Related papers: Operator Spreading in Random Unitary Circuits with…
Random quantum circuits yield minimally structured models for chaotic quantum dynamics, able to capture for example universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of…
We study a model of free fermions on a chain with dynamics generated by random unitary gates acting on nearest neighbor bonds and present an exact calculation of time-ordered and out-of-time-ordered correlators. We consider three distinct…
We study the amount of interference in random quantum algorithms using a recently derived quantitative measure of interference. To this end we introduce two random circuit ensembles composed of random sequences of quantum gates from a…
We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged R\'enyi-$2$ tripartite information in two cases:…
Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many-body systems, but solvability naturally goes along with a degree of non-generic behaviour. By investigating the effect of weakly broken…
We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalises the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a…
Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have…
We consider the iteration of a unitary operator on a separable Hilbert space and study the spreading rates of the associated discrete-time dynamical system relative to a given orthonormal basis. We prove lower bounds for the transport…
The structure of the Heisenberg evolution of operators plays a key role in explaining diverse processes in quantum many-body systems. In this paper, we discuss a new universal feature of operator evolution: an operator can develop a void…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of…
The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been…
We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of…
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…
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 study interacting particle systems on the real line which generalize the Hammersley process [D. Aldous and P. Diaconis, Prob. Theory Relat. Fields 103, 199-213 (1995)]. Particles jump to the right to a randomly chosen point between their…
The spin-dependent scattering process in a system of topological insulator and quantum dot is studied. The unitary scattering process is viewed as a gate transformation applied to an initial state of two electrons. Due to the randomness…
We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time…
Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds…