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We introduce a simulation-free method to estimate the fidelity of large quantum circuits based on the order statistics of measured output probabilities from highly entangled, chaotic states. The approach requires only the…
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the…
The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…
As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some…
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16,…
We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting…
Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…
Fidelity is one of the most valuable and commonly used metrics for assessing the performance of quantum circuits on error-prone quantum processors. Several approaches have been proposed to estimate circuit fidelity without executing it on…
We present a derivation and numerous applications of a compact explicit formula for the average fidelity of a quantum operation on a finite dimensional quantum system. The formula can be applied to averages over particularly relevant…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly,…
The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While…
In this note, we present a novel measure of similarity between two functions. It quantifies how the sub-optimality gaps of two functions convert to each other, and unifies several existing notions of functional similarity. We show that it…
Uhlmann's theorem is a central result in quantum information theory, which associates the closeness of two quantum states with that of their purifications. The theorem also well characterizes a fundamental task: how close a pure quantum…
Gate fidelity -- an average fidelity over all possible input states -- is the workhorse metric for benchmarking quantum gates or circuits, yet fault-tolerant quantum computing ultimately depends on the worst-case behavior, typically…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…