Related papers: Quantum state tomography via non-convex Riemannian…
Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…
We study the convergence issue for the gradient algorithm (employing general step sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity…
The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent…
Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hat\rho$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation.…
We propose a non-convex optimization algorithm, based on the Burer-Monteiro (BM) factorization, for the quantum process tomography problem, in order to estimate a low-rank process matrix $\chi$ for near-unitary quantum gates. In this work,…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $(L/\mu)^2$ (where $L$ is a bound on…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…
This paper provides a unified treatment to the recovery of structured signals living in a star-shaped set from general quantized measurements $\mathcal{Q}(\mathbf{A}\mathbf{x}-\mathbf{\tau})$, where $\mathbf{A}$ is a sensing matrix,…
Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations…
We study the first-order convex optimization problem, where we have black-box access to a (not necessarily smooth) function $f:\mathbb{R}^n \to \mathbb{R}$ and its (sub)gradient. Our goal is to find an $\epsilon$-approximate minimum of $f$…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from…
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive.…