Quantum Simulation with Hybrid Tensor Networks

Tensor network theory and quantum simulation are respectively the key classical computing methods in understanding many-body physics. Here, we introduce framework of hybrid tensor networks with building blocks consisting measurable states classically contractable tensors, inheriting both their distinct features efficient representation wave functions. With example tree networks, demonstrate using a computer whose size is significantly smaller than one target system. We numerically benchmark our method for finding ground state 1D 2D spin systems up to $8\times 8$ $9\times qubits operations only acting on $8+1$ $9+1$ qubits,~respectively. Our approach sheds light large practical problems intermediate-scale computers, potential applications chemistry, physics, field theory, gravity thought experiments.