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We show that n-bit integers can be factorized by independently running a quantum circuit with \(\tilde{O}(n^{3/2})\) gates for \(\sqrt {n}+4\) times, and then using polynomial-time classical post-processing. The correctness of the algorithm relies on a certain number-theoretic conjecture. It is currently not clear if the algorithm can lead to improved physical implementations in practice. [ABSTRACT FROM AUTHOR]

The celebrated minimax principle of Yao says that for any Boolean-valued function f with finite domain, there is a distribution µ over the domain of f such that computing f to error against inputs from µ is just as hard as computing f to error on worst-case inputs. Notably, however, the distribution µ depends on the target error level1: the hard distribution which is tight for bounded error might be trivial to solve to small bias, and the hard distribution which is tight for a small bias level might be far from tight for bounded error levels. In this work, we introduce a new type of minimax theorem which can provide a hard distribution µ that works for all bias levels at once. We show that this works for randomized query complexity, randomized communication complexity, some randomized circuit models, quantum query and communication complexities, approximate polynomial degree, and approximate logrank. We also prove an improved version of Impagliazzo's hardcore lemma. Our proofs rely on two innovations over the classical approach of using Von Neumann's minimax theorem or linear programming duality. First, we use Sion's minimax theorem to prove a minimax theorem for ratios of bilinear functions representing the cost and score of algorithms. Second, we introduce a new way to analyze low-bias randomized algorithms by viewing them as "forecasting algorithms" evaluated by a certain proper scoring rule. The expected score of the forecasting version of a randomized algorithm appears to be a more fine-grained way of analyzing the bias of the algorithm. We show that such expected scores have many elegant mathematical properties--for example, they can be amplified linearly instead of quadratically. We anticipate forecasting algorithms will find use in future work in which a fine-grained analysis of small-bias algorithms is required. [ABSTRACT FROM AUTHOR]

We use digital quantum computing to simulate the creation of particles in a dynamic spacetime. We consider a system consisting of a minimally coupled massive quantum scalar field in a spacetime undergoing homogeneous and isotropic expansion, transitioning from one stationary state to another through a brief inflationary period. We simulate two vibration modes, positive and negative for a given field momentum, by devising a quantum circuit that implements the time evolution. With this circuit, we study the number of particles created after the universe expands at a given rate, both by simulating the circuit and by actual experimental implementation on IBM quantum computers, consisting of hundreds of quantum gates. We find that state-of-the-art error mitigation techniques are useful to improve the estimation of the number of particles and the fidelity of the state. [ABSTRACT FROM AUTHOR]

Hybrid systems consisting of highly transparent channels of low-dimensional semiconductors between superconducting elements allow the formation of quantum electronic circuits. Therefore, they are among the novel material platforms that could pave the way for scalable quantum computation. To this aim, InAs two-dimensional electron gases are among the ideal semiconductor systems due to their vanishing Schottky barrier; however, their exploitation is limited by the unavailability of commercial lattice-matched substrates. We show that in situ growth of superconducting aluminum on two-dimensional electron gases forming in metamorphic near-surface InAs quantum wells can be performed by molecular beam epitaxy on GaAs substrates with state-of-the-art quality. Adaptation of the metamorphic growth protocol has allowed us to reach low-temperature electron mobilities up to 1.3 × 105 cm2/Vs in Si-doped InAs/In0.81Ga0.19As two-dimensional electron gases placed 10 nm from the surface with charge density up to 1 × 1012/cm2. Shubnikov-de Haas oscillations on Hall bar structures show well-developed quantum Hall plateaus, including the Zeeman split features. X-ray diffraction and cross-sectional transmission electron microscopy experiments demonstrate the coexistence of (011) and (111) crystal domains in the Al layers. The resistivity of 10-nm-thick Al films as a function of temperature was comparable to the best Al layers on GaAs, and a superconducting proximity effect was observed in a Josephson junction. [ABSTRACT FROM AUTHOR]

