## UC Berkeley / Lawrence Berkeley Laboratory

#### Quantized tensor train: entanglement analysis of encoding functions in a quantum state

**Jielun Chen, Caltech**

In this talk, I will give an overview of quantized tensor train (QTT). This line of research studies the entanglement of embedding a function discretized on 2^n points into amplitudes of an n-qubit quantum state. We will present existing results on classes of functions and operators with low entanglement under such encoding. Examples include many important functions such as sparse Fourier series, polynomials, and Gaussians, as well as important operators such as convolution, discrete Fourier transform, and derivatives. We will discuss the applications of QTT in high-dimensional differential equations and the implications for quantum computing.