PIQS: an efficient quantum subspace method for dynamical property estimation

Simulating quantum dynamics to extract time-evolving observables constitutes a central challenge in quantum computing, with both fundamental significance and broad practical applications. Classical approaches suffer from the exponential scaling of Hilbert space, while existing quantum algorithms face limitations from deep circuits and sequential error accumulation on near-term devices. This work introduces a physics-informed quantum subspace method for the efficient estimation of dynamical properties of quantum systems. The core innovation is a globally physics-informed loss function that incorporates the time-dependent Schrödinger equation as a physics-based penalty. This enforces quantum evolution constraints directly during optimization, thereby circumventing the error accumulation inherent in stepwise simulations. By strategically relaxing the normalization constraint, we obtain convexified loss functions whose optimization reduces to solving a linear system, guaranteeing global convergence and significantly mitigating the convergence issues and barren plateaus common in variational quantum algorithms. Theoretically, we prove that under suitable conditions the true dynamical solution can be approximated with high accuracy within a subspace whose dimension scales only as O(Tlog⁡(1/ε)), thus breaking the curse of dimensionality in classical simulation. Numerical experiments demonstrate that the proposed method outperforms conventional Trotterization and variational quantum benchmarks in terms of computational cost, convergence speed, and robustness against measurement noise, offering a viable and efficient pathway for practical dynamical simulation on noisy intermediate-scale quantum hardware.