Papers

Quantum phase transitions (QPTs) in odd-mass Nb isotopes are investigated in the framework of the interacting boson-fermion model with configuration mixing. A quantum analysis reveals a Type I QPT (gradual shape-evolution within the intruder configuration) superimposed on a Type II QPT (abrupt crossing of normal and intruder states), thus demonstrating the occurrence of intertwined QPTs. A classical analysis highlights the implications for the single particle motion in the deformed field generated by the even-even Zr cores.

The transition from monolithic to distributed multi-chip quantum architectures has fundamentally altered the circuit compilation landscape, introducing challenges in managing temporal noise variations and minimizing expensive inter-chip operations. We present DeepQMap, a deep reinforcement learning framework that integrates a bidirectional Long Short-Term Memory based Dynamic Noise Adaptation (DNA) network with multi-head attention mechanisms and Rainbow DQN architecture. Unlike conventional static optimization approaches such as QUBO formulations, our method continuously adapts to hardware dynamics through learned temporal representations of quantum system behavior. Comprehensive evaluation across 270 benchmark circuits spanning Quantum Fourier Transform, Grover's algorithm, and Variational Quantum Eigensolver demonstrates that DeepQMap achieves mean circuit fidelity of $0.920 \pm 0.023$, representing a statistically significant 49.3% improvement over state-of-the-art QUBO methods ($0.618 \pm 0.031$, $t_{98} = 4.87$, $p = 0.0023$, Cohen's $d = 2.34$). Inter-chip communication overhead reduces by 79.8%, decreasing from 2.34 operations per circuit to 0.47. The DNA network maintains noise prediction accuracy with coefficient of determination $R^2 = 0.912$ and mean absolute error of 0.87%, enabling proactive compensation for hardware fluctuations. Scalability analysis confirms sustained performance across 20-100 qubit systems, with fidelity remaining above 0.87 even at maximum scale where competing methods degrade below 0.60. Training convergence occurs 8.2$\times$ faster than baseline approaches, completing in 45 minutes versus 370 minutes for QUBO optimization. Very large effect sizes validate practical significance for near-term noisy intermediate-scale quantum computing applications.

Fewest switches surface hopping (FSSH) is a well benchmarked dynamical method for simulating nonadiabatic systems. In particular, the literature shows that for the spin-Boson model Hamiltonian, FSSH with appropriate corrections usually captures the detailed balance well and obtains rate constants within a factor of 2 compared to numerically exact results. In this study, we show that in the deep inverted Marcus regime, the augmented-FSSH (AFSSH, one version that includes decoherence) yields reasonably accurate rate constants but incorrect thermal populations over a broad range of parameters. We present an analytical derivation to understand the AFSSH behavior, and therefore, show that AFSSH obtains correct rate constants owing to the resonance of the time derivative coupling with the exothermicity, but obtains an incorrect thermal population owing to the self-consistency issue. The presented derivation provides an analytical expression for the quantum correction factor for AFSSH simulations in the Marcus inverted regime.

In this review we discuss some results on the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. Both the spectral and algebraic approaches to this topic are addressed, with particular emphasis on their relationship. The analysis is conducted in both the discrete-time and the continuous-time Markovian settings. In the final part of the work, some issues emerging in the infinite-dimensional case are also discussed. In particular, we provide an example of a Markovian evolution whose decoherence-free algebra is a type III von Neumann algebra.

Accurately resolving many-body satellite features in molecular core-level spectra requires theoretical approaches that capture electron correlation both efficiently and systematically. The recently developed time-dependent double coupled-cluster (TD-dCC) ansatz achieves this by combining correlation effects from the N- and (N-1)-electron sectors, but its exact formulation remains computationally demanding. Here we introduce a hierarchy of cost-effective approximate TD-dCC ansatzes derived from truncated Baker-Campbell-Hausdorff (BCH) expansions, which preserve a single-similarity-transformation structure while retaining the essential correlation diagrams responsible for satellite formation. We further develop a detailed component analysis that isolates hole-mediated excitation pathways, which are correlated processes arising from the coupling between ground-state and ionized-state amplitudes. We use it to interpret quasiparticle and satellite features across the hierarchy. Applications to the single-impurity Anderson model and molecular systems (H2O and CH4) demonstrate that the approximate TD-dCC methods closely and efficiently reproduce exact many-body spectral features and quasiparticle weights. In parallel, we construct a fault-tolerant quantum signal processing algorithm for the core-hole Green's function, providing a scalable quantum route for simulating correlated core-level dynamics. Together, these developments establish complementary classical and quantum methodologies for quantitative, many-body-accurate core spectroscopy.