Currently, most quantum homomorphic encryption (QHE) schemes only allow a single evaluator (server) to accomplish computation tasks on encrypted data shared by the data owner (user). In addition, the quantum computing capability of the evaluator and the scope of quantum computation it can perform are usually somewhat limited, which significantly reduces the flexibility of the scheme in quantum network environments. In this paper, we propose a novel (t , n) -threshold QHE (TQHE) network scheme based on the Shamir secret sharing protocol, which allows k (t ≤ k ≤ n) evaluators to collaboratively perform evaluation computation operations on each qubit within the shared encrypted sequence. Moreover, each evaluator, while possessing the ability to perform all single-qubit unitary operations, is able to perform arbitrary single-qubit gate computation task assigned by the data owner. We give a specific (3, 5)-threshold example, illustrating the scheme's correctness and feasibility, and simulate it on IBM quantum computing cloud platform. Finally, it is shown that the scheme is secure by analyzing encryption/decryption private keys, ciphertext quantum state sequences during transmission, plaintext quantum state sequence, and the result after computations on the plaintext quantum state sequence. [ABSTRACT FROM AUTHOR]

Connectivity between qubits plays an irreplaceable role in quantum computation. An urgent task of quantum computation based on atomic arrays is to generate effective coupling between two distant qubits, thereby enhancing connectivity. In this paper, we investigate the realization of two-qubit gates utilizing buffer-atomic configuration, where the non-coding atoms serve as quantum buses to connect the computational qubits. Geometric control is achieved through globally-shined laser pulses in the Rydberg blockade region. It is found that acceleration based on shortcut to adiabaticity can be realized by reshaping the original control waveforms. The proposed distant two-qubit gate demonstrates robustness against systematic errors and random noise. Further numerical simulations indicate that high-fidelity control is maintained even when considering next-nearest-neighbor coupling among the atoms. Thus, our proposal provides a fast and experimentally feasible method for realizing distant two-qubit gates in atomic arrays, which may contribute to improving the scalability of quantum computations. [ABSTRACT FROM AUTHOR]

The concept of quantum acceleration limit has been recently introduced for any unitary time evolution of quantum systems under arbitrary nonstationary Hamiltonians. While Alsing and Cafaro used the Robertson uncertainty relation in their derivation, employed the Robertson–Schrödinger uncertainty relation to find the upper bound on the temporal rate of change of the speed of quantum evolutions. In this paper, we provide a comparative analysis of these two alternative derivations for quantum systems specified by an arbitrary finite-dimensional projective Hilbert space. Furthermore, focusing on a geometric description of the quantum evolution of two-level quantum systems on a Bloch sphere under general time-dependent Hamiltonians, we find the most general conditions needed to attain the maximal upper bounds on the acceleration of the quantum evolution. In particular, these conditions are expressed explicitly in terms of two three-dimensional real vectors, the Bloch vector that corresponds to the evolving quantum state and the magnetic field vector that specifies the Hermitian Hamiltonian of the system. For pedagogical reasons, we illustrate our general findings for two-level quantum systems in explicit physical examples characterized by specific time-varying magnetic field configurations. Finally, we briefly comment on the extension of our considerations to higher-dimensional physical systems in both pure and mixed quantum states. [ABSTRACT FROM AUTHOR]

Quantum computers hold the potential to unlock new discoveries in complex quantum systems by enabling the simulation of physical systems that have heretofore been impossible to implement on classical computers due to intractability. A system of particular interest is that of dirty bosons, whose physics highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bosons in one and two dimensions. Specifically, we explore the disorder-induced delocalized-to-localized transition using adiabatic state preparation. In one dimension, the quantum circuits can be compressed to small enough depths for execution on currently available quantum computers. In two dimensions, the compression scheme is no longer applicable, thereby requiring the use of large-scale classical state vector simulations to emulate quantum computer performance. In addition, simulating interacting bosons via emulation of a noisy quantum computer allowed us to study the effect of quantum hardware noise on the physical properties of the simulated system. Our results suggest that scaling laws control how noise modifies observables versus its strength, the circuit depth, and the number of qubits. Moreover, we observe that noise impacts the delocalized and localized phases differently. A better understanding of how noise alters the observed properties of the simulated system is essential for leveraging near-term quantum devices for simulation of dirty bosons, and indeed for condensed matter systems in general.

Abstract We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we present encoding schemes for numerous nondeterministic polynomial-time complete (NP-complete) problems, encompassing the majority of Karp’s 21 NP-complete problems. We find a number of such computation problems can be encoded by the atom-cavity system at a linear cost of atom number. There are still certain problems that cannot be encoded by the atom-cavity as efficiently, such as quadratic unconstrained binary optimization (QUBO), and the Hamiltonian cycle. For these problems, we provide encoding schemes with a quadratic or quartic cost in the atom number. We expect this work to provide important guidance to search for the practical quantum advantage of the atom-cavity system in solving NP-complete problems. Moreover, the encoding schemes we develop here may also be adopted in other optical systems for solving NP-complete problems, where a similar form of Mattis-type spin glass Hamiltonian as in the atom-cavity system can be implemented.

