English
Related papers

Related papers: Quantum Relative Entropy Decay Composition Yields …

200 papers

Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical…

Quantum Physics · Physics 2025-08-25 Zihan Cheng , Eric Huang , Vedika Khemani , Michael J. Gullans , Matteo Ippoliti

Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The…

Quantum Physics · Physics 2021-08-23 Jonas Haferkamp , Nicholas Hunter-Jones

We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…

Data Analysis, Statistics and Probability · Physics 2015-06-12 O. Afsar , G. B. Bagci , U. Tirnakli

A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…

Quantum Physics · Physics 2017-01-03 Richard Cleve , Debbie Leung , Li Liu , Chunhao Wang

The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being…

Disordered Systems and Neural Networks · Physics 2017-11-28 Robert Juhász , István A. Kovács , Gergő Roósz , Ferenc Iglói

The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive…

Quantum Physics · Physics 2024-12-31 Zimu Li , Han Zheng , Junyu Liu , Liang Jiang , Zi-Wen Liu

Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we…

We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…

Combinatorics · Mathematics 2019-05-17 Chris Godsil , Hanmeng Zhan

In this work, we show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model. This learning model is widely used as an abstract computational model for most generic…

Understanding how fast physical systems can resemble Haar-random unitaries is a fundamental question in physics. Many experiments of interest in quantum gravity and many-body physics, including the butterfly effect in quantum information…

Quantum Physics · Physics 2025-10-01 Thomas Schuster , Fermi Ma , Alex Lombardi , Fernando Brandao , Hsin-Yuan Huang

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…

Quantum Physics · Physics 2026-03-02 Guoding Liu , Zhenyu Du , Zi-Wen Liu , Xiongfeng Ma

This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…

Quantum Physics · Physics 2016-11-29 Felix Leditzky

Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have…

Information Theory · Computer Science 2019-11-05 Jun Zhao , Osman Yagan , Virgil Gligor

For a random graph subject to a topological constraint, the microcanonical ensemble requires the constraint to be met by every realisation of the graph (`hard constraint'), while the canonical ensemble requires the constraint to be met only…

Mathematical Physics · Physics 2018-12-27 Diego Garlaschelli , Frank den Hollander , Andrea Roccaverde

One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…

Data Structures and Algorithms · Computer Science 2022-06-27 Michael Dinitz , Ama Koranteng , Guy Kortsarz

The rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum…

Quantum Physics · Physics 2022-10-05 Peter Brown , Hamza Fawzi , Omar Fawzi

At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct…

Quantum Physics · Physics 2020-03-10 Rawad Mezher , Joe Ghalbouni , Joseph Dgheim , Damian Markham

We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong…

Quantum Physics · Physics 2026-05-06 Marten Folkertsma , Lorenzo Grevink , Jonas Helsen , Alicja Dutkiewicz

Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…

Quantum Physics · Physics 2025-02-18 Chi-Fang Chen , Jordan Docter , Michelle Xu , Adam Bouland , Patrick Hayden

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

Quantum Physics · Physics 2023-03-23 Minzhao Liu , Junyu Liu , Yuri Alexeev , Liang Jiang