The measured relative entropy and measured Rényi relative entropy are quantifiers of the distinguishability of two quantum states $\rho$ and $\sigma$. They are defined as the maximum classical relative entropy or Rényi relative entropy realizable by performing a measurement on $\rho$ and $\sigma$, and they have interpretations in terms of asymptotic quantum hypothesis testing. Crucially, they can be rewritten in terms of variational formulas involving the optimization of a concave or convex objective function over the set of positive definite operators. In this paper, we establish foundational properties of these objective functions by analyzing their matrix gradients and Hessian superoperators; namely, we prove that these objective functions are $\beta$-smooth and $\gamma$-strongly convex / concave, where $\beta$ and $\gamma$ depend on the max-relative entropies of $\rho$ and $\sigma$. A practical consequence of these properties is that we can conduct Nesterov accelerated projected gradient descent / ascent, a well known classical optimization technique, to calculate the measured relative entropy and measured Rényi relative entropy to arbitrary precision. These algorithms are generally more memory efficient than our previous algorithms based on semi-definite optimization [Huang and Wilde, arXiv:2406.19060], and for well conditioned states $\rho$ and $\sigma$, these algorithms are notably faster.

We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its implementation. We design Weyl-Heisenberg gadgets, the qutrit equivalents of Pauli gadgets, and come up with a practical implementation scheme for qutrit HHL. We test HHL with qutrits for simple matrices and verify the results against the expected outcomes. We apply the algorithm to quantum chemistry, and in particular, to the potential energy curve calculations of the model problem of the Hydrogen molecule in the split valence basis. We do so for two cases: 1-qutrit and 2-qutrit input states, where the latter makes use of our gadgets. We compare the number of qudits and the number of gates required between qubit and qutrit HHL implementations. In general, we find that for a fixed precision, the qutrit HHL circuit requires fewer number of qudits and comparable number of two-qudit gates than its qubit counterpart.

Exploring sign structures of quantum wave functions attracts considerable attention due to the potential for advances in modeling complex phases of matter. This stimulates developing different optimization procedures for imitating and manipulating sign structures of quantum states. In this work, utilizing a brute force approach based on a set of single-qubit transformations we evaluate protocols enabling positivization of the one-dimensional $J_1 -J_2$ model ground states in the regime of strong frustration. Based on the obtained positivization results, we show the difference between the cases of periodic and open boundary conditions, and also establish the dependence of the sign structure on parity of the simulated spin chains.

The concept of anamorphic encryption, first formally introduced by Persiano et al. in their influential 2022 paper titled “Anamorphic Encryption: Private Communication Against a Dictator,” enables embedding covert messages within ciphertexts. One of the key distinctions between a ciphertext embedding a covert message and an original ciphertext, compared to an anamorphic ciphertext, lies in the indistinguishability between the original ciphertext and the anamorphic ciphertext. This encryption procedure has been defined based on a public-key cryptosystem. Initially, we present a quantum analogue of the classical anamorphic encryption definition that is based on public-key encryption. Additionally, we introduce a definition of quantum anamorphic encryption that relies on symmetric key encryption. Furthermore, we provide a detailed generalized construction of quantum anamorphic symmetric key encryption within a general framework, which involves taking any two quantum density matrices of any different dimensions and constructing a single quantum density matrix, which is the quantum anamorphic ciphertext containing ciphertexts of both of them. Subsequently, we introduce a definition of computational anamorphic secret-sharing and extend the work of Çakan et al. on computational quantum secret-sharing to computational quantum anamorphic secret-sharing, specifically addressing scenarios with multiple messages, multiple keys, and a single share function. This proposed secret-sharing scheme demonstrates impeccable security measures against quantum adversaries.

Verifying prepared quantum states is crucial for hybrid systems whose subsystems may have different local dimensions. We present a generalized stabilizer framework and associated test that apply to general multi-qudit states, including composite-dimensional and hybrid architectures. Using only adaptive local measurements, our method verifies qutrit-qubit states, arbitrary two-qubit pure states, Bell/Bell-like, GHZ/GHZ-like, graph, hypergraph, multigraph, and multihypergraph states, with efficiencies matching or surpassing the best known schemes.

