Speaker
Description
Efficient simulation of quantum circuits remains a central challenge in quantum information science. We introduce Matrix Product Evolution (MPE), a tensor-network framework that represents the evolution of each qubit as a tensor train organized along the temporal direction of a circuit. Temporal bond dimensions encode correlations accumulated during circuit evolution, and neighboring MPEs are contracted through a zip-up procedure with controlled bond truncation. We derive upper bounds on temporal bond dimensions for different classes of initial states and analyze the impact of post-selection on computational complexity. Numerical experiments on random quantum circuits and one-dimensional quantum Ising circuits demonstrate that the accuracy of MPE strongly depends on the underlying correlation structure. While MPE does not universally outperform conventional matrix product state approaches, it can achieve substantially higher accuracy for post-selected circuits by directly reducing effective temporal degrees of freedom. These results establish MPE as a complementary contraction strategy for tensor-network quantum-circuit simulation.