Efficient Preparation of Quantum Many-Body States Assisted by Measurements

The preparation of quantum states is a critical subroutine in quantum computing, error correction, and quantum simulation. It is therefore essential to devise efficient preparation algorithms and understand their fundamental limitations. In this talk, we consider the problem of preparing many-body quantum states that satisfy an entanglement area law; such states are conveniently represented as tensor networks.

For one-dimensional (1D) states, we will first present a fundamental lower bound on the necessary circuit depth (i.e., time) to prepare them. The bound is logarithmic in the system size and leverages the structure of correlations. Subsequently, we will introduce an explicit algorithm that saturates this bound, offering the optimal possible asymptotic scaling in system size. Then, we will show a further exponential speed-up that can be achieved by utilizing measurements. Finally, we will discuss how in particular cases, like the W-state, allowing for approximate preparation can even lead to circuit depth independent of the system size.

For two-dimensional (2D) entanglement area-law states, we will discuss a preparation scheme that leverages symmetries. The scheme enables the preparation of certain states with long-range entanglement in constant depth using measurements, such as states exhibiting topological order.