We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we present encoding schemes for numerous nondeterministic polynomial-time complete (NP-complete) problems, encompassing the majority of Karp's 21 NP-complete problems. We find a number of such computation problems can be encoded by the atom-cavity system at a linear cost of atom number. There are still certain problems that cannot be encoded by the atom-cavity as efficiently, such as quadratic unconstrained binary optimization (QUBO), and the Hamiltonian cycle. For these problems, we provide encoding schemes with a quadratic or quartic cost in the atom number. We expect this work to provide important guidance to search for the practical quantum advantage of the atom-cavity system in solving NP-complete problems. Moreover, the encoding schemes we develop here may also be adopted in other optical systems for solving NP-complete problems, where a similar form of Mattis-type spin glass Hamiltonian as in the atom-cavity system can be implemented. [ABSTRACT FROM AUTHOR]

We explore the use of fractional controlled-not gates in quantum thermodynamics. The Nth-root gate allows for a paced application of two-qubit operations. We apply it in quantum thermodynamic protocols for charging a quantum battery. Circuits for three (and two) qubits are analysed by considering the generated ergotropy and other measures of performance. We also perform an optimisation of initial system parameters, e.g.,the initial quantum coherence of one of the qubits strongly affects the efficiency of protocols and the system's performance as a battery. Finally, we briefly discuss the feasibility for an experimental realization. [ABSTRACT FROM AUTHOR]

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed. [ABSTRACT FROM AUTHOR]

Private set intersection (PSI) has important application value, however, current quantum PSI protocols are either unsuitable for multi-party scenarios or inefficient. Recently, Imran (arXiv:2303.17196v3, 2023) proposed two quantum secure multi-party greatest common divisor (GCD) protocols that can be used for PSI, but with the downside of information leakage and resource consumption. In this paper, we propose a novel quantum secure multi-party GCD protocol that has higher security and lower complexity. To hide privacy, each party randomly selects a coefficient within a range determined by his input integer, and with the assistance of a semi-honest third party TP, all parties secretly calculate the linear combination of their inputs under these coefficients. Once enough linear combinations are collected, TP calculates the GCD of these combinations, which is equal to the GCD of all input integers. To verify the honesty of participants, a quantum zero-knowledge proof sub-protocol is designed. Analysis shows that our GCD protocol is correct and has security against malicious attacks. Moreover, its complexity is polynomial level and lower than Imran's. Furthermore, we demonstrate the scalability of our GCD protocol in private set operations, such as private set intersection, private set intersection cardinality, private multi-set intersection, etc. [ABSTRACT FROM AUTHOR]

A strategy is developed for writing the time-dependent Schrödinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is calculated for a number of standard perturbation theory examples at first- and second-order. Possible applications include characterization of photonic spectra for bosonic sampling and four-wave mixing in quantum computation and Bardeen tunneling amplitude in quantum mechanics. [ABSTRACT FROM AUTHOR]

Quantum machine learning has made remarkable progress in many important tasks. However, the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms, making them non-end-to-end. Herein, we propose a quantum algorithm for the node embedding problem that maps a node graph’s topological structure to embedding vectors. The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms. With O(log(N)) qubits to store the information of N nodes, our algorithm will not lose quantum advantage for the subsequent quantum information processing. Moreover, owing to the use of a parameterized quantum circuit with O(poly(log(N))) depth, the resulting state can serve as an efficient quantum database. In addition, we explored the measurement complexity of the quantum node embedding algorithm, which is the main issue in training parameters, and extended the algorithm to capture high-order neighborhood information between nodes. Finally, we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.

Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are associated to the boundary conditions imposed on the quantum spin chains via the so-called topological frustration. In this work, we analyze the effects of such frustration on a few-spin system, with a particular focus on the strong even–odd effects induced in the ground-state energy. We then implement a topologically frustrated quantum spin chain on a quantum computer to show that our predictions are visible on current quantum hardware platforms. [ABSTRACT FROM AUTHOR]

In this paper, we further verify the validity of the quantum partial adiabatic search algorithm which was initialized in the previous related works by revisiting its quantum circuit model. The main results got here are as follows. When considering implementing quantum partial adiabatic evolution on a quantum circuit, a correction is given for the time slice estimation for the first stage during this approximation in the previous related works, new evidence is provided for a time complexity cost O (N / M) of quantum partial adiabatic algorithm is impossible, and the correct time complexity O (N / M) of it is emphasized once more according to its circuit correspondence, in which N is the total number of elements in the search problem of which M of them are the marked ones. The findings exposed are hopeful for revisiting quantum partial adiabatic evolution and its connection with the quantum circuit model. [ABSTRACT FROM AUTHOR]

Lattice-based cryptosystems are one of the main post-quantum alternatives to asymmetric cryptography currently in use. Most attacks on these cryptosystems can be reduced to the shortest vector problem (SVP) in a lattice. Previously, the authors proposed a quantum oracle model from Grover's algorithm to implement a hybrid quantum-classical algorithm based on the GaussSieve algorithm and solving SVP. In this paper, a new model of a quantum oracle is proposed and analyzed. Two implementations of the new quantum oracle model are proposed and estimated. The complexity of implementing the new quantum oracle model to attack post-quantum lattice-based cryptosystems that are finalists of the NIST post-quantum cryptography competition is analyzed. Comparison of obtained results for new and existing models of quantum oracle is given. [ABSTRACT FROM AUTHOR]

The hidden subgroup problem (HSP) is a cornerstone problem in quantum computing, which captures many problems of interest and provides a standard framework algorithm for their study based on Fourier sampling, one class of techniques known to provide quantum advantage, and which succeeds for some groups but not others. The quantum hardness of the HSP problem for the dihedral group is a critical question for post-quantum cryptosystems based on learning with errors and also appears in subexponential algorithms for constructing isogenies between elliptic curves over a finite field. In this article, we give an updated overview of the dihedral hidden subgroup problem as approached by the “standard” quantum algorithm for HSP on finite groups, detailing the obstructions for strong Fourier sampling to succeed and summarizing other known approaches and results. In our treatment, we “contrast and compare” as much as possible the cyclic and dihedral cases, with a view to determining bounds for the success probability of a quantum algorithm that uses mm coset samples to solve the HSP on these groups. In the last sections, we prove a number of no-go results for the dihedral coset problem (DCP), motivated by a connection between DCP and cloning of quantum states. The proofs of these no-go results are then adapted to give nontrivial upper bounds on the success probability of a quantum algorithm that uses mm coset samples to solve DCP.

In the realm of control engineering applications, compensating for unknown dynamics and nonlinearities is of paramount importance for shaping closed-loop performance. This paper introduces a novel solution to this challenge: the adaptive controller based on Quantum-Inspired Fuzzy Rules Emulated Network (QFREN). Leveraging its intrinsic learning capacity, QFREN assimilates human knowledge through a series of IF-THEN rules based on quantum computation principles. By defining quantum states for membership functions, the concept of coherent superposition of tracking errors is employed to effectively mitigate the effects of disturbances and nonlinearities. Learning laws are derived to finely calibrate all network and quantum computation parameters, accompanied by a thorough analysis of closed-loop performance to ensure robustness. Experimental validation and comparative assessments substantiate the efficacy of the proposed scheme, showcasing a reduction in tracking error of at least 20 % compared to recent comparative controllers based on data-driven and quantum-neural network schemes. [ABSTRACT FROM AUTHOR]

When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, we present an insightful discussion on the differences between the Bures and the Sjöqvist metrics inside a Bloch sphere. First, we begin with a formal comparative analysis between the two metrics by critically discussing three alternative interpretations for each metric. Second, we explicitly illustrate the distinct behaviors of the geodesic paths on each one of the two metric manifolds. Third, we compare the finite distances between an initial state and the final mixed state when calculated with the two metrics. Interestingly, in analogy with what happens when studying the topological aspects of real Euclidean spaces equipped with distinct metric functions (for instance, the usual Euclidean metric and the taxicab metric), we observe that the relative ranking based on the concept of a finite distance between mixed quantum states is not preserved when comparing distances determined with the Bures and the Sjöqvist metrics. Finally, we conclude with a brief discussion on the consequences of this violation of a metric-based relative ranking on the concept of the complexity and volume of mixed quantum states. [ABSTRACT FROM AUTHOR]

When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, we present an insightful discussion on the differences between the Bures and the Sjöqvist metrics inside a Bloch sphere. First, we begin with a formal comparative analysis between the two metrics by critically discussing three alternative interpretations for each metric. Second, we explicitly illustrate the distinct behaviors of the geodesic paths on each one of the two metric manifolds. Third, we compare the finite distances between an initial state and the final mixed state when calculated with the two metrics. Interestingly, in analogy with what happens when studying the topological aspects of real Euclidean spaces equipped with distinct metric functions (for instance, the usual Euclidean metric and the taxicab metric), we observe that the relative ranking based on the concept of a finite distance between mixed quantum states is not preserved when comparing distances determined with the Bures and the Sjöqvist metrics. Finally, we conclude with a brief discussion on the consequences of this violation of a metric-based relative ranking on the concept of the complexity and volume of mixed quantum states.

