Papers

Quantum networks are expected to be heterogeneous systems, combining distinct qubit platforms, photon wavelengths, and device timescales to achieve scalable, multiuser connectivity. Building and iterating on such systems is costly and slow, which motivates hardware-faithful simulations that explore architecture design space and justify implementation decisions. This paper presents a framework for simulating heterogeneous quantum networks based on SeQUeNCe, a discrete-event simulator of quantum networks. We introduce faithful device models for two representative platforms - Ytterbium atoms and superconducting qubits - to implement entanglement generation and swapping protocols for time-bin encoded photons. Using extensive simulations that account for disparate clock rates and quantum frequency conversion and transduction losses/noise, we map the rate-fidelity trade space and identify the dominant bottlenecks unique to heterogeneous systems. The models are open source and extensible, enabling reproducible evaluation of future heterogeneous designs and protocols.

We investigate the monitored dynamics of many-body quantum systems in which projective measurements of extensive operators are alternated with unitary evolution. Focusing on mean-field models characterized by all-to-all interactions, we develop a general framework that captures the thermodynamic limit, where a semiclassical description naturally emerges. Remarkably, we uncover novel stationary states, distinct from the conventional infinite-temperature state, that arise upon taking the infinite-volume limit. Counterintuitively, this phenomenon is not linked to the closing of the Lindbladian gap in that limit. We provide analytical explanation for this unexpected behavior.

The electromagnetic duality symmetry of Maxwell's equations in vacuum implies that the circular polarization $Q$ of classical electromagnetic waves is conserved. In quantum field theory, the normal-ordered operator $\hat Q$ represents the difference between the number operators of right- and left-handed photons. Previous studies have shown that its expectation value is not conserved for observers propagating in a gravitational field. Here, we show that this Noether symmetry can also be realized in empty waveguides with duality-preserving boundary conditions, and we quantize the source-free Maxwell theory inside a long, cylindrical waveguide undergoing both linear and rotational acceleration from rest. In the vacuum $|0\rangle$ associated to inertial observers, we find that the expectation value $\langle 0| \hat Q |0\rangle $ fails to be conserved for observers co-moving with the waveguide. In particular, frame-dragging effects induce a spectral asymmetry between the right- and left-handed field modes at late times. As a consequence, accelerated detectors co-moving with the rotating waveguide can detect photon-pair excitations from the quantum vacuum, exhibiting an imbalance between opposite helicity modes. This is a relativistic quantum effect, which shows that the classical conservation law associated with duality symmetry is broken in the quantum theory even in flat spacetime, provided we work with non-inertial systems. Our analysis provides a concrete proof of concept for testing this effect in analogue gravity platforms.

There is mounting evidence that entanglement dynamics in chaotic many-body quantum systems in the limit of large subsystems and long times is described by an entanglement membrane effective theory. In this paper, we derive the membrane description in a solvable chaotic large-$N$ model, the Brownian SYK chain. This model has a collective field description in terms of fermion bilinears connecting different folds of the multifold Schwinger-Keldysh path integral used to compute Rényi entropies. The entanglement membrane is a traveling wave solution of the saddle point equations governing these collective fields. The entanglement membrane is characterised by a velocity $v$ and a membrane tension ${\cal E}(v)$ that we calculate. We find that the membrane has finite width for $v<v_B$ (the butterfly velocity), however for $v > v_B$, the membrane splits into two wave fronts, each moving with the butterfly velocity. Our results provide a new viewpoint on the entanglement membrane and uncover new connections between quantum information dynamics and scrambling.

