Zahra Honjani

Alireza Tavakoli, Zahra Honjani, Hedieh Sajedi

With the growing popularity of the Internet, digital images are used and transferred more frequently. Although this phenomenon facilitates easy access to information, it also creates security concerns and violates intellectual property rights by allowing illegal use, copying, and digital content theft. Using watermarks in digital images is one of the most common ways to maintain security. Watermarking is proving and declaring ownership of an image by adding a digital watermark to the original image. Watermarks can be either text or an image placed overtly or covertly in an image and are expected to be challenging to remove. This paper proposes a combination of convolutional neural networks (CNNs) and wavelet transforms to obtain a watermarking network for embedding and extracting watermarks. The network is independent of the host image resolution, can accept all kinds of watermarks, and has only 11 layers while keeping performance. Performance is measured by two terms; the similarity between the extracted watermark and the original one and the similarity between the host image and the watermarked one.

Zahra Honjani, Mohsen Heidari

We study the problem of learning nearly $(s,ε)$-sparse unitaries, meaning that the Pauli spectrum is concentrated on at most $s$ components with at most $ε$ residual mass in Pauli $\ell_1$-norm. This class generalizes well-studied families, including sparse unitaries, quantum $k$-juntas, $2^k$-Pauli dimensional channels, and compositions of depth $O(\log\log n)$ circuits with near-Clifford circuits. Given query access to an unknown nearly sparse unitary $U$, our goal is to efficiently (both in time and query complexity) construct a quantum channel that is close in diamond distance to $U$. We design a learning algorithm achieving this guarantee using $\tilde{O}(s^6/ε^4)$ forward queries to $U$, and running time polynomial in relevant parameters. A key contribution is an efficient quantum algorithm that, given query access to an arbitrary unknown unitary $U$, estimates all Pauli coefficients (up to a shared global phase) whose magnitude exceeds a given threshold $θ$, extending existing sparse recovery techniques to general unitaries. We also study the broader class of unitaries with bounded Pauli $\ell_1$-norm. For that class, we prove an exponential query lower bound $Ω(2^{n/2})$. We introduce a more relaxed accuracy metric which is the diamond distance restricted to a set of input states. Then, we show that, under this metric, unitaries with Pauli $\ell_1$-norm uniformly bounded by $L_1$ are learnable with $\tilde{O}(L_1^8/ε^{16})$.