Related papers: Operator Spreading in Random Unitary Circuits with…
Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walkers from a single source in Z. The inner bound involves a…
Given a closed quantum system, the states that can be reached with a cyclic process are those with the same spectrum as the initial state. Here we prove that, under a very general assumption on the Hamiltonian, the distribution of the mean…
Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104…
In commuting parametric quantum circuits, the Fourier series of the pairwise fidelity can be expressed as the characteristic function of random variables. Furthermore, expressiveness can be cast as the recurrence probability of a random…
We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-complexity grows linearly before saturating at a late-time value of…
We consider the spreading of the wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of non-ergodic extended states $1<\gamma<2$. We show that despite non-trivial fractal dimensions $0 < D_{q}=2-\gamma<1$…
We propose a framework for the derivation and evaluation of distributed iterative algorithms for receiver cooperation in interference-limited wireless systems. Our approach views the processing within and collaboration between receivers as…
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are…
We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble (CUE). Our study includes the full distribution…
We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research…
While many statistical properties of deep random quantum circuits can be deduced, often rigorously and other times heuristically, by an approximation to global Haar-random unitaries, the statistics of constant-depth random quantum circuits…
Unitary randomness underpins both fundamental tasks in quantum information and the modern theory of quantum chaos. On one side, a central concept is that of approximate unitary designs: circuits that look random according to small moments…
We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are…
The distribution function of transmitted charge through a double-barrier junction is studied at zero temperature and at small applied voltage. Both a semiclassical model, in which the transport is described by jump rates, and a quantum…
The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…
Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating…
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal…
We study the problem of efficiently learning an unknown $n$-qubit unitary channel in diamond distance given query access. We present a general framework showing that if Pauli operators remain low-complexity under conjugation by a unitary,…
At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that…
We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual…