HATT: Hamiltonian Adaptive Ternary Tree for Optimizing Fermion-to-Qubit Mapping

TL;DR

This paper presents HATT, a novel Fermion-to-qubit mapping framework that reduces quantum circuit complexity and noise, improving simulation efficiency for Fermionic systems by leveraging Hamiltonian-aware ternary tree structures.

Contribution

HATT introduces a Hamiltonian-adaptive ternary tree method for optimized Fermion-to-qubit mapping, reducing complexity and circuit overhead while preserving key quantum properties.

Findings

Achieves 5-20% reduction in Pauli weight, gate count, and circuit depth.

Reduces algorithm complexity from O(N^4) to O(N^3).

Demonstrates improved noise resistance on Ionq quantum computer.

Abstract

This paper introduces the Hamiltonian-Adaptive Ternary Tree (HATT) framework to compile optimized Fermion-to-qubit mapping for specific Fermionic Hamiltonians. In the simulation of Fermionic quantum systems, efficient Fermion-to-qubit mapping plays a critical role in transforming the Fermionic system into a qubit system. HATT utilizes ternary tree mapping and a bottom-up construction procedure to generate Hamiltonian aware Fermion-to-qubit mapping to reduce the Pauli weight of the qubit Hamiltonian, resulting in lower quantum simulation circuit overhead. Additionally, our optimizations retain the important vacuum state preservation property in our Fermion-to-qubit mapping and reduce the complexity of our algorithm from $O(N^4)$ to $O(N^3)$. Evaluations and simulations of various Fermionic systems demonstrate $5\sim20\%$ reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq quantum computer also show the advantages of our approach in noise resistance in quantum simulations.