Papers

We revisit the problem of learning fermionic linear optics (FLO), also known as fermionic Gaussian unitaries. Given black-box query access to an unknown FLO, previous proposals required $\widetilde{\mathcal{O}}(n^5 / \varepsilon^2)$ queries, where $n$ is the system size and $\varepsilon$ is the error in diamond distance. These algorithms also use unphysical operations (i.e., violating fermionic superselection rules) and/or $n$ auxiliary modes to prepare Choi states of the FLO. In this work, we establish efficient and experimentally friendly protocols that obey superselection, use minimal ancilla (at most $1$ extra mode), and exhibit improved dependence on both parameters $n$ and $\varepsilon$. For arbitrary (active) FLOs this algorithm makes at most $\widetilde{\mathcal{O}}(n^4 / \varepsilon)$ queries, while for number-conserving (passive) FLOs we show that $\mathcal{O}(n^3 / \varepsilon)$ queries suffice. The complexity of the active case can be further reduced to $\widetilde{\mathcal{O}}(n^3 / \varepsilon)$ at the cost of using $n$ ancilla. This marks the first FLO learning algorithm that attains Heisenberg scaling in precision. As a side result, we also demonstrate an improved copy complexity of $\widetilde{\mathcal{O}}(n \eta^2 / \varepsilon^2)$ for time-efficient state tomography of $\eta$-particle Slater determinants in $\varepsilon$ trace distance, which may be of independent interest.

In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.

Recent advances in neural rendering, particularly 3D Gaussian Splatting (3DGS), have enabled real-time rendering of complex scenes. However, standard 3DGS relies on spherical harmonics, which often struggle to accurately capture high-frequency view-dependent effects such as sharp reflections and transparency. While hybrid approaches like Viewing Direction Gaussian Splatting (VDGS) mitigate this limitation using classical Multi-Layer Perceptrons (MLPs), they remain limited by the expressivity of classical networks in low-parameter regimes. In this paper, we introduce QuantumGS, a novel hybrid framework that integrates Variational Quantum Circuits (VQC) into the Gaussian Splatting pipeline. We propose a unique encoding strategy that maps the viewing direction directly onto the Bloch sphere, leveraging the natural geometry of qubits to represent 3D directional data. By replacing classical color-modulating networks with quantum circuits generated via a hypernetwork or conditioning mechanism, we achieve higher expressivity and better generalization. Source code is available in the supplementary material. Code is available at https://github.com/gwilczynski95/QuantumGS

Non-Hermitian (NH) Dirac semimetals describe open gain–loss systems. Yet at charge neutrality, models featuring real spectrum often look Hermitian-like, with NH effects absorbed into renormalized band parameters. Here, we show that a response-based diagnostic of effective non-Hermiticity can be formulated using minimal pseudo-Lorentz-symmetry-breaking deformations, which separate observables that remain captured by parameter redefinitions from those that exhibit irreducible NH structure. For a two-dimensional NH Dirac semimetal in the weak-NH, real-spectrum regime, we analyze Dirac-cone tilt and velocity anisotropy and compute representative probes of spectral structure, quantum geometry, optical response, and viscoelasticity at zero temperature. We find that tilt yields an NH-dependent slope of the density of states that cannot be collapsed to a single effective velocity, while velocity anisotropy can be captured by effective-velocity reparametrization. Furthermore, the quantum metric and collisionless optical conductivities provide NH-insensitive benchmarks (with the nonlinear conductivity symmetry selected), whereas the shear viscosity offers a discriminator through its tensor structure. Our results identify minimal deformations and bulk response channels that enable access to effective non-Hermiticity even when the spectrum remains real.

