Adiabatic Quantum Computation Research Articles

Virtual mitigation of coherent non-adiabatic transitions by echo verification

Transitions out of the ground space limit the performance of quantum adiabatic algorithms, while hardware imperfections impose stringent limitations on the circuit depth. We propose an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. Quasi-adiabatically evolving forward and backward allows for an echo-verified measurement of any observable. In addition to mitigating hardware noise, our method uses positive-time dynamics only. Crucially, the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement.

Quantum Parallel Training of a Boltzmann Machine on an Adiabatic Quantum Computer

AbstractDespite the anticipated speed‐up of quantum computing, the achievement of a measurable advantage remains subject to ongoing debate. Adiabatic Quantum Computers (AQCs) are quantum devices designed to solve quadratic uncostrained binary optimization (QUBO) problems, but their intrinsic thermal noise can be leveraged to train computationally demanding machine learning algorithms such as the Boltzmann Machine (BM). Despite an asymptotic advantage is expected only for large networks, a limited quantum speed up can be already achieved on a small BM is shown, by exploiting parallel adiabatic computation. This approach exhibits a 8.6‐fold improvement in wall time on the Bars and Stripes dataset when compared to a parallelized classical Gibbs sampling method, which has never been outperformed before by quantum approaches.

On the circuit model of two quantum adiabatic search algorithms

On the circuit model of two quantum adiabatic search algorithms

Comparing Adiabatic Quantum Computers for satellite images feature extraction

Adiabatic Quantum Computers (AQCs) are special-purpose devices that promise to speed up the resolution of hard combinatorial optimization problems by exploiting quantum mechanical phenomena. Despite representing one of the most mature quantum computational paradigms, AQCs are often benchmarked on spin-glass problems that conveniently mimic their internal structure, and their performances are usually compared to those of suboptimal Simulated Annealing solvers. In this work, we evaluate the capabilities of AQCs to extract features from a dataset of low-resolution satellite images of airplanes, exploiting an approach based on matrix factorization. We assess the performance of three generations of quantum devices provided by the D-Wave company by analyzing their behavior via selected evaluation metrics as a function of the problem size. We also compare against classical results obtained with a commercial solver. Additionally, we outline a parameter-tuning procedure that allows for harnessing the full potential of AQCs. Although the quantum devices still tend to underperform their classical counterparts, we observe the two most recent AQCs exhibiting superior performance for the tested instances with the smallest size. Additionally, our results indicate incremental performance improvements across new AQCs generations. These observations suggest cautious optimism about the potential future applicability of such computational tools.

Entanglement Trajectory and its Boundary

In this article, we present a novel approach to investigating entanglement in the context of quantum computing. Our methodology involves analyzing reduced density matrices at different stages of a quantum algorithm's execution and representing the dominant eigenvalue and von Neumann entropy on a graph, creating an "entanglement trajectory." To establish the trajectory's boundaries, we employ random matrix theory. Through the examination of examples such as quantum adiabatic computation, the Grover algorithm, and the Shor algorithm, we demonstrate that the entanglement trajectory remains within the established boundaries, exhibiting unique characteristics for each example. Moreover, we show that these boundaries and features can be extended to trajectories defined by alternative entropy measures. The entanglement trajectory serves as an invariant property of a quantum system, maintaining consistency across varying situations and definitions of entanglement. Numerical simulations accompanying this research are available via open access.

Scientometric analysis of quantum-inspired metaheuristic algorithms

Quantum algorithms, based on the principles of quantum mechanics, offer significant parallel processing capabilities with a wide range of applications. Nature-inspired stochastic optimization algorithms have long been a research hotspot. The fusion of quantum mechanics with optimization methods can potentially address NP-hard problems more efficiently and exponentially faster. The potential advantages provided by the ground-breaking paradigm have expedited the scientific output of quantum-inspired optimization algorithms locale. Consequently, a pertinent investigation is required to explain how ground-breaking scientific advancements have evolved. The scientometric approach utilizes quantitative and qualitative techniques to analyze research publications to evaluate the structure of scientific knowledge. Henceforth, the current research presents a scientometric and systematic analysis of quantum-inspired metaheuristic algorithms (QiMs) literature from the Scopus database since its inception. The scientometric implications of the article offer a detailed exploration of the publication patterns, keyword co-occurrence network analysis, author co-citation analysis and country collaboration analysis corresponding to each opted category of QiMs. The analysis reveals that QiMs solely account to 26.66% of publication share in quantum computing and have experienced an impressive 42.59% growth rate in the past decade. Notably, power management, adiabatic quantum computation, and vehicle routing are prominent emerging application areas. An extensive systematic literature analysis identifies key insights and research gaps in the QiMs knowledge domain. Overall, the findings of the current article provide scientific cues to researchers and the academic fraternity for identifying the intellectual landscape and latest research trends of QiMs, thereby fostering innovation and informed decision-making.

