Quantum Circuit Simulation with a Localized Dynamic Time-Dependent Variational Principle

Learn about a novel tensor network method for quantum circuit simulation through this 14-minute conference talk that introduces a locally adaptive formulation of the Time-Dependent Variational Principle (TDVP) designed to overcome limitations of the widely used Time-Evolving Block Decimation (TEBD) algorithm. Discover how TEBD, while effective for short-range interactions and low entanglement growth, suffers from cumulative truncation errors and inefficiencies when simulating long-range gates that require SWAP insertions, artificially increasing entanglement and computational cost. Explore the proposed method that reformulates circuit simulation in the Schrödinger picture by interpreting each gate as a small time-evolution step and projecting its generator onto the tangent space of the MPS manifold. Understand how this local dynamic TDVP approach enables more accurate simulations by preserving MPS geometry and avoiding unnecessary truncations while supporting dynamic bond dimension growth and direct simulation of long-range gates without introducing SWAP gates. Examine the implementation details where single-qubit gates are directly contracted into MPS tensors while multi-qubit gates are handled by slicing the MPS across affected regions and applying localized TDVP projections. Learn about the projector-splitting formalism that applies only relevant summands for affected qubits, reducing computational overhead from 2L−1 projectors (full TDVP) to 2q−1 for a gate acting on q qubits without accuracy loss. Review numerical benchmarks demonstrating that local dynamic TDVP matches TEBD accuracy while requiring significantly fewer MPS parameters, including results from a 36-qubit Trotterized 1D periodic Ising circuit with long-range interactions where TEBD produces rapid entanglement growth and central bond dimension blow-up while TDVP maintains smoother, lower bond growth, establishing this approach as a powerful and scalable alternative for simulating large quantum circuits.