Related papers: A slightly improved upper bound for quantum statis…
In this paper, we introduce a new alternative quantum fidelity for quantum states which perfectly satisfies all Jozsas axioms and is zero for orthogonal states. By employing this fidelity, we derive an improved bound for quantum speed limit…
We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum…
Zero-knowledge proof (ZKP) frameworks have the potential to revolutionize the handling of sensitive data in various domains. However, deploying ZKP frameworks with real-world data presents several challenges, including scalability,…
We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground…
In this work, we address the central problem about how to effectively find the available precision limit of unknown parameters. In the framework of the quantum Ziv-Zakai bound (QZZB), we employ noiseless linear amplification (NLA)techniques…
One-way puzzles (OWPuzzs) introduced by Khurana and Tomer [STOC 2024] are a natural quantum analogue of one-way functions (OWFs), and one of the most fundamental primitives in ''Microcrypt'' where OWFs do not exist but quantum cryptography…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…
The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until…
We initiate the study of non-interactive zero-knowledge (NIZK) arguments for languages in QMA. Our first main result is the following: if Learning With Errors (LWE) is hard for quantum computers, then any language in QMA has an NIZK…
Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM). However, a major challenge is that QLSAs are inexact and sensitive to the condition number of the coefficient matrices of linear systems.…
The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum…
In a recent seminal work, Bitansky and Shmueli (STOC '20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
Sampling problems demonstrating beyond classical computing power with noisy intermediate scale quantum devices have been experimentally realized. In those realizations, however, our trust that the quantum devices faithfully solve the…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…