Synthetic aperture radar image segmentation with quantum annealing

AbstractIn image processing, image segmentation is the process of partitioning a digital image into multiple image segments. Among state‐of‐the‐art methods, Markov random fields can be used to model dependencies between pixels and achieve a segmentation by minimising an associated cost function. Currently, finding the optimal set of segments for a given image modelled as a Markov random fields appears to be NP‐hard. The authors aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of synthetic aperture radar images. For that purpose, the authors propose a hybrid quantum annealing classical optimisation expectation maximisation algorithm to obtain optimal sets of segments. After proposing suitable formulations, the authors discuss the performances and the scalability of authors’ approach on the D‐Wave quantum computer. The authors also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimisation problems.

Quantum‐inspired hybrid algorithm for image classification and segmentation: Q‐Means++ max‐cut method

AbstractFinding brain tumors is a crucial step in medical diagnosis that can have a big impact on how patients turn out. Conventional detection techniques can be laborious and demand a lot of computing power. Brain tumor detection could be made more effective and precise, thanks to the quickly developing field of quantum computing. In this article, we propose a quantum machine learning (QML)‐based method for brain tumor extraction and detection based on quantum computing. To implement our strategy, we use a Hybrid Quantum‐Classical Convolutional Neural Network (HQC‐CNN) that has been trained using a collection of brain MRI images. Additionally, we employ Batchwise Q‐Means++ Clustering for segmenting the images and a Max‐cut approach with Adiabatic Quantum Computation (AQC) to extract the tumor region from the segmented MRI image. Our results highlight the strength of Quanvolutional Layer in Neural Network and reduced time complexity exponentially or quadratically in clustering and max‐cut algorithms respectively and see the potential of quantum computing for improving the accuracy and speed of medical diagnosis and have implications for the future of healthcare technology.

Unlocking the Potential of Quantum Computing: A Comprehensive Review

Quantum computing represents a revolutionary paradigm shift in data processing, promising to revolutionize industries, solve complex computational problems, and propel scientific discovery to unprecedented heights. This research paper provides a comprehensive overview of the current state of quantum computing technology, its basic principles, and applications. The article begins by explaining the basic principles of quantum mechanics, introducing key concepts such as superposition and entrainment that underlie the enormous computing power of quantum computers. The discussion of quantum bits, or qubits, highlights the unique properties of quantum computers that allow them to perform tasks much faster than classical computers. Research papers cover various quantum computer architectures, gate-based quantum computers, adiabatic quantum computers, and quantum annealing devices. Explores challenges and advances in hardware with attention to quantum error correction and quantum breakthroughs. In addition, this paper explores various quantum algorithms and their applications in domains such as cryptography, optimization, material science, and drug discovery. It reviews progress in algorithm development and emphasizes the practical implications of quantum computing for solving real-world problems. Additionally, the research document examines the current state of the Quantum Computing industry and highlights the key players and their contributions to the field. It also touches on the economic and ethical implications of quantum computers, considering security issues and implications for existing computing paradigms. In summary, this comprehensive review reveals the transformative potential of quantum computers and offers valuable insights into current opportunities, challenges, and future prospects. As quantum computing advances, this paper serves as a valuable resource for researchers, policymakers, and industry leaders who want to understand and harness the power of quantum computing.

Floating Block Method for Quantum MonteCarlo Simulations.

Quantum MonteCarlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum MonteCarlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. These new applications require something that is missing from the published literature, an efficient quantum MonteCarlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of ^{4}He, ^{8}Be, ^{12}C, and ^{16}O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

Gravity Data Inversion by Adiabatic Quantum Computing

AbstractA quantum‐enhanced implementation of the binary inversion method for gravity data acquisition is discussed. The subsurface structure of a single density anomaly with an assigned density contrast is calculated by using a D‐Wave adiabatic quantum computer. In particular, an iterative heuristic based on quantum annealing that recovers a sharp shape of the subsurface anomaly is developed. Such a task is accomplished by collecting partial images obtained by quantum annealing processes for optimal Lagrange penalty coefficients. The results are compared with those obtained according to the same cost function minimized via genetic algorithms by conventional hardware on a realistic 2D dataset. The outcomes of this work are promising as the reconstructed model is obtained in tenths of iterations instead of the hundreds required in conventional methods. Moreover, for the part of the computation that resides in the quantum processing unit, the computational cost of the single quantum annealing descent is constant with respect to the number of degrees of freedom of the subsurface grid. The implemented method is likely to reveal its full potential on forthcoming quantum annealing devices, outperforming existing techniques.

Phase‐coded radar waveform design with quantum annealing

AbstractThe Integrated Side Lobe Ratio (ISLR) problem the authors consider here consists in finding optimal sequences of phase shifts in order to minimise the mean squared cross‐correlation side lobes of a transmitted radar signal and a mismatched replica. Currently, ISLR does not seem to be easier than the general polynomial unconstrained binary problem, which is NP‐hard. In their work, the authors aim to take advantage of the scalability of quantum computing to find new optima, by solving the ISLR problem on a quantum annealer. This quantum device is designed to solve quadratic optimisation problems with binary variables (QUBO). After proposing suitable formulation for different instances of the ISLR, the authors discuss the performances and the scalability of their approach on the D‐Wave quantum computer. More broadly, their work enlightens the limits and potential of the adiabatic quantum computation for the solving of large instances of combinatorial optimisation problems.

Integrating genetic markers and adiabatic quantum machine learning to improve disease resistance-based marker assisted plant selection

The goal of this research was to create a more accurate and efficient method for selecting plants with disease resistance using a combination of genetic markers and advanced machine learning algorithms. A multi-disciplinary approach incorporating genomic data, machine learning algorithms and high-performance computing was employed. First, genetic markers highly associated with disease resistance were identified using next-generation sequencing data and statistical analysis. Then, an adiabatic quantum machine learning algorithm was developed to integrate these markers into a single predictor of disease susceptibility. The results demonstrate that the integrative use of genetic markers and adiabatic quantum machine learning significantly improved the accuracy and efficiency of disease resistance-based marker-assisted plant selection. By leveraging the power of adiabatic quantum computing and genetic markers, more effective and efficient strategies for disease resistance-based marker-assisted plant selection can be developed.

Lower bounds for adiabatic quantum algorithms by quantum speed limits

Lower bounds for adiabatic quantum algorithms by quantum speed limits

Universal Quantum Optimization with Cold Atoms in an Optical Cavity.

Cold atoms in an optical cavity have been widely used for quantum simulations of many-body physics, where the quantum control capability has been advancing rapidly in recent years. Here, we show the atom cavity system is universal for quantum optimization with arbitrary connectivity. We consider a single-mode cavity and develop a Raman coupling scheme by which the engineered quantum Hamiltonian for atoms directly encodes number partition problems. The programmability is introduced by placing the atoms at different positions in the cavity with optical tweezers. The number partition problem solution is encoded in the ground state of atomic qubits coupled through a photonic cavity mode, which can be reached by adiabatic quantum computing. We construct an explicit mapping for the 3-SAT and vertex cover problems to be efficiently encoded by the cavity system, which costs linear overhead in the number of atomic qubits. The atom cavity encoding is further extended to quadratic unconstrained binary optimization problems. The encoding protocol is optimal in the cost of atom number scaling with the number of binary degrees of freedom of the computation problem. Our theory implies the atom cavity system is a promising quantum optimization platform searching for practical quantum advantage.

Quantum-Walk-Inspired Dynamic Adiabatic Local Search.

