Related papers: Lower Bounds for Learning Quantum States with Sing…
We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of…
Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make…
How many copies of a mixed state $\rho \in \mathbb{C}^{d \times d}$ are needed to learn its spectrum? To date, the best known algorithms for spectrum estimation require as many copies as full state tomography, suggesting the possibility…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $\rho$, test whether it matches some target state $\sigma$ or is $\epsilon$-far from it. For certifying $d$-dimensional…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
In recent works, much progress has been made with regards to so-called randomized measurement strategies, which include the famous methods of classical shadows and shadow tomography. In such strategies, unknown quantum states are first…
Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which…
Quantum state tomography is an elementary tool to fully characterize an unknown quantum state. As the quantum hardware scales up in size, the standard quantum state tomography becomes increasingly challenging due to its exponentially…
Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. We propose a novel scheme where identical copies of a quantum state are measured jointly so that all Pauli…
Following the first paper on quantum algorithms for SDP-solving by Brand\~ao and Svore in 2016, rapid developments has been made on quantum optimization algorithms. Recently Brand\~ao et al. improved the quantum SDP-solver in the so-called…
We explore the possibility of using "weak" measurements to carry out quantum state tomography. Given a certain fixed number of copies of identically prepared states of a qubit, we simulate state tomography using weak as well as projective…
Classical Shadow Tomography (Huang, Kueng and Preskill, Nature Physics 2020) is a method for creating a classical snapshot of an unknown quantum state, which can later be used to predict the value of an a-priori unknown observable on that…
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both…
The ability to control quantum systems using shaped fields as well as to infer the states of such controlled systems from measurement data are key tasks in the design and operation of quantum devices. Here we associate the success of…
Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the…