We investigate the fundamental limits of entanglement generation under bipartite Hamiltonian dynamics when only finite physical resources-specifically, bounded energy variance-are available. Using the relative entropy of entanglement, we derive a closed analytical expression for the instantaneous entanglement generation rate for arbitrary pure states and Hamiltonians expressed in the Schmidt basis. We find that constraints based solely on the mean energy of the Hamiltonian are insufficient to bound the entanglement generation rate, whereas imposing a variance constraint ensures a finite and well-defined maximum. We fully characterize the Hamiltonians that achieve this optimal rate, establishing a direct relation between their imaginary components in the Schmidt basis and the structure of the optimal initial states. For systems without ancillas, we obtain a closed-form expression for the maximal rate in terms of the surprisal variance of the Schmidt coefficients and identify the family of optimal states and Hamiltonians. We further extend our analysis to scenarios where Alice and Bob may employ local ancillary systems: using a matrix-analytic framework and a refined description of the Hamiltonians allowed by the physical constraints, we derive an explicit optimization formula and characterize the attainable enhancement in entanglement generation.

Natural hyperbolic materials have attracted significant interest in the field of photonics due to their unique optical properties. Based on the initial successful explorations on layered crystalline materials, hyperbolic dispersion was associated with extreme structural anisotropy, despite the rarity of natural materials exhibiting this property. Here we show that non cubic electrides are generally promising natural hyperbolic materials owing to charge localization in interstitial sites. This includes elemental and binary electrides, as well as some two-dimensional materials that show prominent in-plane hyperbolic dispersion. They exhibit low plasma frequencies and a broad hyperbolic window spanning the infrared to the ultraviolet. In semiconductor electrides, anisotropic interband transitions provide an additional mechanism for hyperbolic behaviour. These findings remove the previously held prerequisite of structural anisotropy for natural hyperbolic materials, and open up new opportunities, which might change the current strategy for searching and design photonic materials.

In 2021, Broadbent and Kazmi developed a gate-teleportation-based protocol for computational indistinguishability obfuscation of quantum circuits. This protocol is efficient for Clifford+T circuits with logarithmically many T-gates, where the limiting factor in the efficiency of the protocol is the difficulty, on input a quantum circuit $C$, of the classical task of producing a description of the unitary obtained by conjugating a Pauli $P$ (corresponding to a Bell-measurement outcome) by $C$, where this description only depends on the input-output functionality of $CPC^{\dagger}$. The task above, in turn, is at least as hard as the problem of determining whether two $n$-qubit quantum circuits are perfectly equivalent up to global phase. In 2009, Tanaka defined the corresponding decision problem Exact Non-Identity Check (ENIC) and showed that ENIC is NQP-complete and thus NP-hard as well. Motivated by the 2021 protocol, we consider in this work what happens when we pass from low T-count to low T-depth. We show that, for Clifford+T-circuits of T-depth $O(\log(n))$, deciding ENIC remains NP-hard. In particular, we show this by relating certain decision problems on Pauli coefficients of Clifford+T unitaries to well-known hardness results for codeword weights in binary linear codes. This effectively rules out the possibility, for Clifford+T-circuits of logarithmic T-depth, of either efficient ENIC or efficient gate-teleportation based computational indistinguishability obfuscation, unless P=NP. It also provides a new, independent proof of the hardness of ENIC, even at low T-depth. Along the way, we prove the NP-hardness of some related circuit problems.

The non-Hermitian skin effect (NHSE) fundamentally invalidates the conventional bulk-boundary correspondence (BBC), leading topological diagnostics into a crisis. While the non-Bloch polarization $P_{\beta}$ defined on the generalized Brillouin zone restores momentum-space topology, a direct, robust real-space bulk probe has remained elusive. We resolve this by establishing a universal correspondence between $P_{\beta}$ and the entanglement polarization $\chi$ of the biorthogonal ground state. Introducing a quasi-reciprocal Hamiltonian $\tilde{H}$ that removes the NHSE while preserving bulk topology, we rigorously prove the fundamental identity $P_{\beta} \equiv \chi(\tilde{H})\pmod 1$ in the thermodynamic limit under the quasi-locality assumption. Crucially, we demonstrate that this equivalence transcends the locality constraints that limit traditional topological invariants. While the conventional Resta polarization fails when $\tilde{H}$ becomes non-local due to the divergence of position variance, we reveal that $\chi(\tilde{H})$ remains robustly quantized, protected by the Fredholm index of Toeplitz operators. Our work thus identifies entanglement as the unique real-space diagnostic capable of capturing non-Bloch topology beyond the breakdown of locality, successfully restoring the BBC across diverse non-Hermitian systems such as line-gap, point-gap, and gapless phases, thereby unifying the geometric and entanglement paradigms in non-Hermitian physics.

