Related papers: Unitary k-designs from random number-conserving qu…
A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read `sideways', i.e., along the spatial direction. Here, we show that this provides the ideal framework to…
We investigate protocols for generating a state $t$-design by using a fixed separable initial state and a diagonal-unitary $t$-design in the computational basis, which is a $t$-design of an ensemble of diagonal unitary matrices with random…
Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling usually refers to the process of mapping most initial pure product states under a unitary transformation to states which…
Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and…
A fundamental question asks how uniformly finite sets of pure quantum states can be distributed in a Hilbert space. The Welch bounds address this question, and are saturated by $k$-designs, i.e. sets of states reproducing the $k$-th Haar…
Dual-unitary quantum circuits have recently attracted attention as an analytically tractable model of many-body quantum dynamics. Consisting of a 1+1D lattice of 2-qudit gates arranged in a 'brickwork' pattern, these models are defined by…
Suppose $k$ centers are fit to $m$ points by heuristically minimizing the $k$-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with $p\geq 4$ bounded moments; in…
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…
In this work, we introduce a broad class of circuits, or quantum cellular automata, which we call 'pairwise-difference-conserving circuits' (PDC). These models are characterized by local gates that preserve the pairwise difference of local…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…
This work focuses on optimizing the gates of a quantum circuit with a given topology to approximate the unitary time evolution governed by a Hamiltonian. Recognizing that unitary matrices form a mathematical manifold, we employ Riemannian…
An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…
Improving the efficiency and accuracy of energy calculations has been of significant and continued interest in the area of materials informatics, a field that applies machine learning techniques to computational materials data. Here, we…
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Quantum unitaries of the form $\Sigma_{c}\ket{c}\bra{c}\otimes U_{c}$ are ubiquitous in quantum algorithms. This class encompasses not only standard uniformly controlled gates (UCGs) but also a wide range of circuits with uniformly…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
The advent of near-term digital quantum computers could offer us an exciting opportunity to investigate quantum many-body phenomena beyond that of classical computing. To make the best use of the hardware available, it is paramount that we…
Continuous random processes and fields are regularly applied to model temporal or spatial phenomena in many different fields of science, and model fitting is usually done with the help of data obtained by observing the given process at…