Low-density parity check (LDPC) codes are a well known class of Pauli stabiliser Hamiltonians that furnish fixed-point realisations of nontrivial gapped phases such as symmetry breaking and topologically ordered (including fracton) phases. In this work, we propose symmetry-preserving deformations of these models, in the presence of a transverse field, and identify special points along the deformations with interesting features: (i) the special point is frustration-free, (ii) its ground states include a product state and the code space of the underlying code, and (iii) it remains gapped in the thermodynamic (infinite volume) limit. So the special point realises a first-order transition between (or the coexistence of) the trivial gapped phase and the nontrivial gapped phase associated with the code. In addition, if the original model has a non-invertible duality symmetry, then so does the deformed model. In this case, the duality symmetry is spontaneously broken at the special point, consistent with the associated anomaly. A key step in proving the gap is a coarse-graining/blocking procedure on the Tanner graph of the code that allows us to apply the martingale method successfully. Our model, therefore, provides the first application of the martingale method to a frustration-free model, that is not commuting projector, defined on an arbitrary Tanner graph. We also discuss several familiar examples on Euclidean spatial lattice. Of particular interest is the 2+1d transverse field Ising model: while there is no non-invertible duality symmetry in this case, our results, together with known numerical results, suggest the existence of a tricritical point in the phase diagram.

The task of conclusive exclusion for a set of quantum states is to find a measurement such that for each state in the set, there is an outcome that allows one to conclude with certainty that the state in question was not prepared. Defining classicality of statistics as realizability by a generalized-noncontextual ontological model, we show that there is a quantum-over-classical advantage for how well one can achieve conclusive exclusion. This is achieved in an experimental scenario motivated by the construction appearing in the Pusey-Barrett-Rudolph theorem. We derive noise-robust noncontextuality inequalities bounding the conclusiveness of exclusion, and describe a quantum violation of these. Finally, we show that this bound also constitutes a classical causal compatibility inequality within the bilocality scenario, and that its violation in quantum theory yields a novel possibilistic proof of a quantum-classical gap in that scenario.

We present a universal quantum computing architecture which combines the measurement-driven aspect of MBQC with the circuit model's algorithm dependent generation of qubit entanglement. Our architecture, which we call QGATE, is tailored for discrete-variable photonic quantum computers with deterministic photon sources capable of generating 1D entangled photonic states. QGATE achieves universal quantum computing on a logical data qubit register via the implementation of Clifford operations, QGATE ancilla, and arbitrary angle single-qubit measurements. We realise unitary evolutions defined by multi-qubit Pauli strings via the generation of entanglement between a sub-set of logical qubits and a mutual QGATE ancilla qubit. Measurement of the QGATE ancilla in the appropriate basis then implements a given term of the desired unitary operation. This enables QGATE to both directly perform Hamiltonian evolutions in terms of a series of multi-qubit Pauli operators, in terms of projectors for an arbitrary sparse Hamiltonian, or realise multi-controlled gates enabling direct translation of circuit models to QGATE. We consider examples inspired by quantum chemistry and computational fluid dynamics. We propose an example photonic implementation of QGATE and calculate thresholds of $10.36\pm0.02\%$ or $25.98\pm0.28\%$ on the photonic loss for logical qubits constructed from foliated rotated surface codes, dependent on the deployment of intra-layer or inter-layer fusion respectively.

Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all gates required for universal quantum computation. Code switching addresses this limitation by moving quantum information between different codes that, together, support a universal gate set. Unfortunately, each switch is costly-adding time and space overhead and increasing the logical error rate. Minimizing the number of switching operations is, therefore, essential for quantum computations using code switching. In this work, we study the problem of minimizing the number of code switches required to run a given quantum circuit. We show that this problem can be solved efficiently in polynomial time by reducing it to a minimum-cut instance on a graph derived from the circuit. Our formulation is flexible and can incorporate additional considerations, such as reducing depth overhead by preferring switches during idle periods or biasing the compilation to favor one code over another. To the best of our knowledge, this is the first automated approach for compiling and optimizing code-switching-based quantum computations at the logical level.

Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation schemes, logical circuits are compiled following a place-and-route paradigm, where logical qubits remain statically fixed in space throughout the computation. In this work, we introduce a paradigm shift by exploiting movable logical qubits via teleportation during the logical lattice surgery CNOT gate. Focusing on lattice surgery with the color code, we propose a proof-of-concept compilation scheme that leverages this capability. Numerical simulations show that the proposed approach can substantially reduce the routed circuit depth compared to standard place-and-route compilation techniques. Our results demonstrate that optimizations based on movable logical qubits are not limited to architectures with physically movable qubits, such as neutral atoms or trapped ions - they are also readily applicable to superconducting quantum hardware. An open-source implementation of our method is available on GitHub https://github.com/munich-quantum-toolkit/qecc.

Exactly solvable dissipative models provide an analytical tool for studying the relaxation dynamics in open quantum systems. In this work, we study an exactly solvable model based on an anisotropic variant of the Yao-Lee spin-orbital model, with dissipation acting in the spin sector. We map Liouvillian dynamics to fermions hopping in a doubled Hilbert space under a non-Hermitian Hamiltonian and demonstrate the model's exact solvability. We analyze the model's strong and weak symmetries, which protect an exponentially large manifold of non-equilibrium steady states, establishing the system as a physically feasible dissipative spin liquid. Furthermore, we analyze the transient dynamics in a translationally invariant sector and discover that the single-particle Liouvillian spectrum hosts an exceptional ring in momentum space. We map out a characteristic $\mathcal{PT}$ symmetry breaking transition driven by the dissipation strength, which governs the crossover from oscillatory to decaying relaxation of physical observables. Our work provides a physically motivated, solvable setting for exploring the coexistence of dissipative spin liquid physics and Liouvillian spectral singularities.

We investigate quantum Markov semigroups on bosonic Fock space and identify a broad class of infinite-dimensional dissipative evolutions that exhibit instantaneous Sobolev regularization. Motivated by stability problems in quantum computation, we show that for certain Lindblad operators that are polynomials of creation and annihilation operators, the resulting dynamics immediately transform any initial state into one with finite expectation in all powers of the number operator. A key application is in the bosonic cat code, where we obtain explicit estimates in the trace norm for the speed of convergence. These estimates sharpen existing perturbative bounds at both short and long times, offering new analytic tools for assessing stability and error suppression in bosonic quantum information processing. For example, we improve the strong exponential convergence of the (shifted) $2$-photon dissipation to its asymptotic channel to the uniform topology. For multi-mode systems, a generation theorem in concentrated single-sandwich norms supplies the domain properties required for the regularization argument.

The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as having practical implications. Bell's result was originally proven in a simple bipartite causal structure, but analogous results have also been shown in further causal structures. Here we study the only causal structure with six or fewer nodes in which the question of whether or not there exist quantum correlations that cannot be achieved classically was open. In this causal structure we show that such quantum correlations exist using a method that involves imposing additional restrictions on the correlations. This hence completes the picture of which causal structures of up to six nodes support non-classical quantum correlations. We also provide further illustrations of our method using other causal structures.

We introduce a finite-time protocol that thermalizes a quantum harmonic oscillator, initially in its ground state, without requiring a macroscopic bath. The method uses a second oscillator as an effective environment and implements sudden quenches of the oscillator frequencies and coupling. Owing to the Gaussian nature of the dynamics, the thermalization condition reduces to three solvable equations, yielding exact analytic solutions for a dense discrete set of temperatures and numerical solutions in all other cases. Any target temperature can be approximated with arbitrary precision, with a trade-off between speed and accuracy. The simplicity of the protocol makes it a promising tool for rapid, controlled thermalization in quantum thermodynamics experiments and state preparation.

Quantum key distribution (QKD) security fundamentally relies on the ability to distinguish genuine quantum correlations from classical eavesdropper simulations, yet existing certification methods lack rigorous statistical guarantees under finite-sample conditions and adversarial scenarios. We introduce TARA (Test by Adaptive Ranks), a novel framework combining conformal prediction with sequential martingale testing for quantum anomaly detection that provides distribution-free validity guarantees. TARA offers two complementary approaches. TARA k, based on Kolmogorov Smirnov calibration against local hidden variable (LHV) null distributions, achieving ROC AUC = 0.96 for quantum-classical discrimination. And TARA-m, employing betting martingales for streaming detection with anytime valid type I error control that enables real time monitoring of quantum channels. We establish theoretical guarantees proving that under (context conditional) exchangeability, conformal p-values remain uniformly distributed even for strongly contextual quantum data, confirming that quantum contextuality does not break conformal prediction validity a result with implications beyond quantum certification to any application of distribution-free methods to nonclassical data. Extensive validation on both IBM Torino (superconducting, CHSH = 2.725) and IonQ Forte Enterprise (trapped ion, CHSH = 2.716) quantum processors demonstrates cross-platform robustness, achieving 36% security margins above the classical CHSH bound of 2. Critically, our framework reveals a methodological concern affecting quantum certification more broadly: same-distribution calibration can inflate detection performance by up to 44 percentage points compared to proper cross-distribution calibration, suggesting that prior quantum certification studies using standard train test splits may have systematically overestimated adversarial robustness.