Innovative solutions and developments are being inspected to tackle rising electrical power demand to be supplied by clean forms of energy. The integration of renewable energy generations, varying nature loads, importance of active role of distribution system and consumer participation in grid operation has changed the landscape of classical power grids. Implementation of smarter applications to plan, monitor, operate the grid safely are deemed paramount for efficient, secure and reliable functioning of grid. These smarter applications for modern power systems demand capabilities such as real-time monitoring, dynamic security analysis, stochastic power flow calculations, large-scale data analytics, and high-dimensional combinatorial and constrained optimization. Although sophisticated computations to process gigantic volume of data to produce useful information in a time critical manner is the paradigm of future grid operations, these enhanced functionalities impose significantly higher computational demands compared to traditional approaches used in conventional power systems. Advancements in quantum technologies holds promising solution for dealing with demanding computational complexity of power system related applications. In this article, we lay out clear motivations for seeking quantum solutions for solving computational burden challenges associated with power system applications. Next, we present the fundamental principles of quantum computing, introduce key quantum algorithms, and offer a comparison of the computational load between classical and quantum approaches for few important mathematical problems, indicating their relevance to various power system applications. Additionally, we provide an overview of quantum solutions for various power system related applications available in current literature and suggest future topics for research. We further highlight challenges with existing quantum solutions for exploiting full quantum capabilities. To this end, this article serves as a bridge for power engineers to the quantum domain by outlining fundamental principles of quantum computation, facilitating a smoother transition to the future of power system computations and also provides quantum experts with insights into new application areas for quantum computing within power systems.

Since people became aware of the power of quantum phenomena in the domain of traditional computation, a great number of complex problems that were once considered intractable in the classical world have been tackled. The downsides of quantum supremacy are its high cost and unpredictability. Numerous researchers are relying on quantum simulators running on classical computers. The critical obstacle facing classical computers in the task of quantum simulation is its limited memory space. Quantum simulation intrinsically models the state evolution of quantum subsystems. Qubits are mathematically constructed in the Hilbert space whose size grows exponentially. Consequently, the scalability of the straightforward statevector approach is limited. It has been proven effective in adopting decision diagrams (DDs) to mitigate the memory cost issue in various fields. In recent years, researchers have adapted DDs into different forms for representing quantum states and performing quantum calculations efficiently. This leads to the study of DD-based quantum simulation. However, their advantage of memory efficiency does not let it replace the mainstream statevector and tensor network-based approaches. We argue the reason is the lack of effective parallelization strategies in performing calculations on DDs. In this article, we explore several strategies for parallelizing DD operations with a focus on leveraging them for quantum simulations. The target is to find the optimal parallelization strategies and improve the performance of DD-based quantum simulation. Based on the experiment results, our proposed strategy achieves a 2–3 times faster simulation of Grover's algorithm and random circuits than the state-of-the-art single-thread DD-based simulator DDSIM.

Objective: This study focused on the antioxidant synergistic mechanism between resveratrol and sesamol. Methods: The levels of free radicals and peroxide free radicals in sunflower seed oil were assessed using the 2,2-diphenyl-1-picrylhydrazyl (DPPH) and hydrogen peroxide assays, respectively. The proportion of resveratrol and sesamol were optimized by integrating the measurements with the determination of the induction period. Additionally, quantum chemical simulations were employed to elucidate the underlying reaction processes. Results: Upon heating sunflower seed oil supplemented with resveratrol and sesamol at 180 ℃ for 2 hours, the total content of free radicals was determined as （0.08±0.03） mol/L and （0.20±0.03） mol/L, respectively, in comparison to （0.44±0.01） mol/L in the control sample. Resveratrol exhibited the highest inhibitory efficiency, while sesamol has the strongest scavenging ability of peroxide radicals. The optimal concentrations for their synergistic effect in purified sunflower seed oil were determined as 1 400, 200 mg/kg, and resveratrol had protective effect on sesamol at the degradation rate of 180 ℃. Conclusion: By utilizing quantum chemical methods, it was found that a dynamic equilibrium process exists between the two compounds. As the amount of resveratrol added is seven times that of sesamol, and the reaction is more inclined to supply hydrogen to sesamol radicals by resveratrol.

