#simulatedannealing

Cluster Algorithm CA

A new cluster algorithm revolutionises quantum-guided combinatorial optimisation.

Scientists have discovered a revolutionary new way for solving combinatorial optimisation issues that even the most powerful conventional computers cannot solve. This novel method, developed by Aron Kerschbaumer from ISTA and Peter J. Eder from TUM and Siemens AG, uses quantum mechanics and cluster algorithms to increase efficiency and speed up solution space exploration. This may spur breakthroughs in manufacturing, logistics, materials research, and financial models, which need complex optimisation problems.

Combinatorial optimisation tasks like building the best machine learning models or logistics network routes involve finding the optimum combination among many choices. Identifying Ising spin glasses, disordered magnetic materials having the lowest energy state, is notoriously difficult.

Many issues like the NP-hard Maximum Cut (Max-Cut) problem have complex energy landscapes that can trap traditional algorithms in less-than-ideal configurations due to conflicting interactions or frustration. Conventional methods have trouble breaking out of local minima since they change one variable at a time. Prior cluster algorithms tried to solve this problem by flipping groups of variables at once, but complexity and percolation in spin glass systems made exploration less effective.

New Method: Correlation-Guided Clustering

The team's innovative cluster algorithm (CA) switches groups of variables simultaneously to improve coordination and escape from unsatisfactory setups. A "correlation matrix," precomputed information on variable associations, guides cluster creation, which is the key innovation.

This matrix offers key facts on the energy landscape o f the issue. By using these correlations, the method may quickly avoid local minima by discovering spin groups whose simultaneous flipping, even at low energy levels, produces massive configuration space changes with high acceptance probability.

Simulated annealing (SA), a prominent Monte Carlo (MC)-based optimisation method, flips spin clusters rather than individual spins, which is important. Using the correlation matrix, cluster-building iteratively adds surrounding vertices based on a “link probability” from a randomly picked “seed node”.

The graph's percolation threshold is estimated to correctly normalise this probabilistic technique, preventing clusters from spreading over the system, a critical issue for first cluster algorithms in frustrated systems. Only once is the correlation matrix computed throughout the operation.

Quantum and classical information synergy

Adjustability is a strength of our novel approach for determining guiding correlations. The researchers found a possible crossover between classical and quantum approaches by studying distinct correlations.

Coupling constants (CCs): The issue structure's fundamental interaction strengths are represented by CCs, which provide direction based merely on graph topology. Relationships in semidefinite programming Semidefinite Programming (SDP) correlations, which reflect edge cut probabilities, were obtained by relaxing the Max-Cut problem polynomially (the Goemans and Williamson approximation approach). Thermal correlations from Monte Carlo (MC): The Metropolis-Hastings algorithm samples spin configurations at various temperatures to obtain thermal correlations, which can reveal more about the graph's unhappiness, especially at lower temperatures. QAOA correlations: Quantum advantage matters in QAOA correlations. The hybrid quantum-classical approach QAOA approximates combinatorial optimisation issues by mimicking quantum adiabatic development. The computationally expensive parameter optimisation is only done once, making QAOA-derived correlations beneficial for efficiently sampling high-quality solutions. QAOA or SDP solutions can be improved by post-processing with the approach.

Quantum Guidance Outperforms

Large-scale benchmarking has improved, especially for problem annoyance.

Impact of Frustration: On 3-regular graphs with lesser frustration, CA guided by CCs and random clusters outperformed Simulated Annealing. Random clusters failed, but CCs barely outscored SA on severely frustrated 20-regular graphs. This revealed that coupling constants become less precise as frustration builds, resulting in locally favourable but globally undesirable cluster formations. SDP and MC Improvements: The CA beat the CC-directed version (and SA) for both graph types when guided by SDP and MC correlations. MC correlations were slightly better than SDP correlations for similar approximation ratios, especially at lower temperatures. The algorithm can make better global optimisation decisions since these more informative connections naturally encode more graph displeasure information. Quantum Advantage with QAOA: The main findings show QAOA's quantum advantage. The quantum-guided CA performed better at higher QAOA depths, even though QAOA correlations at the lowest circuit depth (p=1) performed similarly to CCs (an analytically demonstrated relationship). Deeper QAOA circuits gather more accurate issue structural information, improving algorithmic guidance. Additionally, quantum-guided CA with QAOA had a greater acceptance probability for cluster flips. The median acceptance probability climbed to almost 95% at a QAOA depth of p=10, compared to SA or CC-guided CA's 10% acceptance rates. This shows very effective cluster motions and significant solution space exploration.