Quantum high-harmonic generation (HHG) is a prominent and growing field of research with potential capabilities of providing high photon-number entangled states of light. However, there is an open debate regarding the theory level required for correctly describing the quantum aspects of HHG, such as squeezing or entanglement. Previous approaches either semi-classically sampled the quantum electromagnetic field distribution, or employed perturbation theory utilizing the semi-classical simulations as a starting point. Both of these schemes miss out key quantum-optical features as self-consistent numerical simulations of the electron-photon wavefunction are not performed at any stage. In this Letter, we develop a full quantum theory for multipartite entanglement in HHG, solving exactly the light-matter interaction Hamiltonian in a given Hilbert space, and employ it for evaluating the quantum correlations of emitted photons. We show that HHG entanglement oscillates with the driving laser power and exhibits multiple local maxima, which allows fine-tuning HHG entanglement. Such features arise for both above-threshold harmonics and between above- and below-threshold harmonics. By analyzing different types of atomic targets, we find that the long-range behavior of driven electrons can qualitatively change the resulting entanglement, potentially leading to non-universal behavior across systems. Lastly, we show that focal averaging over classical degrees of freedom in fact plays a key role in entanglement measures and can change the qualitative behavior of observables. Our work establishes the state-of-the art in exploring entanglement features in HHG, and paves way for analysis and engineering of entangled multi-photon states in the XUV and ultrafast regime for more complex matter systems.

The accurate and efficient detection of quantum entanglement remains a central challenge in quantum information science. In this work, we study the detection of entanglement of polarized photons for measurement devices that are specified by rotational covariance. We derive explicit positive operator-valued measures (POVMs) showing that any such (idealized) setting is classified by one real measurable parameter r. In particular, we give a POVM formulation of the Klein-Nishina formula for Compton scattering of polarized photons. We provide an SDP-based entanglement certification method with computable bounds that operates on the full measured statistics, also considering semi-device independent scenarios. Furthermore, we show that, while Bell violations are impossible with two rotationally covariant measurements, EPR steering can still be certified under one-sided symmetry constraints. Finally, we demonstrate how our approach can be applied by analyzing a rotationally covariant showcase experiment using scattered polarized light in a selection of soft drinks. Our results motivate further investigation of entanglement detection with lemonade- based detectors.

Amid the International Year of Quantum Science and Technology 2025 (IYQ 2025), a significant portion of global funding has been dedicated to various quantum initiatives, with over 30 countries announcing their respective quantum strategies. Within the Southeast Asia context, Singapore, Thailand, and the Philippines have launched their respective quantum strategies and roadmaps. Meanwhile, six out of eleven Southeast Asia countries have expressed interest in formulating a regional quantum ecosystem to pursue a set of common goals. Quantum technologies, though still in their infancy within the second quantum revolution, have advanced rapidly in recent years. Due to their dual-use nature, quantum technologies are considered emerging and disruptive, often raising concerns from the cybersecurity perspective. While several discussions regarding Malaysia's quantum initiative and strategy are ongoing, it is vital to broaden the conversation and position Malaysia within the regional ecosystem. This paper provides an overview of Malaysia's quantum landscape and a summary of the regional initiatives since the establishment of Southeast Asia Quantum Network. We then analyse Malaysia's strengths in quantum research and provide four recommendations to strengthen the regional ecosystem.

