Variational Fast Forwarding for Efficient Evaluation of Many-Body Green’s Functions

Many-body Green’s functions are essential for characterizing excitation and spectral properties in strongly correlated quantum systems; however, their long-time dynamical evaluation remains computationally intractable on classical computers. Quantum computing offers a promising alternative for simulating such dynamics, yet existing approaches based on Trotterized time evolution suffer from a critical drawback: circuit depth grows linearly with simulated time, severely limiting performance on noisy intermediate-scale quantum (NISQ) devices due to gate errors and decoherence. In this work, we propose a fixed-depth quantum circuit framework to evaluate real-time many-body Green’s functions via Variational Fast Forwarding (VFF). By integrating a fixed-depth VFF-based evolution module into a standard ancilla-assisted interferometric measurement scheme, we enable direct extraction of Green’s function values. Numerical simulations on the two-site Hubbard model demonstrate that the approach reconstructs both the real-time Green’s function and the corresponding frequency-domain spectral function. Under a hardware-motivated noise model, a first-order Trotter circuit with step △ t = 0.1 suffers a fidelity collapse below 0.2 as its depth grows with t, whereas the compiled VFF circuit keeps a state fidelity above 0.8 over the same window. At t = 25 the evolution blocks U ( t ) contain 4751 and 79 CNOT gates. Training uses exact probabilities, without finite-shot sampling. The practical training cost and the performance on larger systems remain open.