Speaker
Description
Abstract:
One of the key issues in studying quantum many-body systems and quantum field theories is characterizing eigenstates of Hamiltonians. However, the exponential growth of the Hilbert space poses a challenge for classical simulations. Tensor Networks, specifically Matrix Product States (MPS), have emerged as a framework to address this by compactly representing many-body wavefunctions through local tensors connected by a virtual bond. We utilize MPS to initialize quantum devices, which can potentially overcome entanglement barriers of classical computers.
We approximate the ground state of the target Hamiltonian by a variational optimization of an MPS. This MPS is subsequently mapped into a quantum circuit composed of one- and two-qubit gates. Subsequent layers are obtained through a variational procedure using the Hamiltonian transformed by the preceding layers, ensuring a consistent iterative optimization. We investigate the efficacy of this approach on several systems, including the ground states of quantum Ising, XY, and Heisenberg models. Our method guarantees that the variational energy improves with each additional layer, consistently approaching the target ground state energy. Furthermore, an increase in fidelity is observed as the number of layers increases.