Quantum mechanics (QM) can be understood as a set of rules that forms the basis for developing all quantum theories. One of these theories is quantum computation (QC), i.e., computation based on QM logic. It is believed that QC provides paths to the problem solution that may not be possible for classical computers. Therefore, it has received attention to solve complex computational problems in different areas. Most of the research efforts, however, have concentrated on problems in theoretical physics and computer science, leaving little attention to solve practical problems in industrial applications. This is particularly true in power system applications where QC is mostly unknown. This paper mainly aims to attract the attention of power system researchers/engineers to QC as a potential solution to address emerging computational challenges of power systems. To this end, the historical development of QC and its fundamental concepts are first described. Then, recent contributions to solving computationally-demanding power system problems such as AC and DC power flow (PF), contingency analysis, state estimation, electromagnetic transients simulation (EMT), fault diagnosis, unit commitment (UC), and facility location–allocation (FLA) problems are discussed. Unfortunately, power system researchers have not yet been able to convincingly demonstrate a quantum advantage in solving large-scale power system problems mainly because we are in the noisy intermediate-scale quantum (NISQ) era, where quantum devices are noisy and have limited quantum resources. However, it may be demonstrated in the future with technological advances and increased research efforts in the area.

Interests surrounding the development of on-chip nonlinear optical devices have been consistently growing in the past decades due to the tremendous applications, such as quantum photonics, all-optical communications, optical computing, on-chip metrology, and sensing. Developing efficient on-chip nonlinear optical devices to meet the requirements of those applications brings the need for new directions to improve the existing photonic approaches. Recent research has directed the field of on-chip nonlinear optics toward the hybrid integration of two-dimensional layered materials (such as graphene, transition metal dichalcogenides, and black phosphorous) with various integrated platforms. The combination of well-known photonic chip design platforms (e.g., silicon, silicon nitride) and different two-dimensional layered materials has opened the road for more versatile and efficient structures and devices, which has the great potential to unlock numerous new possibilities. This review discusses the modeling and characterization of different hybrid photonic integration structures with two-dimensional materials, highlights the current state of the art examples, and presents an outlook for future prospects.

The pulmonary surfactant protein A (SP-A) is a constitutively expressed immune-protective collagenous lectin (collectin) in the lung. It binds to the cell membrane of immune cells and opsonizes infectious agents such as bacteria, fungi, and viruses through glycoprotein binding. SARS-CoV-2 enters airway epithelial cells by ligating the Angiotensin Converting Enzyme 2 (ACE2) receptor on the cell surface using its Spike glycoprotein (S protein). We hypothesized that SP-A binds to the SARS-CoV-2 S protein and this binding interferes with ACE2 ligation. To study this hypothesis, we used a hybrid quantum and classical in silico modeling technique that utilized protein graph pruning. This graph pruning technique determines the best binding sites between amino acid chains by utilizing the Quantum Approximate Optimization Algorithm (QAOA)-based MaxCut (QAOA-MaxCut) program on a Near Intermediate Scale Quantum (NISQ) device. In this, the angles between every neighboring three atoms were Fourier-transformed into microwave frequencies and sent to a quantum chip that identified the chemically irrelevant atoms to eliminate based on their chemical topology. We confirmed that the remaining residues contained all the potential binding sites in the molecules by the Universal Protein Resource (UniProt) database. QAOA-MaxCut was compared with GROMACS with T-REMD using AMBER, OPLS, and CHARMM force fields to determine the differences in preparing a protein structure docking, as well as with Goemans-Williamson, the best classical algorithm for MaxCut. The relative binding affinity of potential interactions between the pruned protein chain residues of SP-A and SARS-CoV-2 S proteins was assessed by the ZDOCK program. Our data indicate that SP-A could ligate the S protein with a similar affinity to the ACE2-Spike binding. Interestingly, however, the results suggest that the most tightly-bound SP-A binding site is localized to the S2 chain, in the fusion region of the SARS-CoV-2 S protein, that is responsible for cell entry Based on these findings we speculate that SP-A may not directly compete with ACE2 for the binding site on the S protein, but interferes with viral entry to the cell by hindering necessary conformational changes or the fusion process.

Grinding in a ball mill is a process with high energy consumption; therefore, a slight improvement in its performance can lead to great economic benefit in the industry. The softness of the product of the grinding circuits prevents loss of energy in the subsequent processes. In addition, controlling the performance of a ball mill is a challenging issue due to its complex dynamic characteristics. The main purpose of this article is to use the ground particle size diagram and acoustic signal in ball mill control, and model their relationship based on least squares method. As a result, by extracting useful data from the the acoustic signal, the optimal condition of the ball mill_ in terms of ground particle size and ball mill load (normal, low, high)_ can be achieved. In doing so, this goal, in this article, innovative ideas such as adaptive quantum basis, sparse representation, SVD and PCA-based methods were used. The proposed method has been practically implemented on the ball mill of Lakan lead-zinc processing plant. Also, a prototype of the device was built. The test results show that the optimal load for the studied ball mill is 10t/h. In this case, the ground particle size is 110-120 microns which is ideal for the purposes of this plant. Also, the power spectrum is in the middle frequency band (frequency range of 300-700 Hz). According to the analysis and results, the proposed method will increase the efficiency of the studied ball mill.

The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface electron system, which is a promising two-dimensional platform for quantum computation. The holonomic gate is realized by a three-level structure that combines the Rydberg states and spin states via an inhomogeneous magnetic field. After a cyclic evolution, the computation bases pick up different geometric phases and thus perform a holonomic gate. Only the electron with spin up experiences the holonomic gate, while the electron with spin down is decoupled from the state-selective driving fields. The arbitrary controlled-U gate encoded on the Rydberg states and spin states can then be realized. The fidelity of the output state exceeds 0.99 with experimentally achievable parameters. [ABSTRACT FROM AUTHOR]

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Since the 1980s, researchers have taken giant steps in understanding how to use quantum mechanics for solving real problems—for example, making a computer that works according to the laws of quantum mechanics. In recent decades, researchers have tried to develop a platform for quantum information and computation that can be integrated into digital and telecom technologies without the need of a cryogenic environment. The current status of research in the field of quantum integrated photonics will be reviewed. A review of the most common integrated photonic platforms will be given, together with the main achievements and results in the last decade. [ABSTRACT FROM AUTHOR]

The field of computer vision has long grappled with the challenging task of image synthesis, which entails the creation of novel high-fidelity images. This task is underscored by the Generative Learning Trilemma, which posits that it is not possible for any image synthesis model to simultaneously excel at high-quality sampling, achieve mode convergence with diverse sample representation, and perform rapid sampling. In this paper, we explore the potential of Quantum Boltzmann Machines (QBMs) for image synthesis, leveraging the D-Wave 2000Q quantum annealer. We undertake a comprehensive performance assessment of QBMs in comparison to established generative models in the field: Restricted Boltzmann Machines (RBMs), Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and Denoising Diffusion Probabilistic Models (DDPMs). Our evaluation is grounded in widely recognized scoring metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), and Inception Scores. The results of our study indicate that QBMs do not significantly outperform the conventional models in terms of the three evaluative criteria. Moreover, QBMs have not demonstrated the capability to overcome the challenges outlined in the Trilemma of Generative Learning. Through our investigation, we contribute to the understanding of quantum computing's role in generative learning and identify critical areas for future research to enhance the capabilities of image synthesis models. [ABSTRACT FROM AUTHOR]

Abstract Graph states are one of the most significant classes of entangled states, serving as the quantum resources for quantum technologies. Recently, integrated quantum photonics is becoming a promising platform for quantum information processing, enabling the generation, manipulation, and measurement of photonic quantum states. This article summarizes state-of-the-art experimental progress and advances in the chip-based photonic graph states.

Stochastic Optical Quantum Circuit Simulator (SOQCS) is a C++ and Python library which offers a framework to define, simulate and study quantum linear optical circuits in presence of various imperfections typically encountered in experiments. Quantum circuits can be defined from basic components, including emitters, linear optical elements, delays and detectors. The imperfections come from partial distinguishability of photons, lossy propagation media, unbalanced beamsplitters and non-ideal emitters and detectors for example. SOQCS also provides various simulator cores and tools to analyze the output. Furthermore, the configuration of detectors also includes postselection. SOQCS is developed using a modular approach in which different modules are applied in an automated easy to use manner. Furthermore, the modular approach allows for further extensions of the SOQCS capabilities in future.

