Sampling rare conformational transitions with a quantum computer

Quantum computing is a multidisciplinary field at the intersectionof quantum physics, computer science, and mathematics, aiming to har-ness quantum mechanical phenomena for computational advantage. Thisarticle provides a comprehensive review of both the foundational princi-ples and advanced theoretical models of quantum computing. We beginwith the basic framework of quantum computation, introducing the con-cept of qubits as two-level quantum systems, the linear algebra of Hilbertspaces, Dirac’s bra–ket notation, and the postulates of quantum mechan-ics (state superposition, unitary evolution, and projective measurement).We then discuss quantum logic gates and circuits, highlighting how clas-sical reversible computation principles extend to universal quantum gatesets. Next, we survey key quantum algorithms (from Shor’s factoring toGrover’s searching and beyond) and the complexity-theoretic implicationsof quantum computers, contrasting the class BQP with classical complex-ity classes. We cover the theoretical foundations of quantum error cor-rection and fault tolerance, explaining how quantum information can beprotected from decoherence using redundancy and how fault-tolerant pro-tocols can, in principle, allow scalable quantum computation despite noisyhardware. We then explore advanced models and paradigms of quantumcomputation, including measurement-based quantum computing (one-wayquantum computing), topological quantum computation with anyons, adi-abatic quantum computing and quantum annealing, continuous-variablequantum computing, and related approaches. We also provide an overviewof quantum information theory as it relates to computation, discussingentanglement, quantum entropy, and information-theoretic limits like theHolevo bound. Finally, we review the leading physical implementations(quantum hardware models) of quantum computers—trapped ions, super-conducting circuits, photonic systems, solid-state spin qubits, and oth-ers—outlining the challenges and achievements of each approach.

During recent years, quantum computers have received increasing attention, primarily due to their ability to significantly increase computational performance for specific problems. Computational performance could be improved for mathematical optimization by quantum annealers. This special type of quantum computer can solve quadratic unconstrained binary optimization problems. However, multi-energy systems optimization commonly involves integer and continuous decision variables. Due to their mixed-integer problem structure, quantum annealers cannot be directly used for multi-energy system optimization.To solve multi-energy system optimization problems, we present a hybrid Benders decomposition approach combining optimization on quantum and classical computers. In our approach, the quantum computer solves the master problem, which involves only the integer variables from the original energy system optimization problem. The subproblem includes the continuous variables and is solved by a classical computer. For better performance, we apply improvement techniques to the Benders decomposition. We test the approach on a case study to design a cost-optimal multi-energy system. While we provide a proof of concept that our Benders decomposition approach is applicable for the design of multi-energy systems, the computational time is still higher than for approaches using classical computers only. We therefore estimate the potential improvement of our approach to be expected for larger and fault-tolerant quantum computers.

This paper delves into the fusion of quantum computing and robotics, focusing on motion planning in cluttered environments. Traditional algorithms struggle with complex problems where many constraints need to be satisfied. Hence, optimization-based approaches such as Constrained Quadratic Models (CQM) have become increasingly popular. Our work presents a 3D tracking algorithm based on CQM uniquely adapted for quantum computers to address computational challenges. With their parallel processing capabilities, Quantum computers offer a groundbreaking approach to optimizing complex problems. We formulate the CQM problem for efficient resolution on the D-Wave quantum computer, showcasing its superiority over classical counterparts. Our application centers on real-time planning in a target-chaser tracking scenario, highlighting the quantum advantage in handling the computation complexity of constrained problems. This paper bridges the quantum-robotics gap and sets the stage for future research in quantum-enhanced robotic motion planning.

The development of quantum computers over the past few years is probably one of the significant advancements in the history of quantum computing. D-Wave quantum computer has been available for more than eight years. IBM has made its quantum computer accessible via its cloud service. Also, Microsoft, Google, Intel, and NASA have been heavily investing in the development of quantum computers and their applications. The quantum computer seems to be no longer just for physicists and computer scientists but also for information system researchers. This paper introduces the basic concepts of quantum computing and describes well-known quantum applications for non-physicists. Also, the current status of the developments in quantum computing is presented.

In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field for near-term quantum computers, both by using gate-based QC via the Quantum Approximate Optimization Algorithm and by quantum annealing using the Ising model. However, demonstrating an advantage over classical methods in real-world applications remains an active area of research. In this work, we investigate the robustness verification of ReLU networks, which involves solving many-variable mixed-integer programs (MIPs), as a practical application. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified by classical methods. To alleviate this issue, we propose to use QC for neural network verification and introduce a hybrid quantum procedure to compute provable certificates. By applying Benders decomposition, we split the MIP into a quadratic unconstrained binary optimization and a linear program which are solved by quantum and classical computers, respectively. We further improve existing hybrid methods based on the Benders decomposition by reducing the overall number of iterations and placing a limit on the maximum number of qubits required. We show that, in a simulated environment, our certificate is sound, and provides bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulations and on quantum hardware.

