Related papers: Faster Mixing of Higher-Dimensional Random Reversi…
It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be…
We introduce and study modular truncations of the Ackermann function viewed as self-maps on finite rings. These maps form a hierarchy of rapidly increasing compositional complexity indexed by recursion depth. We investigate their structural…
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic…
Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and have recently emerged using optics based physical systems. Here we examine the inverse problem…
This paper presents models for transforming standard reversible circuits into Linear Nearest Neighbor (LNN) architecture without inserting SWAP gates. Templates to optimize the transformed LNN circuits are proposed. All minimal LNN circuits…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
The reversible circuit synthesis problem can be reduced to permutation group. This allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used to find tight bounds on the synthesis of 3-bit reversible circuits…
We study the formation of short-depth designs beyond the unitary group. We provide a range of results on several groups of broad interest in quantum information science: the Clifford group, the orthogonal group, the unitary symplectic…
Gate camouflaging is a known security enhancement technique that tries to thwart reverse engineering by hiding the functions of gates or the connections between them. A number of works on SAT-based attacks have shown that it is often…
Constructing ensembles of circuits which efficiently approximate the Haar measure over various groups is a long-standing and fundamental problem in quantum information theory. Recently it was shown that one can obtain approximate designs…
We study constructions of $k \times n$ matrices $A$ that both (1) satisfy the restricted isometry property (RIP) at sparsity $s$ with optimal parameters, and (2) are efficient in the sense that only $O(n\log n)$ operations are required to…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry…
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…
We consider probabilistic circuits working over the real numbers, and using arbitrary semialgebraic functions of bounded description complexity as gates. In particular, such circuits can use all arithmetic operations +, -, x, /,…
We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the…
High-precision, robust quantum gates are essential components in quantum computation and information processing. In this study, we present an alternative perspective, exploring the potential applicability of quantum gates that exhibit…
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…
Recent works investigated the generalization properties in deep neural networks (DNNs) by studying the Information Bottleneck in DNNs. However, the mea- surement of the mutual information (MI) is often inaccurate due to the density…
In this Letter we set up a suggestive number theory interpretation of a quantum ladder system made of N coupled chains of spin 1/2. Using the hard-core boson representation and a leg-Hamiltonian made of a magnetic field and a hopping term,…