We investigate the irreconcilability issue that arises when translating the search algorithm from the Continuous Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. For the AQC formulation to evolve along the same path as the CTQW, it requires a constant energy gap in the Hamiltonian throughout the AQC schedule. To resolve the constant gap issue, we modify the CTQW-inspired AQC catalyst Hamiltonian from an XZ operator to a Z oracle operator. Through simulation, we demonstrate that the total running time for the proposed approach for AQC with the modified catalyst Hamiltonian remains optimal as CTQW. Inspired by this solution, we further investigate adaptive scheduling for the catalyst Hamiltonian and its coefficient function in the adiabatic path of Grover-inspired AQC to improve the adiabatic local search.

Multi-tower heliostat field optimization by means of adiabatic quantum computer

In this work, the possible use of quantum annealers for the optimization of multi-tower systems is studied. These systems are constituted by multiple solar towers and a set of mirrors (heliostats) reflecting the incident sun radiation toward a receiver on top of a tower of choice. The optimization consists in choosing on which tower each of the heliostats should focus the reflected radiation in order to optimize the global collected energy and, therefore, is inherently discrete. In this work, we formulated it in Quadratic Unconstrained Binary Optimization (QUBO) form and solved it with the use of quantum annealers. Results are shown for systems ranging from 2 to 9 towers and from tenths to thousands of heliostats. It is demonstrated that quantum annealers, used in hybrid mode, are effective in finding good solutions. The results are compared with the ones obtained with classical annealers showing comparable performances.

Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning

Adiabatic quantum computers, such as the quantum annealers commercialized by D-Wave Systems Inc., are routinely used to tackle combinatorial optimization problems. In this article, we show how to exploit them to accelerate equilibrium Markov chain Monte Carlo simulations of computationally challenging spin-glass models at low but finite temperatures. This is achieved by training generative neural networks on data produced by a D-Wave quantum annealer, and then using them to generate smart proposals for the Metropolis-Hastings algorithm. In particular, we explore hybrid schemes by combining single spin-flip and neural proposals, as well as D-Wave and classical Monte Carlo training data. The hybrid algorithm outperforms the single spin-flip Metropolis-Hastings algorithm. It is competitive with parallel tempering in terms of correlation times, with the significant benefit of a much shorter equilibration time.

Quantum annealing solution for the unrelated parallel machine scheduling with priorities and delay of task switching on machines

Quantum computing has emerged in recent years as an alternative to classical computing, which could improve the latter in solving some types of problems. One of the quantum programming models, Adiabatic Quantum Computing, has been successfully used to solve problems such as graph partitioning, traffic routing, and task scheduling. In this paper, the focus is on the scheduling of the problem of unrelated parallel machines, where the processing time of tasks on any of the available processing elements is known. Moreover, the proposed model is extended in two relevant aspects for this kind of problem: the existence of some degree of priority of tasks, and the introduction of a delay or penalty every time a processing unit or machine changes the type of task that executes.In all cases, the problem is expressed as Quadratic Unconstrained Binary Optimization, which can be subsequently solved using quantum annealers. The quantum nonlinear programming framework discussed in this work consists of three steps: quadratic approximation of cost function, a binary representation of parameter space, and solving the resulting Quadratic Unconstrained Binary Optimization on the quantum annealer platform D-Wave. One of the novelties in tackling this problem is the compaction of the model bearing in mind the repetitions of each task, to allow solving larger scheduling problems with the quantum resources available in the experimentation platform. An estimation of the number of qubits required in relation to the scheduling parameters is analyzed. The models have been implemented on the D-Wave platform and validated with respect to other traditional methods. Furthermore, the proposed extensions to consider priorities and to switch the delay of tasks have been analyzed using a case study.

Optimization on large interconnected graphs and networks using adiabatic quantum computation

In this paper, we demonstrate that it is possible to create an adiabatic quantum computing algorithm that solves the shortest path between any two vertices on an undirected graph with at most [Formula: see text] qubits, where [Formula: see text] is the number of vertices of the graph. We do so without relying on any classical algorithms, aside from creating an ([Formula: see text]) adjacency matrix. The objective of this paper is to demonstrate the fact that it is possible to model large graphs on an adiabatic quantum computer using the maximum number of qubits available and random graph generators such as the Barabási–Albert and the Erdős–Rényi methods which can scale based on a power law.