Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These aim at efficiently estimating quality set gates way is resistant state preparation and measurement errors. Over years many versions been developed, however comprehensive theoretical treatment randomized has missing. In this work, we develop rigorous framework general enough encompass virtually all known as well novel, more flexible...

We report on the experimental realization of electric quantum walks, which mimic effect an field a charged particle in lattice. Starting from textbook implementation discrete-time we introduce extra operation each step to implement field. The recorded dynamics such exhibits features closely related Bloch oscillations and interband tunneling. In particular, explore regime strong fields, demonstrating contrasting behaviors: resonances versus dynamical localization depending whether accumulated...

Open quantum many-body systems play an important role in optics and condensed matter physics, capture phenomena like transport, the interplay between Hamiltonian incoherent dynamics, topological order generated by dissipation. We introduce a versatile practical method to numerically simulate one-dimensional open dynamics using tensor networks. It is based on representing mixed states locally purified form, which guarantees that positivity preserved at all times. Moreover, approximation error...

The phenomenon of many-body localization has received a lot attention recently, both for its implications in condensed-matter physics allowing systems to be an insulator even at nonzero temperature as well the context foundations quantum statistical mechanics, providing examples showing absence thermalization following out-of-equilibrium dynamics. In this work, we establish novel link between dynamical properties--a vanishing group velocity and transport--with entanglement properties...

We study the asymptotic position distribution of general quantum walks on a lattice, including with random coin, which is chosen from step to by Markov chain. In unitary (i.e., non-random) case, we allow any operator, commutes translations, and couples only sites at finite distance each other. For example, single walk could be composed succession different shift coin operations in usual sense, lattice dimension dimension. find ballistic scaling, establish direct method for computing divided...

We study a spin-$\frac{1}{2}$12-particle moving on one-dimensional lattice subject to disorder induced by random, space-dependent quantum coin. The discrete time evolution is given family of random unitary walk operators, where the shift operation assumed be deterministic. Each coin an independent identically distributed variable with values in group two-dimensional matrices. derive sufficient conditions probability distribution coins such that system exhibits dynamical localization. Put...

We show that the presence of an interaction in quantum walk two atoms leads to formation a stable compound, molecular state. The wave function molecule decays exponentially relative position atoms; hence it constitutes true bound Furthermore, for certain class interactions, we develop effective theory and find dynamics is described by its own right. propose setup experimental realization as well sketch possibility observe quasi-particle effects many-body systems.

We study one-dimensional quantum walks in a homogenous electric field. The field is given by phase which depends linearly on position and applied after each step. long time propagation properties of this system, such as revivals, ballistic expansion, Anderson localization, depend very sensitively the value field, $\ensuremath{\Phi}$, e.g., whether $\ensuremath{\Phi}/(2\ensuremath{\pi})$ rational or irrational. relate these to continued fraction expansion When only with finite accuracy,...

We outline a theory of symmetry protected topological phases one-dimensional quantum walks. assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase classification by integer or binary indices extends known for translation invariant systems terms their band structure. However, our requires no invariance whatsoever, we define this general setting under arbitrary symmetric local perturbations, even those that cannot be...

With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about operations. However, current are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation turn it into new paradigm characterizing gate-sets. A single experiment-random sequence estimation-solves wealth estimation problems, with all complexity moved to classical post-processing. derive robust...

Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized allows for relatively resource economical estimation average gate fidelity gates from Clifford group, assuming identical noise levels all gates, making use suitable sequences randomly chosen gates. In this work, we report significant progress on randomized benchmarking, by showing that it can be applied individually a broad class outside even varying per gate. This is...

We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, invariance, gap condition, and some symmetry the tenfold way. The largely matches one recently obtained (arXiv:1611.04439) for similar setting leaving out invariance. However, case has finer distinctions, because may be connected only by breaking invariance along way, retaining an even number sites. Similarly, if are considered equivalent...

The first cases of COVID-19 caused by the SARS-CoV-2 virus were reported in China December 2019. disease has since spread globally. Many countries have instated measures to slow virus. Information about a country can inform gradual reopening and help avoid second wave infections. Our study focuses on Denmark, which is opening up when this performed (end-May 2020) after lockdown mid-March.We perform phylogenetic analysis 742 publicly available Danish genome sequences put them into context...

Describing a particle in an external electromagnetic field is basic task of quantum mechanics. The standard scheme for this known as "minimal coupling", and consists replacing the momentum operators Hamiltonian by modified ones with added vector potential. In lattice systems it not so clear how to do this, because there no continuous translation symmetry, hence are momenta. Moreover, when time also discrete, walk systems, Hamiltonian, only unitary step operator. We present unified framework...

Interacting quantum many-body systems are expected to thermalize, in the sense that evolution of local expectation values approaches a stationary value resembling thermal ensemble. This intuition is notably contradicted exhibiting localisation (MBL). In stark contrast non-interacting case Anderson localisation, entanglement states grows without limit over time, albeit slowly. this work, we establish novel link between information theory and notions condensed matter physics, capturing...

Abstract We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version minimal coupling principle. show that for all irrational absolutely continuous spectrum these systems is empty, prove Anderson localization almost (irrational) fields. This result closes gap which was left open in original study walks: characterization typical Additionally, we derive an analytic explicit expression Lyapunov...

This paper uncovers and exploits a link between central object in harmonic analysis, the so-called Schur functions, very hot topic of symmetry protected topological phases quantum matter. connection is found setting walks, i.e. analogs classical random walks. We prove that indices classifying walks are encoded by matrix functions built out walk. main result reduces calculation these to linear algebra problem: calculating finite-dimensional unitaries obtained evaluating such at points ±1 ....

Quantum hardware has the potential to efficiently solve computationally difficult problems in physics and chemistry reap enormous practical rewards. Analogue quantum simulation accomplishes this by using dynamics of a controlled many-body system mimic those another system; such method is feasible on near-term devices. We show that previous theoretical approaches analogue suffer from fundamental barriers which prohibit scalable experimental implementation. By introducing new mathematical...

Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if underlying graph contains cycle, e.g. as projected entangled pair (PEPS), then set tensor given bond dimension not closed. Its closure variety. Recent work has shown on boundary this variety can yield more efficient representations for physical interest, but it remained unclear how to systematically find optimize over such...