Boron vacancies ($V_B^-$) in hexagonal boron nitride (hBN) have emerged as a promising platform for two-dimensional quantum sensors capable of operating at atomic-scale proximity. However, the mechanisms responsible for photoluminescence quenching in thin hBN sensing layers when placed in contact with absorptive materials remain largely unexplored. In this Letter, we investigate non-radiative Förster resonance energy transfer (FRET) between $V_B^-$ centers and either monolayer graphene or 2D semiconductors. Strikingly, we find that the FRET rate is negligible for hBN sensing layers thicker than 3 nm, highlighting the potential of $V_B^-$ centers for integration into ultra-thin quantum sensors within van der Waals heterostructures. Furthermore, we experimentally extract the intrinsic radiative decay rate of $V_B^-$ defects.

We develop an image theory for the recently proposed single-bounce quantum gravimeter. Free fall and quantum bounce of a matter wave-packet are described through decompositions over a basis of continuous energies. This leads to a much clearer interpretation of the origin of quantum interferences, associated to semi-classical estimations. We then give new tools to explore the space of parameters, and discuss the expected accuracy of the free-fall acceleration measurement.

For a subclass of a general $\mathcal{PT}-$symmetric Hamiltonian obeying anti-commutation relation with its conjugate, a Hermitian basis is found that spans the bi-orthonormal energy eigenvectors. Using the modified projectors constructed from these eigenvectors, the generalized density matrix of the $\mathcal{PT}-$symmetric evolution is calculated, and subsequently, ergotropy for a closed system is obtained. The $\mathcal{PT}-$symmetric system, in an open system scenario, is studied to understand ergotropy under different regimes of non-Hermiticity of the Hamiltonian. The consistency of the three laws of thermodynamics for the $\mathcal{PT}-$symmetric system in an open system scenario is also analyzed.

The theoretical description of broadband, multimode quantum pulses undergoing a second-order $\chi^{(2)}$-nonlinear interaction can be quite intricate, due to the large dimensionality of the underlying phase space. However, in many cases only a few broadband (temporal) modes are relevant before and after the nonlinear interaction. Here we present an efficient framework to calculate the relation between the quantum states at the input and output of a nonlinear element in their respective relevant modes. Since the number of relevant input and output modes may differ, resulting in an open quantum system, we introduce the generalized Bloch-Messiah decomposition (GBMD), reducing the description to an equal number of input and output modes. The GBMD enables us to calculate the multimode Wigner function of the output state by convolving the rescaled Wigner function of the reduced input quantum pulse with a multivariate Gaussian phase-space function. We expand on this result by considering two examples input states: A Fock state in a single broadband mode and a two-mode squeezed vacuum, both in the THz-frequency regime, up-converted to a single output broadband mode of optical frequencies. We investigate the effect, the convolution and thermalization due to entanglement breakage have on the output Wigner function by calculating the von Neumann entropy of the output Wigner function. The methods presented here can be used to optimize the amplification or frequency conversion of broadband quantum states, opening an avenue to the generation and characterization of optical quantum states on ultrafast time scales.

We propose a formulation of quantum measurement within a modified framework of frames, in which a quantum system - a single qubit - is directly coupled to a classical measurement bit. The qubit is represented as a positive probability distribution over two classical bits, a and a', denoted by p(aa'). The measurement apparatus is described by a classical bit $\alpha = \pm 1$, initialized in the pure distribution $p(\alpha) = \frac{1}{2}(1 + \alpha)$. The measurement interaction is modeled by a quasi-bistochastic process $ S(bb'\beta \mid aa'\alpha)$ - a bistochastic map that may include negative transition probabilities, while acting on an entirely positive state space. When this process acts on the joint initial state $p(aa')p(\alpha)$, it produces a collapsed state $p(bb'\mid\beta)$, yielding the measurement outcome $\beta$ with the correct quantum-mechanical probability $p(\beta)$. This approach bypasses the von Neumann chain of infinite couplings by treating the measurement register classically, while capturing the nonclassical nature of measurement through the quasi-bistochastic structure of the interaction.

