Local subspace variational quantum compilation for quantum many-body simulations on near-term quantum computers

Implementing the time-evolution operator is essential for simulating quantum many-body systems on quantum computers. However, standard Trotterization methods often yield deep quantum circuits, posing a significant challenge for noisy near-term quantum computers. Here, we present Local Subspace Variational Quantum Compilation (LSVQC), a hybrid quantum-classical algorithm for compiling the time-evolution operator into shallow-depth quantum circuits. The LSVQC employs variational optimization to reproduce the action of the target time-evolution operator within a physically relevant subspace. Optimization is performed on spatially local subsystems, based on the Lieb-Robinson bound. This allows cost function evaluation using small-scale quantum devices or classical computers. We demonstrate the LSVQC’s effectiveness by performing numerical simulations on a spin-lattice model and an ab initio effective model of strongly correlated material Sr₂CuO₃. It is shown that the LSVQC achieves a 95% reduction in circuit depth compared to Trotterization while maintaining accuracy. Future work will explore extending the LSVQC to ground state calculation on early fault-tolerant quantum computers.