This paper introduces Fermihedral, a compiler framework focusing on discovering the optimal Fermion-to-qubit encoding for targeted Fermionic Hamiltonians. Fermion-to-qubit encoding is a crucial step in harnessing quantum computing for efficient simulation of Fermionic quantum systems. Utilizing Pauli algebra, Fermihedral redefines complex constraints and objectives of Fermion-to-qubit encoding into a Boolean Satisfiability problem which can then be solved with high-performance solvers. To accommodate larger-scale scenarios, this paper proposed two new strategies that yield approximate optimal solutions mitigating the overhead from the exponentially large number of clauses. Evaluation across diverse Fermionic systems highlights the superiority of Fermihedral, showcasing substantial reductions in implementation costs, gate counts, and circuit depth in the compiled circuits. Real-system experiments on IonQ's device affirm its effectiveness, notably enhancing simulation accuracy.
Fermihedral introduces a novel compiler framework for optimal fermion-to-qubit encoding by converting the encoding task into a SAT problem, enhancing the simulation of fermionic quantum systems on quantum computers.
The framework implements a two-step strategy involving conversion to Boolean satisfiability problems solved by SAT solvers and employs clause reduction techniques to manage scalability.
The evaluation of Fermihedral shows significant improvements over existing encoding schemes, demonstrating up to 60% reduction in implementation costs and enhanced simulation accuracy on IonQ's quantum device.
Fermihedral's approach not only optimizes quantum simulations, particularly for fermionic systems, but also opens new avenues for quantum computing applications and algorithmic developments.
The quest for simulating fermionic quantum systems on quantum computers has led to the development of various fermion-to-qubit encoding schemes. A new compiler framework, Fermihedral, revolutionizes this landscape by optimally solving the fermion-to-qubit encoding problem, converting the encoding task into a Boolean Satisfiability (SAT) problem. This approach remolds the encoding process with notable implications for quantum computing, particularly in simulating fermionic systems efficiently.
Fermihedral introduces a two-step strategy to simplifying and solving the fermion-to-qubit encoding as a SAT problem:
Clause Reduction Techniques: To address the infeasibility posed by the exponentially large number of clauses, Fermihedral applies two novel techniques:
The effectiveness of Fermihedral is demonstrated through comprehensive evaluations:
This pioneering work opens up new vistas for quantum simulation:
Fermihedral marks a significant advancement in quantum computing, particularly in the simulation of fermionic systems. By solving the fermion-to-qubit encoding problem optimally through SAT solutions and introducing strategies for manageable scalability, it sets a new precedent for the efficiency and practicality of quantum simulations. As we delve deeper into the era of quantum computing, such breakthroughs are pivotal, not just for theoretical exploration but also for harnessing quantum computing's full potential in solving real-world problems.