Uncertainty is fundamental in modern power systems, where renewable generation and fluctuating demand make stochastic optimization indispensable. The chance constrained unit commitment problem (UCP) captures this uncertainty but rapidly becomes computationally challenging as the number of scenarios grows. Quantum computing has been proposed as a potential route to overcome such scaling barriers. In this work, we evaluate the applicability of quantum annealing platforms to the chance constrained UCP. Focusing on a scenario approximation, we reformulated the problem as a mixed integer linear program and solved it using DWave hybrid quantum classical solver alongside Gurobi. The hybrid solver proved competitive under strict runtime limits for large scenario sets (15,000 in our experiments), while Gurobi remained superior on smaller cases. QUBO reformulations were also tested, but current annealers cannot accommodate stochastic UCPs due to hardware limits, and deterministic cases suffered from embedding overhead. Our study delineates where chance constrained UCPs can already be addressed with hybrid quantum classical methods, and where current quantum annealers remain fundamentally limited.

Quantum information protocols offer significant advantages in properties such as security, anonymity, and privacy for communication and computing tasks. An application where guaranteeing the highest possible security and privacy is critical for democratic societies is electronic voting. As computational power continues to evolve, classical voting schemes may become increasingly vulnerable to information leakage. In this work, we present the experimental demonstration of an information-theoretically secure and efficient electronic voting protocol that, crucially, does not rely on election authorities, leveraging the unique properties of quantum states. Our experiment is based on a high-performance source of Greenberger-Horne-Zeilinger (GHZ) states and realizes a proof-of-principle implementation of the protocol in two scenarios: a configuration with four voters and two candidates employing privacy enhancement techniques and an election scenario supporting up to eight voters and sixteen candidates. The latter is particularly well-suited for secure board-level elections within organizations or small-scale governmental contexts.

The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but its simulation remains challenging because long-range interactions give rise to a large number of interaction terms. Here we present Q2FMM, an efficient quantum algorithm for simulating this model within the Trotter product formula. Inspired by the fast multipole method, Q2FMM replaces site-site interactions with interactions between hierarchical coarse-grained boxes across multiple length scales. In addition, the multipole expansions of boxes are reused for their parent boxes, further enhancing the efficiency. To enable this hierarchical reuse coherently, we design a reversible quantum circuit that removes garbage information through uncomputing. The resulting circuit depth for a single Trotter step scales polylogarithmically with system size.

We study how electrons move across a graphene sheet when it encounters two magnetic barriers with a region in between that is continuously driven by laser light. Rather than acting as a static obstacle, this illuminated middle section becomes a Floquet cavity that opens new transport channels through controlled photon absorption and emission. By combining Floquet theory with the transfer matrix method, we track electron transmission through both the main energy band and the emerging photon-assisted sidebands. We find that the laser does more than modify the potential–it reshapes how electrons interact between the magnetic barriers, enabling a switch from ordinary transmission to transport dominated by photon exchange. Because the magnetic field and the optical drive are applied to separate sections of the device, the system supports interference between cyclotron-filtered motion and discrete photon-pumping channels, producing Fano resonances and angle-dependent transmission zeros that cannot appear in double magnetic or double laser barrier systems alone. Under well-defined conditions, the distance between the magnetic barriers controls the coupling between Floquet channels, allowing highly tunable resonances and even perfect transmission, despite strong magnetic confinement. We also observe that low-energy carriers are efficiently blocked by the magnetic regions, while conductance steadily rises with energy until it reaches a clear saturation plateau. This hybrid design provides a versatile way to steer graphene electrons by balancing optical pumping and magnetic momentum filtering.

