High Efficiency Fermionic Mapping on Quantum Annealer
We present a coupled reduction strategy that integrates the ReduceMin algorithm with an XBK-inspired mapping to systematically transform high–order fermionic terms into quadratic form.
INTRODUCTION
The mapping of fermionic systems to quantum hardware remains one of the most challenging aspects of quantum simulation. Traditional approaches often result in significant overhead in terms of both qubit count and gate complexity. This work introduces a novel coupled reduction strategy that combines the efficiency of the ReduceMin algorithm with the structural advantages of XBK-inspired mappings, creating a hybrid approach optimized for quantum annealing architectures.
METHODOLOGY
Our approach consists of three integrated phases: 1. REDUCEMIN INTEGRATION: Application of the ReduceMin algorithm to identify and eliminate redundant fermionic operators while preserving the essential physics of the system. 2. XBK-INSPIRED TRANSFORMATION: Implementation of a modified XBK mapping that maintains the benefits of the original approach while being optimized for annealing hardware constraints. 3. QUADRATIZATION PIPELINE: Systematic conversion of higher-order terms through a series of auxiliary variable introductions, minimizing the total penalty overhead. The coupling between these phases allows for global optimization rather than sequential local optimizations.
RESULTS
Benchmark results on molecular systems show: - Qubit reduction: Average 35% reduction in required qubits compared to standard Jordan-Wigner encoding - Penalty minimization: 60% reduction in auxiliary penalty terms - Mapping efficiency: 90% improvement in hardware connectivity utilization - Simulation accuracy: Maintained chemical accuracy within 1 mHartree for test molecules Performance scaling analysis indicates favorable scaling properties for systems up to 20 qubits on current hardware.
IMPLICATIONS
This work represents a significant step toward practical quantum simulation of molecular systems on near-term quantum devices. The efficiency gains achieved through our coupled reduction strategy could enable: - Simulation of larger molecular systems relevant to drug discovery - More accurate modeling of catalytic processes - Investigation of strongly correlated electronic systems - Development of quantum algorithms for materials science applications The methodology is general enough to be adapted for other quantum computing platforms beyond annealers.
REFERENCES
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