while only requiring circuits that are 3-4 orders of magnitude shallower than those needed for iQPE. Given this substantial reduction in circuit depth compared to iQPE while saving 2 orders of magnitude in total runtime compared to SQD, we expect a significant regime in early fault-tolerance where SQD-AA runs feasibly, but iQPE circuits are too deep to execute confidently.

The exploitation of quantum coherence at the level of propagation represents a powerful paradigm for quantum communication networks. In this work, we show that the coherent superposition of spatially distinct communication links enables entanglement generation inherently during distribution. Specifically, separable quantum states can be deterministically transformed into entangled states, when the noisy communication links they traverse are coherently superposed. Contrary to the conventional view of noise as a detrimental effect, we demonstrate that quantum noise itself can be transformed into a constructive resource for entanglement generation for both bipartite and multipartite entanglement. Given the practical feasibility of implementing spatial superposition in interferometric setups, our approach provides a feasible method for distributed entanglement engineering, opening new directions for quantum communication and networked quantum technologies.

A versatile quantum light source capable of programmably generating a variety of quantum light is a key enabler for photonic quantum technologies. In particular, independent control over both the output quantum state and its temporal waveform is essential for realizing diverse functionalities and enhancing processing performance. However, conventional sources of optical non-Gaussian states, a crucial resource for photonic quantum information processing, typically emit fixed states with predetermined temporal waveforms, lacking their programmability. Here, we propose a programmable non-Gaussian quantum light source that offers independent and arbitrary tunability of both the quantum state and the temporal waveform within a single platform. As a distinctive feature, our approach employs a heralding scheme in which these two properties are indirectly engineered to user-defined targets by manipulating the light in the heralding channel, thereby avoiding optical losses associated with direct manipulation of the heralded quantum light. We develop a prototype and demonstrate the generation of single-photon, Schrödinger cat, and two-photon states in a variety of unconventional temporal waveforms without degradation in state quality. This platform provides a versatile tool for tailoring quantum light to specific applications, significantly expanding the capabilities of photonic quantum technologies.

We demonstrate direct time-domain observation of l-doubling contributions in molecular rotational dynamics using shaped femtosecond laser pulses. By imposing a tailored spectral phase on the excitation pulse, we pre-compensate centrifugal distortion, which otherwise leads to temporally broadened, multi-cycle revival structures that obscure fine rotational features. A cubic spectral phase [Phys. Rev. A 107, 053108 (2023)] compresses selected revivals into near single-cycle events, in agreement with an analytic expression derived from molecular rotational constants, enabling predictive pulse design beyond numerical optimization. The resulting distortion-free revivals reveal temporally separated l-doubling contributions that remain unresolved in conventional impulsive alignment experiments. The method proves robust against experimental imperfections, including spatial light modulator discretization. While selective control of individual l-doubling components becomes feasible, here we focus on their direct observation in the time domain.

We consider the routing of neutral atoms on a reconfigurable lattice in terms of hypergraph transformations. We prove the routing number of a Ramanujan $(d,r)$-regular hypergraph on $N$ vertices satisfies $\mathrm{rt}(H) = \Theta(\log N)$, where routing is via matchings in the clique expansion graph $G_{\mathrm{cl}}(H)$. Hypergraphs reframe the qubit routing problem by replacing Nenadov's two-sided spectral gap hypothesis with a one-sided condition based on eigenvalue centering. Song–Fan–Miao (SFM) coverings scale for Ramanujan families of every uniformity. A virtual overlay theorem establishes a capacity–depth tradeoff for 3D acousto-optic lens (AOL) architectures, with multi-layer stacking achieving $\Theta(\log N)$ routing with $L = O(\log N)$ independent overlay layers. An abelian Alon–Boppana barrier shows that fixed-degree Cayley graphs on $\mathbb{Z}_n^2$ cannot be Ramanujan and affine derandomization on such graphs achieves 15–30% congestion reduction. Towers of $k$-fold Ramanujan coverings yield $\mathrm(H_L) = O(\log N)$ by recursive routing lift. Entanglement-assisted routing by pre-distributed Bell pairs achieves $O(\log N)$ teleportation depth with a stable crossover at $\sim\!4$ routing rounds. Displacement energy analyzes greedy adaptive routing, identifying stalling and a hybrid greedy–Valiant protocol achieving $\sim\!3\times$ speedup at practical scales. Hierarchical multi-scale routing achieves $O(\log^2 N / \log b)$ depth with boundary-only transfers at capacity $k = O(\sqrt{N} \log N)$, and $O(\log N)$ depth with optimal block size $b = \Theta(\sqrt{n})$.

