Quantum Circuit Optimization Algorithm Inspired by Density Matrix Renormalization Group

Recent advances in quantum computing have facilitated the exploration of quantum many-body simulations. Variational Quantum Algorithms (VQAs) have gained attention as a hybrid approach that combines classical optimization with quantum computation, showing promise for solving practical problems, such as quantum chemical calculations and combinatorial optimization. However, significant challenges remain in implementing VQAs on quantum computers. Inherent errors in quantum devices cause increased qubit decoherence as circuit depth grows. Thus, designing circuits with minimal gate operations and effective error suppression is crucial. Additionally, optimizing circuits with numerous parameters is challenging and prone to convergence to local minima. Therefore, refining variational methods to achieve better convergence and efficient preparation of initial condition is necessary.

To address these issues, we propose a quantum circuit optimization algorithm based on the Density Matrix Renormalization Group (DMRG). Our method sequentially optimizes quantum circuits layer by layer using DMRG, with a bond dimension of 2, thereby constructing a multi-layered circuit structure. We demonstrate the effectiveness of this algorithm by applying it to a quantum spin Hamiltonian. Specifically, we found that our approach efficiently constructs quantum circuit representations of the ground state for large-scale systems with a few hundred qubits, which are challenging for conventional VQAs.