The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface electron system, which is a promising two-dimensional platform for quantum computation. The holonomic gate is realized by a three-level structure that combines the Rydberg states and spin states via an inhomogeneous magnetic field. After a cyclic evolution, the computation bases pick up different geometric phases and thus perform a holonomic gate. Only the electron with spin up experiences the holonomic gate, while the electron with spin down is decoupled from the state-selective driving fields. The arbitrary controlled-U gate encoded on the Rydberg states and spin states can then be realized. The fidelity of the output state exceeds 0.99 with experimentally achievable parameters.

We suggest a new technique for developing noisy tree data structures. We call it a "walking tree". As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound. [ABSTRACT FROM AUTHOR]

A large class of optimisation problems can be mapped to the Ising model where all details are encoded in the coupling of spins. The task of the original mathematical optimisation is then equivalent to finding the ground state of the corresponding spin system which can be achieved via quantum annealing relying on the adiabatic theorem. Some of the inherent disadvantages of this procedure can be alleviated or resolved using a stochastic approach, and by coupling to the external environment. We show that careful engineering of the system-bath coupling at an individual spin level can further improve annealing. [ABSTRACT FROM AUTHOR]

Grinding in a ball mill is a process with high energy consumption; therefore, a slight improvement in its performance can lead to significant economic benefits in the industry. The softness of the product of the grinding circuits prevents loss of energy in the subsequent processes. In addition, controlling the mill's performance is challenging due to its complex dynamic characteristics. The primary purpose of this article is to use the ground particle size diagram and acoustic signal in ball mill control, and model their relationship based on the least squares method. As a result, by extracting valuable data from the acoustic signal, the optimal condition of the ball mill_ in terms of ground particle size and ball mill load (standard, low, high)_ can be achieved. In doing so, in this article, innovative ideas such as adaptive quantum basis, sparse representation, SVD, and PCA-based methods were used. The proposed method has been practically implemented on the ball mill of the Lakan lead-zinc processing plant. Also, a prototype of the device was built. The test results show that the optimal load for the studied ball mill is 10t/h. In this case, the ground particle size is 110-120 microns, which is ideal for this plant. Also, the power spectrum is in the middle-frequency band (300-700 Hz). According to the analysis and results, the proposed method will increase the efficiency of the studied ball mill. [ABSTRACT FROM AUTHOR]

Due to the development of quantum computing, there is a need for the development and analysis of cryptosystems resistant to attacks using a quantum computer (post-quantum cryptography algorithms). The security of many well-known post-quantum cryptosystems based on lattice theory depends on the complexity of solving the shortest vector problem (SVP). In this paper, a model of quantum oracle developed from Grover's algorithm is described to implement a hybrid quantum–classical algorithm based on GaussSieve. This algorithm can be used for attacks on cryptosystems whose security depends on solving the SVP. Upper bounds for the number of qubits and the depth of the circuit were obtained for two implementations of the proposed quantum oracle model: minimizing the number of qubits and minimizing the circuit depth. The complexity of implementing the proposed quantum oracle model to attack post-quantum lattice-based cryptosystems that are finalists of the NIST post-quantum cryptography competition is analyzed. [ABSTRACT FROM AUTHOR]

Reversible Boolean function (RBF) is a one-to-one function which maps n-bit input to n-bit output. Reversible logic synthesis has been widely studied due to its connection with low-energy computation as well as quantum computation. In this paper, we give a structured decomposition for even RBFs. Specifically, for n≥q 6, any even n-bit RBF can be decomposed to 7 blocks of (n-1)-bit RBF, where 7 is a constant independent of n and the positions of these blocks have a large degree of freedom. Moreover, if the (n-1)-bit RBFs are required to be even as well, we show for n≥q 10, even n-bit RBF can be decomposed to 10 even (n-1)-bit RBFs. In short, our decomposition has block depth 7 and even block depth 10. Our result improves Selinger's work in block depth model, by reducing the constant from 9 to 7 and from 13 to 10, when the blocks are limited to be even. We emphasize that our setting is a bit different from Selinger's work. In Selinger's constructive proof, each block is placed in one of two specific positions and thus the decomposition has an alternating structure. We relax this restriction and allow each block to act on arbitrary (n-1) bits. This relaxation keeps the block structure and provides more candidates when choosing the positions of blocks.