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Hybrid Sequential Quantum Computing Integrates Classical and Quantum Methods for Improved Combinatorial Optimization

In order to address complicated combinatorial optimisation problems, a novel paradigm called Hybrid Sequential Quantum Computing (HSQC) has been introduced. It provides a methodical integration of classical and quantum techniques inside an organized workflow. At Kipu Quantum GmbH and the University of the Basque Country EHU, Pranav Chandarana, Sebastián V. Romero, Alejandro Gomez Cadavid, and their colleagues have demonstrated a notable improvement in performance by reliably recovering ground-state solutions to difficult higher-order unconstrained binary optimisation (HUBO) problems.

In estimated runtimes, the team achieved speedups of up to 700 times over simulated annealing and up to 9 times over memetic tabu search when applied to a 156-qubit superconducting processor, a state-of-the-art commercial CPU. These outcomes demonstrate that Hybrid Sequential Quantum Computing HSQC is a scalable and adaptable methodology that can produce notable performance gains.

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Classical Challenges and Quantum Promise

Combinatorial optimization needs more inventive ideas to solve complex problems. Quantum computing is rapidly growing as researchers investigate its potential to solve difficult optimisation problems that regular computers cannot. Gate-based algorithms, quantum annealing systems, and hybrid classical-quantum methods are used in current research.

Demonstrating quantum advantage that is, finding quicker or better answers to problems in the actual world is a key objective in this field. A variety of hardware platforms are being developed, such as IBM Quantum, which is creating gate-based quantum computers using the Qiskit framework, and D-Wave Systems, which is a pioneer in the field of quantum annealing machines. Other platforms, like Rydberg atom and trapped ion quantum computers, are also being studied by researchers.

Quantum annealing, variational quantum Eigensolvers (VQE), and the quantum approximate optimisation algorithm (QAOA) are some of the quantum algorithms being developed to address optimisation. Additional methods include quantum simulated annealing, which frequently makes use of Rydberg atoms, and digitalized adiabatic quantum computing. These methods are being used to solve a wide range of issues, including multi-objective optimisation, protein folding, Boolean satisfiability, and the quadratic assignment problem. Enhancing current classical optimisation methods with quantum algorithms is a major area of research. This includes creating hybrid algorithms that combine the two methods or pre- or post-processing quantum results using conventional solvers.

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The HSQC Methodology: A Systematic, Stage-Wise Workflow

By utilising each paradigm where it excels, scientists have developed Hybrid Sequential Quantum Computing especially to address the drawbacks of both classical and quantum computing. Within an organized, step-by-step workflow, this innovative methodology methodically combines classical and quantum computing techniques.

The method carefully blends two essential stages: quantum refining and classical investigation.

1. Classical Exploration: To begin the investigation, the solution landscape of difficult higher-order unconstrained binary optimisation (HUBO) problems is comprehensively explored using classical optimizers. This process effectively finds early combinations that show promise. The solution terrain is effectively explored using classical heuristics.
2. Quantum Refinement: These potential solutions are then further refined by utilising quantum optimisation. Classical algorithms are frequently trapped by energy barriers, which the quantum step is made to tunnel past. Certain quantum approaches are employed in this refinement process.
3. Final Classical Optimisation: In the method under study, a final classical solver was used to further optimize the quantum-enhanced state and obtain exact-optimal or nearby solutions after the quantum refinement stage.

Bias-field digitized counterdiabatic quantum optimisation (BF-DCQO) was the particular quantum optimisation technique used in the Hybrid Sequential Quantum Computing HSQC framework for this investigation.

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Implementation and Breakthrough Results

Two different HSQC instantiations were created to illustrate the flexibility of the HSQC framework. HUBO problem-solving experiments conducted on a heavy-hexagonal superconducting quantum processor with 156 qubits.

Two fundamental Hybrid Sequential Quantum Computing HSQC procedures were put into practice by the researchers:

• Workflow 1: BF-DCQO, memetic tabu search, and simulated annealing combined.
• Workflow 2: involves using BF-DCQO for simulated annealing and then doing it again.

The outcomes repeatedly shown that ground-state solutions to these difficult HUBO issues are recovered by HSQC. Importantly, this was accomplished quickly often in a matter of seconds.

HSQC successfully tackles the difficulties of complicated combinatorial optimisation by fusing the advantages of quantum optimisation, which burrows through barriers and refines candidate solutions, with the strengths of classical heuristics, which effectively explore the solution terrain. According to the Hybrid Sequential Quantum Computing HSQC is a scalable and adaptable framework that can result in notable performance gains. Research is still being done on error-mitigation strategies and noise-aware algorithms to address issues like noisy quantum hardware.

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