Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices (1809.02573v2)

Abstract: Due to little consideration in the hardware constraints, e.g., limited connections between physical qubits to enable two-qubit gates, most quantum algorithms cannot be directly executed on the Noisy Intermediate-Scale Quantum (NISQ) devices. Dynamically remapping logical qubits to physical qubits in the compiler is needed to enable the two-qubit gates in the algorithm, which introduces additional operations and inevitably reduces the fidelity of the algorithm. Previous solutions in finding such remapping suffer from high complexity, poor initial mapping quality, and limited flexibility and controllability. To address these drawbacks mentioned above, this paper proposes a SWAP-based BidiREctional heuristic search algorithm SABRE, which is applicable to NISQ devices with arbitrary connections between qubits. By optimizing every search attempt,globally optimizing the initial mapping using a novel reverse traversal technique, introducing the decay effect to enable the trade-off between the depth and the number of gates of the entire algorithm, SABRE outperforms the best known algorithm with exponential speedup and comparable or better results on various benchmarks.

• The paper introduces the SABRE algorithm that significantly reduces additional SWAP operations and improves qubit mapping efficiency on NISQ devices.
• It employs reverse traversal and a look-ahead heuristic to refine initial mappings and balance circuit depth with gate count.
• Empirical results demonstrate up to a 91% reduction in extra gates for small circuits and consistent improvements for larger systems.

Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices

The paper "Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices" presents a significant advance in the efficient execution of quantum algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices. Given the inherent hardware constraints of NISQ devices, such as limited qubit connectivity, the execution of arbitrary quantum algorithms requires sophisticated mapping techniques to ensure compatibility with these devices. The primary contribution of the paper is the development of the SWAP-based BidiREctional heuristic search algorithm (SABRE), designed to optimize qubit mapping on platforms with arbitrary qubit connectivity.

Challenges in Qubit Mapping

The execution of quantum algorithms on NISQ devices is impeded by limited inter-qubit connectivity, which restricts the application of two-qubit gates—critical for quantum entanglement. The logical-to-physical qubits mapping requires frequent adjustments, introducing additional SWAP operations that degrade overall algorithm fidelity. The authors have identified inefficiencies in previous mapping solutions, which suffered from high complexity and lacked an effective initial mapping mechanism capable of global optimization.

Methodology: The SABRE Algorithm

SABRE introduces a heuristic approach that addresses the limitations of existing methods by focusing on three key innovations:

1. SWAP-Based Heuristic Search: Unlike exhaustive search methods with exponential complexity, SABRE narrows the search space significantly, enabling faster computations. The algorithm dynamically assesses SWAP gate candidates based on a heuristic cost function to achieve an efficient mapping transition.
2. Reverse Traversal for Initial Mapping Optimization: Leveraging the reversibility of quantum circuits, SABRE improves initial mapping by conducting reverse circuit traversals. This approach integrates global information without compromising the mapping efficacy, reducing transformation overhead.
3. Look-Ahead Heuristic with Decay Effect: SABRE employs a look-ahead mechanism in its heuristic function to evaluate the implications of SWAPs beyond the immediate front-layer gates, trading off between circuit depth and gate count. The decay effect further refines this balance by encouraging non-overlapping SWAP operations, thus optimizing parallelism.

Results and Implications

The empirical evaluation of SABRE against 26 benchmarks and comparisons with the Best Known Algorithm (BKA) shows superior performance. SABRE achieves up to 91% reduction in additional gates for smaller circuits and a consistent 10% reduction for larger circuits while demonstrating substantial runtime improvements. Unlike BKA, SABRE exhibits robust scalability, handling larger qubit systems efficiently with manageable computational resources.

Future Prospects

Although SABRE's adaptability to irregular qubit connectivity and its efficiency is evident, ongoing advancements in quantum hardware may necessitate continual refinements in mapping strategies. Future research can enhance precision in hardware modeling, incorporate variability-aware tactics, and expand the algorithm's applicability to different quantum gate sets on diverse architectures.

In summary, SABRE exemplifies a sophisticated integration of algorithmic efficiency and practical adaptability, providing a crucial tool for leveraging the computational power of emerging NISQ devices while navigating their unique constraints. This work paves the way for more reliable and scalable quantum computing applications in an era characterized by rapid technological evolution.