The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality, players cooperate much more often. Inspired by prior work employing quantum strategies in the prisoners dilemma, we showed that when similar quantum mechanics principles are applied to the centipede game, it leads to two new quantum Nash equilibria that are superior to the classical solution. Furthermore, by implementing our algorithm on Qiskit, we confirmed that leveraging quantum strategies, rather than strategies like backward induction, to solve the centipede game provided better payoffs for both players and more accurately modeled the games real-life outcomes. Ultimately, we propose a generalized conjecture for similarly structured quantum games.

Entanglement has been identified as a key resource for enhancing charging performance in quantum batteries. We show that the kicked-Ising model at the self-dual point provides an explicit charging mechanism, where maximal entanglement growth yields maximal energy injection. Identifying the Floquet dynamics as a Clifford quantum cellular automata and considering exact diagonalization in momentum space, we analytically characterize the charging process, featuring a stable performance while achieving maximal charging. We further propose a fixed time window protocol that accelerates charging toward the continuously driven transverse-field limit. Spin-correlator analysis reveals that scrambling and light-cone spreading govern charging performance. The protocols remain compatible with diverse platforms, underscoring their scalability and practical feasibility.

Estimating vibrational entropy is a significant challenge in thermodynamics and statistical mechanics due to its reliance on quantum mechanical properties. This paper introduces a quantum algorithm designed to estimate vibrational entropy via energy derivatives. Our approach block encodes the exact expression for the second derivative of the energy and uses quantum linear systems algorithms to deal with the reciprocal powers of the gaps that appear in the expression. We further show that if prior knowledge about the values of the second derivative is used then our algorithm can $\epsilon$-approximate the entropy using a number of queries that scales with the condition number $\kappa$, the temperature $T$, error tolerance $\epsilon$ and an analogue of the partition function $\mathcal{Z}$, as $\widetilde{O}\left(\frac{\mathcal{Z}\kappa^2 }{\epsilon T}\right)$. We show that if sufficient prior knowledge is given about the second derivative then the query scales quadratically better than these results. This shows that, under reasonable assumptions of the temperature and a quantum computer can be used to compute the vibrational contributions to the entropy faster than analogous classical algorithms would be capable of. Our findings highlight the potential of quantum algorithms to enhance the prediction of thermodynamic properties, paving the way for advancements in fields such as material science, molecular biology, and chemical engineering.

Using programmable analog quantum annealing processors, we implement a sampling-based magnetic hysteresis protocol to probe the counterintuitive notion of magnetic memory in antiferromagnetic models. A key component of this protocol responsible for the hysteresis is a transverse field, which enables state transitions, while the longitudinal magnetic field sweep is done via a longitudinal control field. We observe intriguing non-monotonic magnetization, alongside full saturation and reversal of the hysteresis curve, Barkhausen-like noise, as well as emergent magnetic domains mediated by quantum fluctuations that give rise to the magnetic memory effect in antiferromagnets.

We study the asymptotic dynamics of open quantum systems in the Heisenberg picture. We find an explicit expression for the attractor subspace and the dynamics that takes place in it. We present the relationship between the attractor subspaces in the Schrödinger and Heisenberg pictures and, in particular, the connection between their algebraic structures. An unfolding theorem of the asymptotics, as well as the fine structure of the recently introduced Choi-Effros decoherence-free algebra, are also discussed. Finally, we show how to extend all the results to the class of Schwarz maps.

Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable through quantum strategies, is rarely accessible analytically. In this work, we introduce a general construction of Bell inequalities for which this bound can be computed exactly. Our framework generalizes both the Clauser-Horne-Shimony-Holt and Gisin's elegant inequalities, yielding Bell expressions maximally violated by any number of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, our inequalities also enable the device-independent certification of Majorana fermions, understood as multiqubit realizations of Clifford algebra generators. Importantly, we identify an additional equivalence that must be incorporated into the definition of self-testing beyond invariance under local isometries and transposition. This equivalence arises from partial transposition applied to the shared state and to the measurements, which in specific cases leaves all observed correlations unchanged.

Generalized Parton Distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED2), within the Hamiltonian formulation of lattice field theory. Quasi-distributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasi-parton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

Quantum phenomena such as entanglement provide powerful resources for enhancing classical sensing. Here, we theoretically show that collective entanglement of spin qubits, arising from a condensation of particle-hole pairs, can strongly amplify transitions between ground and excited spin states, potentially improving signal contrast in optically detected magnetic resonance. This collective state exhibits an $\mathcal{O}(\sqrt{N})$ enhancement of the transition amplitude with respect to an applied microwave field, where $N$ is the number of entangled spin qubits. We computationally realize this amplification using an ensemble of $N$ triplet spins with magnetic dipole interactions, where the largest transition amplitudes occur at geometries for which the condensation of particle-hole pairs is strongest. This effect, robust to noise, originates from the concentration of entanglement into a single collective mode, reflected in a large eigenvalue of the particle-hole reduced density matrix – an entanglement witness of condensation analogous to off-diagonal long-range order, though realized here in a finite system. These results offer a design principle for quantum sensors that exploit condensation-inspired entanglement to boost sensitivity in spin-based platforms.

We study the quantum dynamics in Krylov space of a spatially flat, homogeneous, and isotropic universe sourced with a massless scalar field within Wheeler-DeWitt (WDW) quantum cosmology and loop quantum cosmology (LQC) frameworks. The availability of a physical Hilbert space and physical Hamiltonian and the presence of an internal clock enable us to construct the Krylov basis analytically by applying the Lanczos algorithm. We then evaluate both the Krylov state and operator complexity for WDW quantum cosmology and LQC on this basis. In regimes where the wave function of the universe is sharply peaked, our results indicate that the Krylov complexity grows quadratically with the scalar field clock for the state and operator complexities in both the WDW quantum cosmology and LQC. We further show that the operator complexity is exactly twice the state complexity in these regimes. We discuss the interpretation of the global behavior of these systems by calculating the Krylov entropy for both quantum cosmological frameworks. We observe that in LQC, the Krylov complexity and entropy remain finite at the bounce, whereas in the WDW quantum cosmology, they diverge at the big bang/crunch singularity. Our work provides the first example of computing Krylov complexity for a system with a totally constrained Hamiltonian and no external time, a framework to calculate a purely quantum-mechanical entropy in quantum cosmology, and, to our knowledge, the first direct bridge between Krylov complexity and canonical quantum cosmology, as a first step toward understanding how polymerized quantum geometry modifies complexity and entropy.

QDNA-ID is a trust-chain framework that links physical quantum behavior to digitally verified records. The system first executes standard quantum circuits with random shot patterns across different devices to generate entropy profiles and measurement data that reveal device-specific behavior. A Bell or CHSH test is then used to confirm that correlations originate from genuine non classical processes rather than classical simulation. The verified outcomes are converted into statistical fingerprints using entropy, divergence, and bias features to characterize each device. These features and metadata for device, session, and random seed parameters are digitally signed and time stamped to ensure integrity and traceability. Authenticated artifacts are stored in a hierarchical index for reproducible retrieval and long term auditing. A visualization and analytics interface monitors drift, policy enforcement, and device behavior logs. A machine learning engine tracks entropy drift, detects anomalies, and classifies devices based on evolving patterns. An external verification API supports independent recomputation of hashes, signatures, and CHSH evidence. QDNA-ID operates as a continuous feedback loop that maintains a persistent chain of trust for quantum computing environments.

Fine-tuning BERT for text classification can be computationally challenging and requires careful hyper-parameter tuning. Recent studies have highlighted the potential of quantum algorithms to outperform conventional methods in machine learning and text classification tasks. In this work, we propose a hybrid approach that integrates an n-qubit quantum circuit with a classical BERT model for text classification. We evaluate the performance of the fine-tuned classical-quantum BERT and demonstrate its feasibility as well as its potential in advancing this research area. Our experimental results show that the proposed hybrid model achieves performance that is competitive with, and in some cases better than, the classical baselines on standard benchmark datasets. Furthermore, our approach demonstrates the adaptability of classical-quantum models for fine-tuning pre-trained models across diverse datasets. Overall, the hybrid model highlights the promise of quantum computing in achieving improved performance for text classification tasks.