Extensive theoretical and experimental work has established high-fidelity electron shuttling in Si/SiGe systems, whereas demonstrations in Si/SiO2, also known as silicon metal-oxide-semiconductor (SiMOS), devices remain at an early stage. To help address this, we perform full 3D simulations of conveyor-belt charge shuttling in a realistic SiMOS device, building on earlier 2D modelling. We solve the Poisson and time-dependent Schrodinger equations for varying shuttling speeds and gate voltages, focusing on potential pitfalls of typical SiMOS devices such as oxide-interface roughness, gate fabrication imperfections, and charge defects along the transport path. The simulations reveal that for low clavier-gate voltages, the additional oxide screening in multi-layer gate architectures causes conveyor-belt shuttling to collapse to the bucket-brigade mode, inducing considerable orbital excitation in the process. Increasing the confinement restores conveyor-belt operation, which we find to be robust against interface roughness, gate misalignment, and charge defects buried in the oxide. However, our results indicate that defects located at the Si/SiO2-interface can induce considerable orbital excitation. For lower conveyor gate biases, positive defects in the transport channel can even capture passing electrons. Hence we identify key challenges and find operating regimes for reliable charge transport in SiMOS architectures.

We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random matrix Hamiltonian, which can be written as a sum of two non-commutating operators, one can obtain an expression for the density of states of the Hamiltonian from the known density of states of the two component operators by assuming that these operators are mutually free and by using the free additive convolution. In many examples of interacting quantum systems and random matrix models, this procedure is known to provide a reasonably accurate approximation to the exact numerical density of states. We review some of the examples that are known in the literature where this procedure works very well, and also discuss some of the limitations of this method in situations where the free probability approximation fails to provide a sufficiently accurate description of the exact density of states. Subsequently, we describe a perturbation scheme that can be developed from the subordination formulas for the Cauchy transform of the density of states and use it to obtain approximate analytical expressions for the density of states in various models, such as the Rosenzweig-Porter random matrix ensemble and the Anderson model with on-site disorder.

Conventional classical solvers are commonly used for solving matrix equation systems resulting from the discretization of SIEs in computational electromagnetics (CEM). However, the memory requirement would become a bottleneck for classical computing as the electromagentic problems become much larger. As an alternative, quantum computing has a natural "parallelization" advantage with much lower storage complexity due to the superposition and entanglement in quantum mechanics. Even though several quantum algorithms have been applied for the SIEs-based methods in the literature, the size of the matrix equation systems solvable using them is still limited. In this work, we use a hybrid quantum-classical scheme to solve the EFIE for analyzing electromagentic scattering from three-dimensional (3D) perfect electrically conducting objects with arbitrary shapes in CEM for the first time. Instead of directly solving the original EFIE matrix equation system using the quantum algorithms, the hybrid scheme first designs the preconditioned linear system and then uses a double-layer iterative strategy for its solution, where the external iteration layer builds subspace matrix equation systems with smaller dimension and the internal iteration layer solves the smaller systems using the quantum algorithms. Two representative quantum algorithms, HHL and VQLS, are considered in this work, which are executed on the quantum simulator and quantum computer platforms. We present the theoretical time complexity analysis of the hybrid quantum-classical scheme and perform numerical experiments to investigate the accuracy and efficiency of the hybrid scheme. The results show that the computational complexity of the hybrid VQLS-classical scheme is lower than the conventional fast solvers in classical computing, which indicates the hybrid scheme is more promising for analyzing large-scale electromagnetic problems.

In the paper, we consider the problem of searching for the Largest empty rectangle in a 2D map, and the one-dimensional version of the problem is the problem of searching for the largest empty segment. We present a quantum algorithm for the Largest Empty Square problem and the Largest Empty Rectangle of a fixed width $d$ for $n\times n$-rectangular map. Query complexity of the algorithm is $\tilde{O}(n^{1.5})$ for the square case, and $\tilde{O}(n\sqrt{d})$ for the rectangle with a fixed width $d$ case, respectively. At the same time, the lower bounds for the classical case are $\Omega(n^2)$, and $\Omega(nd)$, respectively. The Quantum algorithm for the one-dimensional version of the problem has $O(\sqrt{n}\log n\log\log n)$ query complexity. The quantum lower bound for the problem is $\Omega(\sqrt{n})$ which is almost equal to the upper bound up to a log factor. The classical lower bound is $\Omega(n)$. So, we obtain the quadratic speed-up for the problem.