This paper introduces Model-space Quantum Imaginary Time Evolution (MSQITE), a framework that incorporates model space into quantum imaginary time evolution (QITE) for stable ground and excited state estimations using quantum computers. MSQITE propagates a model space to the exact one while maintaining orthogonality, enabling simultaneous description of multiple states. The quantum Lanczos (QLanczos) algorithm is extended to accelerate convergence. MSQITE outperforms standard QLanczos and folded-spectrum QITE (FSQITE) in excited state simulations. Spin contamination is effectively removed by shifting the imaginary time propagator, efficiently capturing excited states with specific spin quantum numbers. The impact of different unitary approximation levels in MSQITE is also investigated. Noise simulations for the H₄ system demonstrate the algorithm's effectiveness over QITE.

Takashi Tsuchimochi, Yoohee Ryo, Siu Chung Tsang, Seiichiro L. Ten-no