Related papers: Operator growth in random quantum circuits with sy…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
Operator scrambling denotes the evolution of a simple operator into a complicated one (in the Heisenberg picture), which characterizes quantum chaos in many-body systems. More specifically, a simple operator evolves into a linear…
We introduce a new family of quantum circuits for which the scrambling of a subspace of non-local operators is classically simulable. We call these circuits `super-Clifford circuits', since the Heisenberg time evolution of these operators…
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…
The spread and scrambling of quantum information is a topic of considerable current interest. Numerous studies suggest that quantum information evolves according to hydrodynamical equations of motion, even though it is a starkly different…
We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
Operator entanglement is a well-established measure of operator complexity across a system bipartition. In this work, we introduce a measure for the ability of a unitary channel to generate operator entanglement, representing an…
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…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic…
The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered…
The dynamics of a one dimensional quantum walker on the lattice with two internal degrees of freedom, the coin states, is considered. The discrete time unitary dynamics is determined by the repeated action of a coin operator in U(2) on the…
Random permutation circuits were recently introduced as minimal models for local many-body dynamics that can be interpreted both as classical and quantum. Standard dynamical complexity indicators such as damage spreading and…
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…
Operator spreading provides a new characterization of quantum chaos beyond the semi-classical limit. There are two complementary views of how the characteristic size of an operator, also known as the butterfly light cone, grows under…
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…
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…