Errors are the primary bottleneck preventing practical quantum computing. This challenge is exacerbated in the distributed quantum computing regime, where quantum networks introduce additional communication-induced noise. While error mitigation techniques such as Zero Noise Extrapolation (ZNE) have proven effective for standalone quantum processors, their behavior in distributed architectures is not yet well understood. We investigate ZNE in this setting by comparing Global optimization (ZNE is applied prior to circuit partitioning), against Local optimization (ZNE is applied independently to each sub-circuit). Partitioning is performed on a monolithic circuit, which is then transformed into a distributed implementation by inserting noisy teleportation-based communication primitives between sub-circuits. We evaluate both approaches across varying numbers of quantum processing units (QPUs) and under heterogeneous local and network noise conditions. Our results demonstrate that Global ZNE exhibits superior scalability, achieving error reductions of up to $48\%$ across six QPUs. Moreover, we observe counterintuitive noise behavior, where increasing the number of QPUs improves mitigation effectiveness despite higher communication overhead. These findings highlight fundamental trade-offs in distributed quantum error mitigation and raise new questions regarding the interplay between circuit structure, partitioning strategies, and network noise.

Measurement-induced phase transitions (MIPT) give rise to novel dynamical states of quantum matter realized by balancing unitary evolution and measurements. We present large-scale numerical simulations of a trapped-ion native MIPT, argued to belong to the universality class described by the Haar non-unitary conformal field theory. First, through a finite-size analysis we obtained the critical measurement rate, and correlation length exponent, which falls close to the percolation value. Second, by leveraging a monotone computable via semi-definite programming, we uncover robust algebraic decay of genuine multiparty entanglement (GME) versus separation for 2, 3, and 4 parties. The corresponding critical exponents are lower-bounded by those of the multiparty mutual information, which we determine up to 4 parties, and conjecture to be (k+2) for k parties. Additionally, we derive lower bounds for both GME and multiparty mutual information.

Decoy-state QKD with phase-randomized weak coherent pulses is typically analyzed assuming independent, precisely prepared intensities. Real sources, however, can exhibit correlated intensity drift across rounds, potentially leaking intensity information and breaking the standard decoy-state reduction to linear programs. Cauchy–Schwarz (CS) constraints can restore security by coupling $n$-photon yields across intensities, but they introduce nonlinear square-root constraints that are commonly handled via outer linearisation around channel-model-based reference points. We propose a reproducible alternative: first solve the full CS-constrained parameter-estimation problems using the interior-point nonlinear solver IPOPT, then use the resulting candidate solution as the linearisation point for the outer optimisation that certifies a valid lower bound on the asymptotic key rate. Simulations for both coarse-grained model-independent correlations and fine-grained truncated-Gaussian models show consistently tighter key-rate bounds than canonical reference points, and in some cases allow certifying optimality when both optimisation stages coincide.

We derive constraints on renormalization group (RG) flows and stability of phases in nonequilibrium systems using quantum information inequalities. These constraints involve conditional mutual information (CMI), which quantifies correlations between spatially separated regions not mediated by their surroundings. First, assuming CMI is UV finite, we derive a monotonicity constraint on its crossover scaling function. Under certain assumptions, this implies that the CMI scaling exponent cannot increase along the RG flow. Second, we bound the CMI of a convex mixture of states in terms of the CMI of individual components. We use this inequality to infer perturbative stability of spontaneous symmetry breaking states against quantum channels that explicitly break symmetry. We illustrate these constraints through several examples, including decoherence-driven transitions in classical symmetry-broken states, area-law CMI in anisotropic conserved dynamics, and even transitions in pure quantum states. We also discuss implications for classical nonequilibrium steady states.

Although in general boundary conditions do not affect the bulk properties of a system, some of them are special and defy such expectation. This is the case, for instance, of those inducing geometrical frustration in a classical magnet. Recently, the study of such settings in quantum systems (dubbed topological frustration) has uncovered peculiar features, interesting both from a fundamental and technological point of view. In this work, we present and discuss the behavior of several quantum resources in presence of TF, namely the (disconnected) entanglement entropy and the non-stabilizerness Renyi entropy. We will show that, compared to their non-frustrated counterparts, TF adds a distinct contribution to these resources, due to a stable, delocalized, topological excitation. Remarkably, this contribution can be calculated analytically, due to its similarities with that of a W-state.

Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor networks have been an essential tool for studying such quantum systems, owing to their ability to efficiently capture the entanglement properties of the systems they represent. One of the well-known tensor network architectures, namely matrix product states (MPS), is the standard method for simulating one-dimensional QMBS. Here, we propose a simple, yet efficient, method to augment the already available MPS algorithms to simulate the dynamics of time-dependent Hamiltonians with better accuracy and a faster convergence rate, giving a second-order convergence compared to the first-order convergence of the standard method. We apply our proposed method to simulate the dynamics of a chain of single spins associated with nitrogen-vacancy color centers in diamonds, which has potential applications for practical and scalable quantum technologies, and find that our method improves the average error for a system of few NV centers by a factor of about 1000 for moderate step sizes. Our work paves the way for efficient simulation of QMBS under the influence of time-dependent Hamiltonians.

We derive a universal bound on the efficiency with which "dissipated" work can generate distinguishable changes in a quantum many-body state at a finite temperature, as quantified by the quantum Fisher information. The bound follows solely from the analytic structure of equilibrium many-body correlators and is independent of all microscopic details. It takes a frequency-resolved form with a characteristic crossover at the Planckian scale, $\omega_\star\sim k_B T/\hbar$. We find that Planckian scatterers sit at the edge of optimality, displaying maximal relaxation rate before information-dissipation efficiency collapses. This suggests strange metals are not just fast dissipators, but the fastest that remain efficient in generating distinguishability. The bounded quantity can be evaluated directly from optical conductivity measurements in strongly correlated electronic systems, offering a unique window into how dissipation generates distinguishable changes.

We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to estimate expectation values $\{\mathrm{tr}(O_i\rho)\}_{i=1}^m$ to accuracy $\epsilon$ in $L_p$-norm, using possibly adaptive measurements that act on $O(\mathrm{polylog}(d))$ number of copies of $\rho$ at a time. We focus on the regime where $\epsilon$ is below an instance-dependent threshold. Our main contribution is an instance-optimal characterization of the sample complexity as $\tilde{\Theta}(\Gamma_p/\epsilon^2)$, where $\Gamma_p$ is a function of $\{O_i\}_{i=1}^m$ defined via an optimization formula involving the inverse Fisher information matrix. Previously, tight bounds were known only in special cases, e.g. Pauli shadow tomography with $L_\infty$-norm error. Concretely, we first analyze a simpler oblivious variant where the goal is to estimate an observable of the form $\sum_{i=1}^m \alpha_i O_i$ with $\|\alpha\|_q = 1$ (where $q$ is dual to $p$) revealed after the measurement. For single-copy measurements, we obtain a sample complexity of $\Theta(\Gamma^{\mathrm{ob}}_p/\epsilon^2)$. We then show $\tilde{\Theta}(\Gamma_p/\epsilon^2)$ is necessary and sufficient for the original problem, with the lower bound applying to unbiased, bounded estimators. Our upper bounds rely on a two-step algorithm combining coarse tomography with local estimation. Notably, $\Gamma^{\mathrm{ob}}_\infty = \Gamma_\infty$. In both cases, allowing $c$-copy measurements improves the sample complexity by at most $\Omega(1/c)$. Our results establish a quantitative correspondence between quantum learning and metrology, unifying asymptotic metrological limits with finite-sample learning guarantees.

In this work we study the relationship between quantum random walks on graphs and Krylov/spread complexity. We show that the latter's definition naturally emerges through a canonical method of reducing a graph to a chain, on which we can identify the usual Krylov structure. We use this identification to construct families of graphs corresponding to special classes of systems with known complexity features and conversely, to compute Krylov complexity for graphs of physical interest. The two main outcomes are the analytic computation of the Lanczos coefficients for the SYK model for an arbitrary number $q$ of interacting fermions and the complete characterization of Krylov complexity for the hypercube graph in any number of dimensions. The latter serves as the starting point for an in-depth comparison between Krylov and circuit complexities as they purportedly arise in the context of black holes. We find that while under certain conditions Krylov complexity follows the growth and saturation pattern ascribed to such systems, the timescale at which saturation happens can generally be shorter than what is predicted by random unitary circuits, due to the effects of quantum speed-ups commonly occurring when comparing quantum and classical random walks.

Cold atoms have become a powerful platform for quantum-simulating lattice gauge theories in higher spatial dimensions. However, such realizations have been restricted to the lowest possible truncations of the gauge field, which limit the connections one can make to lattice quantum electrodynamics. Here, we propose a feasible cold-atom quantum simulator of a $(2+1)$-dimensional U$(1)$ lattice gauge theory in a spin $S=1$ truncation, featuring dynamical matter and gauge fields. We derive a mapping of this theory onto a bosonic computational basis, stabilized by an emergent gauge-protection mechanism through quantum Zeno dynamics. The implementation is based on a single-species Bose–Hubbard model realized in a tilted optical superlattice. This approach requires only moderate experimental resources already available in current ultracold-atom platforms. Using infinite matrix product state simulations, we benchmark real-time dynamics under global quenches. The results demonstrate faithful evolution of the target gauge theory and robust preservation of the gauge constraints. Our work significantly advances the experimental prospects for simulating higher-dimensional lattice gauge theories using larger gauge-field truncations.

We study Heisenberg antiferromagnets through a graph-theoretic representation of their Hamiltonians. In the computational basis of a fixed-magnetization sector, the Heisenberg Hamiltonian equals a constant minus the weighted Laplacian of a graph whose vertices are spin configurations and whose edges connect configurations related by exchanging two antiparallel spins on a lattice bond. We call this graph the Hilbert graph (HG) which is isomorphic to the token graph of the lattice over which the Hamiltonian is defined. The exact ground-state energy is then determined by the largest eigenvalue of the HG Laplacian, which is the spectral relaxation of weighted Max-Cut on the HG. With the amplitudes fixed, the phase-dependent part of the variational energy defines an antiferromagnetic classical XY model on the HG, with couplings set by the amplitudes. Restricting the variational state to be real, i.e., restricting its phases to $\{0,\pi\}$, reduces the fixed-amplitude energy minimization to solving an antiferromagnetic Ising model and hence a weighted Max-Cut on the HG. When the weights are generated from non-degenerate ground-state amplitudes, the optimal phases give the ground-state sign structure which can be recovered from the weights in time polynomial in the size of the HG. On the Hamiltonian side, a diagonal sign transformation removes all positive off-diagonal matrix elements if and only if the HG is bipartite, which reproduces the Marshall sign rule on bipartite lattices through the graph two-coloring problem; otherwise, the minimal remaining positive weight equals the sum of HG edge weights left uncut by the Max-Cut. This graph formulation establishes a common framework for understanding wave function sign structure, Hamiltonian stoquasticity, non-convexity of phase optimization in variational Monte Carlo, and the average sign in quantum Monte Carlo.

The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the optimal estimation precision of quantum sensors. A typical quantum sensor involves a qubit(e.g. a spin-1/2) probe undergoing an unknown rotation, here the unknown rotation angle is the parameter to be estimated. A well known limitation is that if the rotation axis is unknown, the maximal quantum Fisher information is impossible to attain. This limitation has been lifted recently by leveraging entanglement between the probe qubit and an ancilla qubit. Namely, through measurement of the ancilla after the axis is revealed, one can prepare the probe that is optimal for any unknown rotation axis. This proposal, however, works only for a spin-1/2. Considering large spin probes can achieve a larger quantum Fisher information, offering enhanced metrological advantage, we here utilize the entanglement between a large spin probe and an ancilla to achieve optimal quantum Fisher information for estimating the rotation angle, without prior knowledge of the rotation axis. Different from the previous spin-1/2 case, achieving the optimal precision with large spins generally requires post-selection, resulting in a success probability dependent on the dimension of the Hilbert space. Furthermore, we extend the encoding state from the maximally entangled case to general entangled states, showing that optimal metrology can still be achieved with a certain success probability.

The standard method for benchmarking quantum error-correction is randomized fault-injection testing. The state-of-the-art tool stim is efficient for error correction implementations with distances of up to 10, but scales poorly to larger distances for low physical error rates. In this paper, we present a scalable approach that combines stratified fault injection with extrapolation. Our insight is that some of the fault space can be sampled efficiently, after which extrapolation is sufficient to complete the testing task. As a result, our tool scales to distance 17 for a physical error rate of 0.0005 with a two-hour time budget on a desktop. For this case, it estimated a logical error rate of $1.51 \times 10^{-11}$ with high confidence.

We introduce a propagation-based approach to thermal state simulation by adapting Pauli and Majorana propagation to imaginary-time evolution in the Schrödinger picture. Our key observation is that high-temperature states can be sparse in the Pauli or Majorana bases, approaching the identity at infinite temperature. By formulating imaginary-time evolution directly in these operator bases and evolving from the maximally mixed state, we access a continuum of temperatures where the state remains efficiently representable. We provide analytic guarantees for small-coefficient truncation and Pauli-weight (Majorana-length) truncation strategies by quantifying the error growth and the impact of backflow. Large-scale numerics on the 1D J1-J2 model (energies) and the triangular-lattice Hubbard model (static correlations) validate efficiency at high temperatures.

We investigate the hardware requirements for quantum teleportation in an intercity-scale network topology consisting of two metropolitan-scale networks connected via a long-distance backbone link. Specifically, we identify the minimal improvements required beyond the state-of-the-art to achieve an end-to-end expected teleportation fidelity of $2/3$, which represents the classical limit. To this end, we formulate the hardware requirements computation as optimisation problems, where the hardware parameters representing the underlying device capabilities serve as decision variables. Assuming a simplified noise model, we derive closed-form analytical expressions for the teleportation fidelity and rate when the network is realised using heterogeneous quantum hardware, including a quantum repeater chain with a memory cut-off. Our derivations are based on events defined by the order statistics of link generation durations in both the metropolitan networks and the backbone, and the resulting expressions are validated through simulations on the NetSquid platform. The analytical expressions facilitate efficient exploration of the optimisation parameter space without resorting to computationally intensive simulations. We then apply this framework to a representative realisation in which the metropolitan nodes are based on trapped-ion processors and the backbone is composed of ensemble-based quantum memories. Our results suggest that teleportation across metropolitan distances is already achievable with state-of-the-art hardware when the data qubit is prepared after end-to-end entanglement has already been established, whereas extending teleportation to intercity scales requires additional, though plausibly achievable, improvements in hardware performance.

Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and long-lived quantum memory, capabilities which remain challenging to realize in practice. In this work, we introduce a quantum digital signature scheme that operates with only classical communication, using the classical shadows of states produced by random circuits as public keys. We provide theoretical and numerical evidence supporting the conjectured hardness of learning the private key (the circuit) from the public key (the shadow). A key technical ingredient enabling our scheme is an improved state-certification primitive that achieves higher noise tolerance and lower sample complexity than prior methods. We realize this certification by designing a high-rate error-detecting code tailored to our random-circuit ensemble and experimentally generating shadows for 32-qubit states using circuits with $\geq 80$ logical ($\geq 582$ physical) two-qubit gates, attaining 0.90 $\pm$ 0.01 fidelity. With increased number of measurement samples, our hardware-demonstrated primitives realize a proof-of-principle quantum digital signature, demonstrating the near-term feasibility of our scheme.

Altermagnetism has recently emerged as a third fundamental branch of magnetism, combining the vanishing net magnetization of antiferromagnets with the high-momentum-dependent spin splitting of ferromagnets. This study provides a comprehensive real- and momentum-space analysis of topological phases in two-dimensional d-wave altermagnets. By employing a tight-binding Hamiltonian, we characterize the topological phase transition occurring at a critical intra-sublattice hopping strength ($t_a^C$). We examine the emergence of Dirac nodal points and the resulting Berry curvature singularities, supported by a visual analysis of pseudospin texture winding. Crucially, we analize spin splitting, effective altermagnetic strength, and investigate the transport implications of these phases, uncovering giant conductivity anisotropy and spin-dependent “steering” effects driven by group velocity distribution across the Fermi surface. Beyond bulk properties, we analyze the edge state topology in ribbon geometries through the lens of information-theoretic markers like fidelity-susceptibility and inverse participation ratio, offering a robust alternative to traditional Chern number calculations, without relying on translational symmetry. Our results demonstrate that the hybridization of edge states in ultra-narrow nanoribbons opens a controllable energy gap, a feature we exploit to propose a novel topological altermagnetic field-effect transistor design where ballistic and spatially spin-polarized transport can be electrostatically gated. This work establishes a theoretical and information-theoretic framework for “edgetronics” in altermagnetic materials, paving the way for next-generation, high-speed spintronic and “spin-splitter” logic devices and architectures.

The superconducting qubit quantum computer is one of the most promising quantum computing architectures for large-scale integration due to its maturity and close proximity to the well-established semiconductor manufacturing infrastructure. From an education perspective, it also bridges classical microwave electronics and quantum electrodynamics. In this paper, we will review the basics of quantum computers, superconductivity, and Josephson junctions. We then introduce important technologies and concepts related to DiVincenzo's criteria, which are the necessary conditions for the superconducting qubits to work as a useful quantum computer. Firstly, we will discuss various types of superconducting qubits formed with Josephson junctions, from which we will understand the trade-off across multiple design parameters, including their noise immunity. Secondly, we will discuss different schemes to achieve entanglement gate operations, which are a major bottleneck in achieving more efficient fault-tolerant quantum computing. Thirdly, we will review readout engineering, including the implementations of the Purcell filters and quantum-limited amplifiers. Finally, we will discuss the nature and review the studies of two-level system defects, which are currently the limiting factor of qubit coherence time. DiVincenzo's criteria are only the necessary conditions for a technology to be eligible for quantum computing. To have a useful quantum computer, large-scale integration is required. We will review proposals and developments for the large-scale integration of superconducting qubit devices. By comparing with the application of electronic design automation (EDA) in semiconductors, we will also review the use of EDA in superconducting qubit quantum computer design, which is necessary for its large-scale integration.

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li$\leftrightarrows$Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series to $\hbar=0$ unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit $\hbar\to0$. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.

We demonstrate the existence of a dynamical quantum phase transition (DQPT) in a dissipative collective-spin model that exhibits the boundary time crystal (BTC) phase. We initialize the system in the ground state of the Hamiltonian in either the BTC or the non-BTC phase, and drive it across the BTC transition. The driving is done by an abrupt quench or by a finite-time linear ramp of a Hamiltonian control parameter under Markovian Lindblad dynamics. We diagnose DQPTs through zeros of the fidelity-based Loschmidt echo between the initial state and the evolving mixed state, which induce nonanalytic cusp-like features in the associated rate function. For quenches into the BTC phase, the Loschmidt echo exhibits repeated zeros due to the emergent time-periodic steady state, whereas for quenches into the non-BTC phase, the overlap vanishes and remains zero once the dynamics relaxes to a stationary state. We further show that the DQPT persists under the ramp protocol followed by unitary evolution with the final Hamiltonian. Finally, we analyze the finite-size scaling of the first critical time and find convergence to a constant in the thermodynamic limit, with distinct power-law approaches for the quench and the ramp protocols.

Multipartite entanglement determines the strength and range of interactions in many-body quantum systems. Yet, it is hard to evaluate it, due to the complex structures of quantum states. Here, we introduce a generic method to quantify the k <= N-partite entanglement of an N-particle system, by maximizing an arbitrary bipartite entanglement measure within subsystems of size up to k. The resulting classification of multipartite states captures their experimental cost: creating a k-partite entangled state requires at least k-1 two-particle entangling gates. Further, we analytically calculate the newly defined k-partite entanglement of formation, which generalizes an important bipartite entanglement measure, in several classes of states, including the W states of any dimension.

In this paper, we present the reduction of a recently introduced generalized quantum scheme of Chodos and Cooper to Levinson-Smith and Liénard classes of nonlinear system that enable us to furnish a wider class of acceptable solutions. In particular, for the Levinson-Smith equations, we find their relevance to position-dependent mass quantum systems, with an interesting off-shoot that solitonic-like solutions emerge from the condition of the level surface in the system. On the other hand, for the Liénard type, which has coefficients of odd and odd symmetry in the present set up, we demonstrate that closed form solutions exist on carrying out conversion to the typical Abel form.

Digitized adiabatic quantum factorization is a hybrid algorithm that exploits the advantage of digitized quantum computers to implement efficient adiabatic algorithms for factorization through gate decompositions of analog evolutions. In this paper, we harness the flexibility of digitized computers to derive a digitized adiabatic algorithm able to reduce the gate-demanding costs of implementing factorization. To this end, we propose a new approach for adiabatic factorization by encoding the solution of the problem in the kernel subspace of the problem Hamiltonian, instead of using ground-state encoding considered in the standard adiabatic factorization proposed by Peng $et$ $al$. [Phys. Rev. Lett. 101, 220405 (2008)]. Our encoding enables the design of adiabatic factorization algorithms belonging to the class of Quadratic Unconstrained Binary Optimization (QUBO) methods, instead the Polinomial Unconstrained Binary Optimization (PUBO) used by standard adiabatic factorization. We illustrate the performance of our QUBO algorithm by implementing the factorization of integers $N$ up to 8 bits. The results demonstrate a substantial improvement over the PUBO formulation, both in terms of reduced circuit complexity and increased fidelity in identifying the correct solution.

Dense ensembles of nitrogen-vacancy (NV), substitutional-nitrogen (P1), and surface spins in diamond are leading platforms for quantum sensing, masers, and many-body physics, and in all of them polarization moves by resonant flip-flops (pairwise spin exchanges). We show that the Ising part of the dipolar Hamiltonian, which moves no polarization, sets how fast polarization moves. It detunes every flip-flop by exactly the difference of the Ising fields that the other spins exert on the pair, and these fields come from the very couplings that drive hopping. Dipolar transport thus throttles its own rate, an effect we call the Ising blockade, which models have so far absorbed into a measured or fitted disorder width. Deep in the blockade and at fixed composition, the diffusion constant scales as $D \propto J_0\rho^{1/3}$ (coupling $J_0$, density $\rho$) instead of the Förster-type $J_0^2\rho^{4/3}$. Without fitting, the theory predicts the NV linewidth and all five P1 diffusion constants of [Nature 597, 45 (2021)] within $2\sigma$; without the Ising term at the same couplings, it overshoots them five- to fifteenfold. On a spin-locked surface [Phys. Rev. Lett. 134, 050801 (2025)], the same blockade acts coherently: in exact dynamics, over a third of the spins stay polarized far longer than flip-flops alone allow, accounting for the measured four- to ninefold slowdown.

Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.

The analysis of the computational power of single-query quantum algorithms is important because they must extract maximal information from one oracle call, revealing fundamental limits of quantum advantage and enabling optimal, resource-efficient quantum computation. This paper proposes a formulation of single-query quantum decision trees as weighted graphs. This formulation has the advantage that it facilitates the analysis of the $L_1$ spectral norm of the algorithm output. This advantage is based on the fact that a high $L_1$ spectral norm of the output of a quantum decision tree is a necessary condition to outperform its classical counterpart. We propose heuristics for maximizing the $L_{1}$ spectral norm, show how to combine weighted graphs to generate sequences with strictly increasing norm, and present functions exhibiting exponential quantum advantage. Finally, we establish a necessary condition linking single-query quantum advantage to the asymptotic growth of measurement projector dimensions.