Related papers: Efficient quantum tomography II
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
The outcomes of quantum mechanical experiments are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the…
Quantum Wielandt's inequality gives an optimal upper bound on the minimal length $k$ such that length-$k$ products of elements in a generating system span $M_n(\mathbb{C})$. It is conjectured that $k$ should be of order $\mathcal{O}(n^2)$…
Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and…
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem,…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…
Quantum neural networks (QNNs) have been a promising framework in pursuing near-term quantum advantage in various fields, where many applications can be viewed as learning a quantum state that encodes useful data. As a quantum analog of…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading this advantage is achieved for information retrieval from an optical memory, whose…
Quantum information science may lead to technological breakthroughs in computing, cryptography and sensing. For the implementation of these tasks, however, complex devices with many components are needed and the quantum advantage may easily…
We investigate asymptotic probabilistic phenomena arising from the application of the Schensted row insertion algorithm, a key component of the Robinson-Schensted-Knuth (RSK) correspondence, to random inputs. Our analysis centers on a…
Recent results have established dramatic advantages in learning properties of quantum states when a quantum computer is available to process or jointly measure multiple copies of the unknown quantum state. Learning tasks can be accomplished…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In…
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis.…