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Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy…
Byzantine fault tolerant protocols enable state replication in the presence of crashed, malfunctioning, or actively malicious processes. Designing such protocols without the assistance of verification tools, however, is remarkably…
Security protocols stipulate how the remote principals of a computer network should interact in order to obtain specific security goals. The crucial goals of confidentiality and authentication may be achieved in various forms, each of…
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
We propose an efficient protocol to fully reconstruct a set of high-fidelity quantum gates. Usually, the efficiency of reconstructing high-fidelity quantum gates is limited by the sampling noise. Our protocol is based on a perturbative…
Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present Bayesian phase…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
Clustered standard errors and approximate randomization tests are popular inference methods that allow for dependence within observations. However, they require researchers to know the cluster structure ex ante. We propose a procedure to…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
Random selection, leader election, and collective coin flipping are fundamental tasks in fault-tolerant distributed computing. We study these problems in the full-information model where despite decades of study, key gaps remain in our…
We present a comprehensive steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA proposed in recent literature. In threshold-ALOHA, each terminal suspends its transmissions until the Age of…
Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such…
Threshold selection plays a key role for various aspects of statistical inference of rare events. Most classical approaches tackling this problem for heavy-tailed distributions crucially depend on tuning parameters or critical values to be…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…
Quantum Internet signifies a remarkable advancement in communication technology, harnessing the principles of quantum entanglement and superposition to facilitate unparalleled levels of security and efficient computations. Quantum…
We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…
Simultaneous testing of one hypothesis at multiple alpha levels can be performed within a conventional Neyman-Pearson framework. This is achieved by treating the hypothesis as a family of hypotheses, each member of which explicitly concerns…
In multiple testing scenarios, typically the sign of a parameter is inferred when its estimate exceeds some significance threshold in absolute value. Typically, the significance threshold is chosen to control the experimentwise type I error…
Decoy state protocols are a useful tool for many quantum key distribution systems implemented with weak coherent pulses, allowing significantly better secret bit rates and longer maximum distances. In this paper we present a method to…