Quantum Hardware Efficiently Selects Auxiliary Variables for QUBO Formulations, Reducing Compilation Overhead

Translating complex optimisation problems into a form suitable for quantum computers often requires converting them into Quadratic Unconstrained Binary Optimisation (QUBO) formulations, a process that typically involves adding auxiliary variables. Damian Rovara, Lukas Burgholzer, and Robert Wille, from the Technical University of Munich and Software Competence Center Hagenberg, demonstrate a new method for selecting these auxiliary variables that directly addresses the limitations of current quantum hardware. Their approach moves beyond simply minimising the number of variables, instead prioritising the creation of a structured interaction graph that aligns with the connectivity of qubits in real quantum processors. This careful selection significantly reduces the complexity of the resulting quantum circuits, achieving a nearly 40% reduction in circuit depth compared to conventional methods and paving the way for more efficient and scalable quantum optimisation.

NISQ Algorithm Compilation and Optimisation Techniques

This research surveys techniques for optimizing quantum algorithms on near-term quantum computers, known as Noisy Intermediate-Scale Quantum (NISQ) devices. These devices are limited by qubit count, connectivity, and coherence, presenting significant challenges for practical implementation. The work focuses on methods to make algorithms, particularly the Quantum Approximate Optimization Algorithm (QAOA), more efficient on current and future hardware, reducing the complexity of representing optimization problems for quantum computation. The design of effective mixer operators for QAOA is also a key area of investigation, with software tools like MQT and Qiskit automating these optimization processes and refining techniques for handling constraints within quantum formulations. The study categorizes these techniques, detailing methods for problem modeling, circuit optimization, and mixer design. It highlights the importance of constraint handling and the role of specialized software tools in automating the optimization process, acknowledging key challenges including limited qubit connectivity, short coherence times, and the difficulty of scaling optimization techniques to larger problems.

Auxiliary Variable Selection for Quantum Optimization

Scientists have developed a new method for translating complex optimization problems into a format suitable for quantum computers, addressing limitations imposed by qubit connectivity. This method directly addresses device constraints during the QUBO formulation stage, rather than attempting to resolve connectivity issues after formulation is complete. By carefully selecting auxiliary variables to maintain a predictable interaction pattern, researchers reduce the complexity of subsequent compilation, achieving a significant reduction in circuit depth, an average improvement of 39.

2% observed in problems involving 16 variables. This study pioneers a method that integrates QUBO formulation and circuit compilation, streamlining the process and minimizing performance degradation. By considering hardware limitations from the outset, the team avoids substantial compilation overhead, paving the way for more efficient execution of optimization algorithms on near-term quantum devices. The team’s implementation is publicly available, facilitating further research and development.

QUBO Mapping Simplifies Quantum Circuit Complexity

Scientists have developed a novel method for constructing quantum circuits that significantly reduces computational demands for near-term quantum computers. Conventional methods for selecting auxiliary variables often create interaction graphs incompatible with the physical constraints of quantum computers, leading to substantial compilation overhead. To overcome this, researchers devised an approach that constructs an interaction graph with a regular structure and limited complexity, enabling efficient mapping to various architectures, achieving an average depth reduction of 39.

2% for problems involving 16 variables. The team achieved this improvement by carefully selecting auxiliary variables to maintain a regular interaction structure, simplifying the mapping process onto the quantum hardware. As the problem size increases, the benefits of this approach become even more pronounced, suggesting a pathway towards more efficient quantum algorithms for practical optimization tasks.

Reduced Circuit Depth For Quantum Algorithms

This work presents a novel approach to constructing efficient quantum algorithms by carefully selecting auxiliary variables during the transformation of complex optimization problems into a format suitable for quantum computers. The researchers addressed the difficulty of mapping abstract algorithms onto the limited connectivity of actual quantum hardware, achieving a significant reduction in circuit depth, nearly 40% compared to conventional methods, translating to faster computation times. The team’s algorithm constructs quantum circuits that are more easily adapted to various quantum architectures, even as the number of variables in the problem increases. This improvement in circuit depth was achieved while acknowledging a trade-off in circuit width, requiring a slightly larger number of qubits.

The researchers emphasize compatibility with existing quantum compilation techniques, offering further potential for optimization, with future work focusing on combining this approach with advanced compilers and exploring qubit reuse to minimize qubit requirements. The authors note that the performance gains are most pronounced as problem size increases, demonstrating the scalability of their method. An open-source implementation of all proposed techniques is publicly available, facilitating further research and development, representing a significant step towards realizing the potential of quantum computers for solving complex optimization problems by bridging the gap between theoretical algorithms and practical hardware limitations.