Future View

This work advances computational problem-solving by demonstrating significant synergy between classical and quantum computing. The revolutionary cluster algorithm's low-energy correlations to avoid percolation in frustrated systems are highly impactful.

Unfortunately, important research questions remain. Whether quantum algorithms' speedup, especially as system size expands, justifies the computing labour needed to obtain high-quality correlations will be crucial.

Robotic Inspection

D-Wave Quantum Annealers Improve Industrial Optimisation and Promise for Hard Problems

D-Wave Systems' hybrid quantum-classical algorithms and quantum annealers are extending industrial applications, accelerating quantum computing. These technologies are increasingly being researched for their ability to address computationally challenging optimisation problems in complex industrial contexts. Recent investigations show that they can compete with classical techniques for certain issue kinds and are feasible in robotic inspection.

D-Wave's technology is being used to optimise robotic inspection pathways for industrial components with complex three-dimensional geometries from CAD models. The Travelling Salesman Problem (TSP) is reframed in three dimensions. The renowned combinatorial optimisation problem TSP finds the shortest path that stops at exactly one of a defined group of “cities” before returning to the starting point. To alter this problem for robotic inspection, researchers use realistic constraints like open-route requirements and flawed network designs.

D-Wave's quantum-based solvers, which combine classical optimisation approaches with quantum processing principles, have been likened to Google OR-Tools and GUROBI. D-Wave's hybrid solvers (NL-Hybrid and CQM-Hybrid) have produced competitive solution quality while substantially reducing calculation times for car doors, bumpers, toy bears, aircraft parts, and H-spheres in five industry case studies.

Even if Gurobi sometimes produces somewhat better results, D-Wave's solvers' speed advantage is an attractive trade-off, especially in dynamic production contexts where flexibility and quick response are crucial. According to the research, D-Wave solvers provide solutions with AR values between 0.62 and 0.94, indicating near-optimal inspection trajectories. The research measures solution quality using the Approximation Ratio (AR) metric and computing efficiency using the Run Time (RT) metric.

Quantum annealing is a metaheuristic that finds the global minimum of an objective function using quantum fluctuations. Quantum annealers set a system of qubits in an initial ground state and let it grow adiabatically to a final state that encodes the solution, unlike gate-based quantum computers that use controlled qubits in non-binary states. It uses quantum mechanical tunnelling over potential barriers to escape local minima better than classic “hill climbing” methods like Simulated Annealing (SA).

D-Wave's quantum annealers, particularly the Advantage QPU with the Pegasus architecture, are promising quantum processing devices. Pegasus topology, a substantial improvement over previous generations, links each qubit to 15 others. These annealers are not universal quantum computers and have fewer applications than gate-based systems, but they are ideal for optimisation problems, especially those related to the Ising model or QUBO problems.

D-Wave's hybrid solvers are also compared against top-tier classical solvers like CPLEX, Gurobi, and IPOPT on a wider range of optimisation problems. These hybrid solvers address quantum computer scaling limits by dividing problems down and executing parts normally and others on the Quantum Processing Unit (QPU). D-Wave's cloud-based Leap Hybrid Solvers automatically apply constraint penalty terms using quantum hardware and traditional algorithms like Tabu search and simulated annealing.

The hybrid solver of D-Wave provided optimal Binary Linear Programming (BLP) results with linear constraints comparable to CPLEX and Gurobi. However, more variables made it slower to calculate, especially near its scalability limit. At D-Wave's variable limit, adding constraints increased calculation time and decreased solution quality compared to traditional solvers.

D-Wave found poor solutions, often two times the ideal, while addressing integer/binary linear programming problems with quadratic constraints, suggesting it may become stranded in local minima. However, it solved some variable counts faster than IPOPT and CPLEX.

D-Wave's hybrid solver performs best in Binary Quadratic Programming (BQP), which theoretically replicates the Ising Hamiltonian, making these problems ideal for quantum annealers. In this scenario, D-Wave consistently found optimal solutions faster than CPLEX (topped at 1000s runtime) and IPOPT for BQP with 500 binary variables.

Despite longer run times, D-Wave

LeapHybridCQMSolver couldn't compete with Gurobi in computing time and solution quality for Mixed-Integer Linear Programming (MILP) on a power sector Unit Commitment problem. D-Wave may address MILP problems, however its computing advantage appears to be limited to quadratic binary objective functions or limitations.