Quantum Simulation of the SSH Model Reveals Topological Phase Transitions with Variational Circuits

On April 10, 2025, researchers Qing Xie, Kazuhiro Seki, Tomonori Shirakawa, and Seiji Yunoki published a study titled Digital quantum simulation of the Su-Schrieffer-Heeger model using a parameterized quantum circuit, detailing their exploration of topological phase transitions in quantum systems. Their work, supported by Quantinuum’s trapped-ion qubit technology, demonstrated how variational quantum circuits can simulate the evolution of energy and entanglement across distinct topological states, providing insights into the dynamics of quantum phase transitions.

The study simulates the noninteracting Su-Schrieffer-Heeger (SSH) model using a parameterized quantum circuit to investigate topological phase transitions. When initial and target states share the same topological phase, energy decreases exponentially, entanglement entropy stabilizes quickly, and mutual information remains localized. Conversely, when phases differ, energy decreases polynomially, entanglement grows logarithmically before declining, and mutual information spreads ballistically. A topological phase transition is identified via polarization changes during circuit evolution. Experimental validation on an 18-site system with 19 qubits confirms these findings.

Quantum computing has made significant progress in translating complex physical systems into computational models. A key challenge in this field is mapping fermionic systems, such as electrons in materials, onto quantum computers, which operate using qubits. Recent research has focused on improving these mappings to enhance the efficiency and applicability of quantum simulations.

Fermions, such as electrons, obey specific physical laws that differ from qubits. Translating fermionic problems into a form suitable for quantum computation requires careful mapping. This process is crucial because it allows researchers to leverage quantum computers to study complex systems like superconductors and topological insulators.

Several studies have contributed to this field. In 2005, researchers developed methods to map fermionic Hamiltonians into spin models, facilitating the use of quantum computers for studying fermionic systems. A 2018 study explored optimizing these mappings to reduce resource requirements, making simulations more feasible on current quantum hardware. Additionally, a novel approach using ternary trees was introduced in 2020 to achieve optimal fermion-to-qubit mappings, enhancing the accuracy and efficiency of quantum simulations.

The development of practical tools has been pivotal in advancing this research. For instance, researchers have successfully simulated models like BCS (related to superconductivity) using digital quantum techniques, demonstrating the potential for studying complex materials. The creation of compilers like tket has enabled retargetable implementations across different quantum devices, bridging the gap between theoretical mappings and real-world applications.

These advancements hold significant implications for various fields. Improved simulations can deepen our understanding of materials with complex properties, such as topological insulators. Enhanced mapping techniques also contribute to developing new quantum control strategies, potentially leading to more robust and scalable quantum computing approaches.

The progress in fermion-to-qubit mappings represents a substantial step forward in quantum computing. By improving the efficiency and practicality of these mappings, researchers are unlocking new possibilities for simulating complex systems and advancing our understanding of quantum mechanics. This innovation enhances computational capabilities and opens avenues for breakthroughs in materials science and quantum technology development.