Quantum computing is an information processing paradigm that uses quantum-mechanical properties to speedup computationally hard problems. Gate-based quantum computers and Quantum Annealers (QAs) are two commercially available hardware platforms that are accessible to users today. Although promising, existing gate-based quantum computers consist of only a few dozen qubits and are not large enough for most applications. On the other hand, existing QAs with few thousand qubits have the potential to solve some domain-specific optimization problems. QAs are single instruction machines and to execute a program, the problem is cast to a Hamiltonian, embedded in the hardware, and a single quantum machine instruction (QMI) is run. Unfortunately, noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials.Due to the limited programmability of QAs users execute the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble QUantum AnneaLing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the 2041-qubit D-Wave QA show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%) without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to further bridge the difference between the baseline and ideal by an average of 55% (and up to 68%).

Quantum computations are very important branch of modern cryptology. According to the number of working physical qubits available in general-purpose quantum computers and in quantum annealers, there is no coincidence, that nowadays quantum annealers allow to solve larger problems. In this paper we focus on solving discrete logarithm problem (DLP) over binary fields using quantum annealing. It is worth to note, that however solving DLP over prime fields using quantum annealing has been considered before, no author, until now, has considered DLP over binary fields using quantum annealing. Therefore, in this paper, we aim to bridge this gap. We present a polynomial transformation of the discrete logarithm problem over binary fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem, using approximately 3n2 logical variables for the binary field F2n. In our estimations, we assume the existence of an optimal normal base in the given fields. Such a QUBO instance can then be solved using quantum annealing.

Earthquake rupture forecasting is a critical component of seismic hazard analysis and requires identifying physically plausible rupture paths across complex fault networks. At its core, this task could be formulated as a large-scale combinatorial optimization problem, which involves selecting an optimal subset of fault segments from a set of candidates. Such problems pose significant challenges for traditional algorithms, as the number of admissible multi-fault ruptures grows combinatorially. Current operational workflows rely on locally applied plausibility filters. While computationally efficient, such greedy local heuristics risk excluding globally competitive rupture scenarios, particularly in regions with dense fault connectivity and competing rupture pathways. This work investigates whether quantum annealing hardware can serve as a sampling accelerator for exploring the ensemble of physically plausible ruptures beyond what is currently accessible to classical approaches. Designing a problem formulation that remains scientifically meaningful while respecting the constraints of current quantum hardware (size, noise, etc.) is nontrivial, and naïve encodings often collapse under these limitations. We encode rupture plausibility modeling as low energy solutions to a quadratic unconstrained binary optimization (QUBO) problem defined on a fault-network middle graph. Binary variables represent activated fault segments, while local interaction terms encode Coulomb stress transfer (as a proxy for pairwise rupture compatibility), continuity preferences, and branching behavior. Here, we adopt a classical-quantum hybrid workflow: the quantum annealer is used to sample globally competitive rupture candidates, while classical post-processing implements physical constraints to filter out non-physical ruptures. The workflow is demonstrated on a subset of the fault network used in the 2023 USGS National Seismic Hazard Model including over 200 fault segments, using both simulated thermal and quantum annealing on D-Wave hardware. Results show that our hardware-aware formulation and conditioning enable robust sampling on comparatively large fault-network instances. Views on quantum computing are polarized: some overstate its power, while others dismiss it as impractical. Our results help bridge this by establishing a concrete, testable pathway for integrating quantum annealing into rupture-modeling workflows on existing purpose-built quantum devices.—---This work is supported by the ICSC National Research Centre for High Performance Computing, Big Data and Quantum Computing (CN00000013, CUP D53C22001300005) within the European Union-NextGenerationEU program (National Recovery and Resilience Plan (PNRR) - Mission 4 Component 2 Investment 1.4.)

The paper contains an analysis of four software programs that solve the symmetric traveling salesman problem on a quantum annealer. Three are designed to find approximate solutions. One is designed to find an optimal tour. These programs demonstrate that an application can run across both classical and quantum computing platforms and take advantage of what each can do best. We add value by using a uniform structure for our analysis so that a consistent standard is used to evaluate the software programs. Also we add value by designing a software experiment to test the ability of the D-Wave quantum computer to optimally solve the traveling salesman problem. Our design combines the best attributes of the programs that are reviewed in this paper. Our design assumes that the variables of the traveling salesman problem can be embedded in the qubits, which excludes the problems in the TSP Library until the D-Wave Pegasus computer is available. We note applications of the asymmetric traveling salesman problem that are in the literature and include these problems in the recommendation for an experiment.

