Related papers: A Robust Compressive Quantum State Tomography Algo…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
We propose a new protocol for on-line quantum system estimation on the basis of continuous weak-measurements with the help of compressive sensing and the optimization algorithm. By directly measuring the state of the probe system, we…
Augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging, optimal control and so on.…
Quantum noise is currently limiting efficient quantum information processing and computation. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using…
Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various…
An earlier work [18] proposes a method for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution using an outer approximation method. This should be an efficient prescription for…
We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between…
Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our…
Characterizing the dynamics of quantum systems is a central task for the development of quantum information processors (QIPs). It serves to benchmark different devices, learn about their specific noise, and plan the next hardware upgrades.…
Recently, tremendous progress has been made in the field of quantum science and technologies: different platforms for quantum simulation as well as quantum computing, ranging from superconducting qubits to neutral atoms, are starting to…
The techniques of low-rank matrix recovery were adapted for Quantum State Tomography (QST) previously by D. Gross et al. [Phys. Rev. Lett. 105, 150401 (2010)], where they consider the tomography of $n$ spin-$1/2$ systems. For the density…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
The development of large-scale platforms for quantum information requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout…
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…
The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find…
The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…
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,…
Quantum state tomography aims to estimate the state of a quantum mechanical system which is described by a trace one, Hermitian positive semidefinite complex matrix, given a set of measurements of the state. Existing works focus on…