Optimization and Quantum Simulation of Fermions

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-toqubit 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-toqubit mapping and reduce the complexity of our algorithm from $O\left(N^{4}\right)$ to $O\left(N^{3}\right)$ . Evaluations on various Fermionic systems demonstrate $5 \sim 25 \%$ reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq device also show the advantages of HATT in noise resistance in quantum simulations.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-toqubit 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-toqubit mapping and reduce the complexity of our algorithm from $O\left(N^{4}\right)$ to $O\left(N^{3}\right)$. Evaluations on various Fermionic systems demonstrate $5 \sim 25 \%$ reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq device also show the advantages of HATT in noise resistance in quantum simulations.

arXiv:2409.02010IEEE International Symposium on High-Performance Computer Architecture (HPCA)Mar 1, 20252 citations

Quantum simulation of fermions: geometric locality and error mitigation

Jiang Zhang, Jarrod R. McClean, Ryan Babbush +1 more

Bulletin of the American Physical SocietyMar 7, 20190 citations

COSMA: Communication-aware Optimization of Fermionic Simulation Kernels for Modular Quantum Architectures

Enrico Russo, Francesco G. Blanco, Elio Vinciguerra +3 more

Quantum simulation is a leading application of quantum computing, but scaling to chemically relevant problems requires modular architectures composed of interconnected quantum processing units. In such systems, inter-core quantum communication becomes a major performance bottleneck. In this work, we present COSMA, a communication-aware compilation framework for fermionic simulation kernels targeting modular quantum architectures. Our approach jointly optimizes fermion-to-qubit mapping, Pauli scheduling, and qubit allocation to minimize inter-core state transfers. Evaluated on molecular benchmarks, COSMA achieves up to $2.5\times$ reduction in communication cost compared to state-of-the-art baselines, with a median improvement of $1.7\times$ . These results demonstrate that cross-layer co-design is essential for efficient and scalable quantum simulation on multi-core quantum hardware.Quantum simulation is a leading application of quantum computing, but scaling to chemically relevant problems requires modular architectures composed of interconnected quantum processing units. In such systems, inter-core quantum communication becomes a major performance bottleneck. In this work, we present COSMA, a communication-aware compilation framework for fermionic simulation kernels targeting modular quantum architectures. Our approach jointly optimizes fermion-to-qubit mapping, Pauli scheduling, and qubit allocation to minimize inter-core state transfers. Evaluated on molecular benchmarks, COSMA achieves up to $2.5\times$ reduction in communication cost compared to state-of-the-art baselines, with a median improvement of $1.7\times$. These results demonstrate that cross-layer co-design is essential for efficient and scalable quantum simulation on multi-core quantum hardware.

quant-pharXiv:2607.09381Jul 13, 20260 citations

Implementation of the iFREDKIN gate in scalable superconducting architecture for the quantum simulation of Fermionic systems

Per Liebermann, Pierre-Luc Dallaire-Demers, Frank K. Wilhelm

We present a Superconducting Planar ARchitecture for Quantum Simulations (SPARQS) intended to implement a scalable qubit layout for quantum simulators. To this end, we describe the iFREDKIN gate as a controlled entangler for the simulation of Fermionic systems that is advantageous if it can be directly implemented. Using optimal control, we show that and how this gate can be efficiently implemented in the SPARQS circuit, making it a promising platform and control scheme for quantum simulations. Such a quantum simulator can be built with current quantum technologies to advance the design of molecules and quantum materials.We present a Superconducting Planar ARchitecture for Quantum Simulations (SPARQS) intended to implement a scalable qubit layout for quantum simulators. To this end, we describe the iFREDKIN gate as a controlled entangler for the simulation of Fermionic systems that is advantageous if it can be directly implemented. Using optimal control, we show that and how this gate can be efficiently implemented in the SPARQS circuit, making it a promising platform and control scheme for quantum simulations. Such a quantum simulator can be built with current quantum technologies to advance the design of molecules and quantum materials.

arXiv:1701.07870Jan 26, 20176 citations

O\left(N^{4}\right)

O\left(N^{3}\right)

. Evaluations on various Fermionic systems demonstrate

5 \sim 25 \%

reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq device also show the advantages of HATT in noise resistance in quantum simulations.

2.5\times

reduction in communication cost compared to state-of-the-art baselines, with a median improvement of

1.7\times

. These results demonstrate that cross-layer co-design is essential for efficient and scalable quantum simulation on multi-core quantum hardware.