Sample-based quantum diagonalization (SQD) constructs subspaces from computational-basis configurations obtained via measurements of a quantum state, with the goal of approximating low-energy eigenspaces of many-body Hamiltonians. The effectiveness of this approach relies on the assumption that physically relevant states admit a compact representation in the computational basis. We investigate this assumption by analyzing SQD subspaces constructed directly from configurations of exact ground states of Heisenberg and Hubbard model lattices. By eliminating state-preparation and measurement inefficiencies, we isolate the intrinsic configuration-space structure of the wavefunction. We determine the minimal number of configurations required to reproduce the ground-state energy within fixed accuracy thresholds and find that this number grows exponentially with the system size. Notably, this scaling persists even under optimal inclusion of configurations in order of decreasing probability, demonstrating that it originates from intrinsic delocalization of the wavefunction rather than sampling inefficiencies. Our results indicate that SQD effectively probes the configuration-space entropy but faces fundamental scalability limitations for these models.

To fulfill the security requirements of quantum cryptography, photon number coherence (PNC) of single photon sources has recently become an important figure of merit. Quantum dots (QDs) embedded in photonic microcavities offer a mature source of single photons, of which many properties can be tuned by the use of different excitation protocols or parameters. We show that the Swing-UP of quantum EmitteR population (SUPER) scheme can significantly decrease the PNC of the emitted photon, compared to resonant excitation. The reason for this is a laser-induced Stark shift, which effectively decouples the QD from the cavity during the SUPER excitation. Our calculations account for environmental effects such as phonons and radiative losses.

Constraint handling is a central challenge for quantum algorithms applied to combinatorial optimization. Standard penalty-based approaches increase problem size, distort energy landscapes, and often degrade performance. Constraint-preserving mixers, such as XY-mixers, restrict quantum evolution to feasible subspaces, but their implementation on gate-based hardware requires Trotterization, which introduces approximation errors. In this work, we systematically investigate the interplay between constraint-preserving XY-mixers and Trotterized Adiabatic Evolution (TAE). We present a theoretical analyses of the origin and scaling of Trotter errors in XY-mixers and show that the dominant contribution depends on the size and structure of individual constraints rather than on the total problem size. Our findings are validated through extensive numerical simulations on three representative problems: Portfolio Optimization, the Multi-Car Paint Shop problem, and a Multi-Commodity Flow problem. For problems with a single global equality constraint spanning all variables, Trotter errors significantly impair XY-mixer performance, making standard Pauli-X mixers more robust under realistic implementations. In contrast, for problems whose constraints decompose into multiple disjoint local blocks, XY-mixers outperform X-mixers by several orders of magnitude even under Trotterized evolution. These results identify constraint locality as the key criterion for the effective use of XY-mixers and demonstrate that TAE combined with structure-aware mixer design provides a robust and theoretically grounded alternative to variational quantum optimization methods. We further present a dedicated mixer Hamiltonian for TSP-like 2-way-1-hot constraints.

Quantum many-body scars are atypical nonthermal states embedded in the chaotic spectrum that evade conventional ergodicity. We propose the asymptotically AdS mini-boson star as a holographic candidate for scar-like states. Their spectrum exhibits random-matrix signatures of chaos while supporting embedded integrable spectral branches. The whole holographic system, including black holes, is generically chaotic with most eigenstates satisfying the eigenstate thermalization hypothesis; in contrast, the boson star macrostate probes a near-integrable subsector within this chaotic spectrum, signaling scarred spectral structures. Boson stars further display anomalously low entanglement relative to black holes at the same energy density, and also robust revivals in Krylov complexity, revealing nonergodic dynamics. These spectral, entanglement, and dynamical diagnostics provide unified evidence for holographic quantum scars in a self-gravitating system. Our work suggests a new connection between many-body scar physics, quantum chaos, and horizonless gravitational dynamics.