Trajectory forecasting for autonomous driving must deliver accurate, calibrated multi-modal futures under tight compute and latency constraints. We propose a compact hybrid quantum architecture that aligns quantum inductive bias with road-scene structure by operating in an ego-centric, lane-aligned frame and predicting residual corrections to a kinematic baseline instead of absolute poses. The model combines a transformer-inspired quantum attention encoder (9 qubits), a parameter-lean quantum feedforward stack (64 layers, ${\sim}1200$ trainable angles), and a Fourier-based decoder that uses shallow entanglement and phase superposition to generate 16 trajectory hypotheses in a single pass, with mode confidences derived from the latent spectrum. All circuit parameters are trained with Simultaneous Perturbation Stochastic Approximation (SPSA), avoiding backpropagation through non-analytic components. In the Waymo Open Motion Dataset, the model achieves minADE (minimum Average Displacement Error) of \SI{1.94}{m} and minFDE (minimum Final Displacement Error) of \SI{3.56}{m} in the $16$ models predicted over the horizon of \SI{2.0}{s}, consistently outperforming a kinematic baseline with reduced miss rates and strong recall. Ablations confirm that residual learning in the lane frame, truncated Fourier decoding, shallow entanglement, and spectrum-based ranking focus capacity where it matters, yielding stable optimization and reliable multi-modal forecasts from small, shallow quantum circuits on a modern autonomous-driving benchmark.

In this paper, the approach for considering fast charged particles scattering on targets of complex structure, which contains some isolated substructures, was expanded to account quadratic potential terms. Based on this approach, the differential cross section for scattering on the set of parallel planes with uniformly distributed atoms in each plane was obtained. It was shown that for this case the differential scattering cross section splits into coherent and incohent cross sections in the eikonal approximation analogously with the Born approximation.

Edge states of chiral topologically ordered phases are commonly described by chiral Luttinger liquids, effective theories that are exact only in the hydrodynamic limit. Motivated by recent bulk observations of fractional Chern insulators (FCIs) in two-dimensional materials and by synthetic realizations in ultracold atoms, we revisit this framework and quantify deviations from the hydrodynamic limit due to lattice effects. Using a combination of analytical arguments and numerical simulations, we disentangle universal from nonuniversal edge properties. We outline experimental probes in excitonic FCIs and in ultracold atom systems, and in particular propose time-resolved edge spectroscopy to directly access the predicted exponents and velocities.

We introduce a reinforcement learning algorithm designed to identify the fixed points of a given quantum operation. The method iteratively constructs the unitary transformation that maps the computational basis onto the basis of fixed points through a reward-penalty scheme based on quantum measurements. In cases where the operation corresponds to a Hamiltonian evolution, this task reduces to determining the Hamiltonian eigenstates. The algorithm is first benchmarked on random Hamiltonians acting on two and three qubits and then applied to many-body systems of up to six qubits, including the transverse-field Ising model and the all-to-all pairing Hamiltonian. In both cases, the algorithm is demonstrated to perform successfully; in the pairing model, it can also reveal hidden symmetries, which can be exploited to restrict learning to specific symmetry sectors. Finally, we discuss the possibility of post-selecting high-fidelity states even when full convergence has not been reached.

Quantum many-body scars are special eigenstates that violate the eigenstate thermalization hypothesis while residing at finite energy density along with thermalizing eigenstates. The spin-1 XY model is known to host a family of such exceptional states originating from long-lived quasiparticle excitations that exhibit anomalously low entanglement entropy and long-time periodic revivals, resulting in weak ergodicity breaking. We study the stability of these scarred states against typical U(1) symmetry preserving perturbation in the XY chain. While perturbation theory can describe the deformed scar states at small system sizes, finite-size scaling of the perturbation matrix elements indicate that the scars ultimately thermalize in larger chains. Nonetheless, we demonstrate that the long-range order associated with the scars decays under the perturbation, and we estimate the relaxation timescale of oscillatory dynamics in certain local observables to be of order $\lambda^{-2}$, where $\lambda$ is the perturbation strength.