Related papers: Classical shadows over symmetric spaces
We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are…
Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine…
The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
We study single-copy shadow tomography in the adversarial robust setting, where the goal is to learn the expectation values of $M$ observables $O_1, \ldots, O_M$ with $\varepsilon$ accuracy, but $\gamma$-fraction of the outcomes can be…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective…
We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…
We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density…
Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical…
Recently a new algorithm for sampling posteriors of unnormalised probability densities, called ABC Shadow, was proposed in [8]. This talk introduces a global optimisation procedure based on the ABC Shadow simulation dynamics. First the…
Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…
Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…
Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a…
The goal of demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity…
Simulating large quantum systems is the ultimate goal of quantum computing. Variational quantum simulation (VQS) gives us a tool to achieve the goal in near-term devices by distributing the computation load to both classical and quantum…
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is…
We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…