Adiabatic quantum computing (AQC) is a model of computation that uses quantum mechanical processes operating under adiabatic conditions. As a form of universal quantum computation, AQC employs the principles of superposition, tunneling, and entanglement that manifest in quantum physical systems. The AQC model of quantum computing is distinguished by the use of dynamical evolution that is slow with respect to the time and energy scales of the underlying physical systems. This adiabatic condition enforces the promise that the quantum computational state will remain well-defined and controllable thus enabling the development of new algorithmic approaches. Several notable algorithms developed within the AQC model include methods for solving unstructured search and combinatorial optimization problems. In an idealized setting, the asymptotic complexity analyses of these algorithms indicate computational speed-ups may be possible relative to state-of-the-art conventional methods. However, the presence of non-ideal conditions, including non-adiabatic dynamics, residual thermal excitations, and physical noise complicate the assessment of the potential computational performance. A relaxation of the adiabatic condition is captured in the complementary computational heuristic of quantum annealing, which accommodates physical systems operating at finite temperature and in open environments. While quantum annealing (QA) provides a more accurate model for the behavior of actual quantum physical systems, the possibility of non-adiabatic effects obscures a clear separation with conventional computing complexity. A series of technological advances in the control of quantum physical systems have enabled experimental AQC and QA. Prominent examples include demonstrations using superconducting electronics, which encode quantum information in the magnetic flux induced by a weak current operating at cryogenic temperatures. A family of devices developed specifically for unconstrained optimization problems has been applied to solve problems in specific domains including logistics, finance, material science, machine learning, and numerical analysis. An accompanying infrastructure has also developed to support these experimental demonstrations and to enable access of a broader community of users. Although AQC is most commonly applied in superconducting technologies, alternative approaches include optically trapped neutral atoms and ion-trap systems. The significant progress in the understanding of AQC has revealed several open topics that continue to motivate research into this model of quantum computation. Foremost is the development of methods for fault-tolerant operation that will ensure the scalability of AQC for solving large-scale problems. In addition, unequivocal experimental demonstrations that differentiate the computational power of AQC and its variants from conventional computing approaches are needed. This will also require advances in the fabrication and control of quantum physical systems under the adiabatic restrictions.

Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a novel computing platform designed to solve NP-hard optimization problems. Starting with a 16-qubit prototype announced in 2007, the company has launched and sold increasingly larger models: the 128-qubit D-Wave One system was announced in 2010 and the 512-qubit D-Wave Two system arrived on the scene in 2013. A 1,000-qubit model is expected to be available in 2014. This monograph presents an introductory overview of this unusual and rapidly developing approach to computation. We start with a survey of basic principles of quantum computation and what is known about the AQC model and the QA algorithm paradigm. Next we review the D-Wave technology stack and discuss some challenges to building and using quantum computing systems at a commercial scale. The last chapter reviews some experimental efforts to understand the properties and capabilities of these unusual platforms. The discussion throughout is aimed at an audience of computer scientists with little background in quantum computation or in physics.

Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP-hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. The paper starts by drawing parallels between classical and quantum optimisation problems, highlighting their conceptual similarities and differences. Two main paradigms for quantum hardware are then discussed: analogue and gate-based quantum computers. While analog devices such as quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation algorithm and the quantum alternating operator ansatz framework, are discussed in detail. However, it is still unclear whether these techniques will yield quantum advantage, even with advancements in hardware and noise reduction. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.

Using quantum computers for computational chemistry and materials science will enable us to tackle problems that are intractable on classical computers. In this paper, we show how the relative energy of defective graphene structures can be calculated by using a quantum annealer. This simple system is used to guide the reader through the steps needed to translate a chemical structure (a set of atoms) and energy model to a representation that can be implemented on quantum annealers (a set of qubits). We discuss in detail how different energy contributions can be included in the model and what their effect is on the final result. The code used to run the simulation on D-Wave quantum annealers is made available as a Jupyter Notebook. This Tutorial was designed to be a quick-start guide for the computational chemists interested in running their first quantum annealing simulations. The methodology outlined in this paper represents the foundation for simulating more complex systems, such as solid solutions and disordered systems.

Clustering bike sharing stations using Quantum Machine Learning: A case study of Toronto, Canada

In this new era of Quantum Computing, a transformative paradigm is emerging for the enhancement of Cyber Security using the special-purpose systems like D-Wave's quantum annealers which helps the encryption system become more resilient. As quantum computing evolves, it provides new paradigms for breaking the traditional encryption methods, as the recent breakthroughs is accomplished by researchers from Shanghai University that uses D-Wave's quantum annealing capabilities in providing the researchers to successfully demonstrated the potential to compromise widely used encryption systems, including RSA and AES. The usage of quantum annealing (QA) that makes the D-Wave’s a specialized quantum system which enables an efficient computation in tackling cryptographic problems, demonstrates the implications for the data security and privacy by applying the quantum-classical hybrid architectures. This research aims to get attention on the urgent need for developing a new security measures in response to the vulnerabilities exposed by the quantum advancements which emphasizes the crucial role of D-Wave's in unlocking the complexities of quantum computing and its implications for the future of cybersecurity.