Related papers: Random phase vector for calculating the trace of a…
We demonstrate a novel approach to reservoir computation measurements using random matrices. We do so to motivate how atomic-scale devices could be used for real-world computational applications. Our approach uses random matrices to…
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values…
We show how random matrix theory can be applied to develop new algorithms to extract dynamic factors from macroeconomic time series. In particular, we consider a limit where the number of random variables N and the number of consecutive…
A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography.…
We develop a generic framework to bound the phase error rate for quantum key distribution protocols using passive detection setups with imperfections and memory effects. This framework can be used in proof techniques based on the entropic…
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…
In the fields of quantum mechanics and quantum information science, the traces of reduced density matrix powers play a crucial role in the study of quantum systems and have numerous important applications. In this paper, we propose a…
Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses…
We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived…
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…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and…
Quantum random number generator (QRNG) utilizes the intrinsic randomness of quantum systems to generate completely unpredictable and genuine random numbers, finding wide applications across many fields. QRNGs relying on the phase noise of a…