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Quantum hardware has the potential to efficiently solve computationally difficult problems in physics and chemistry to reap enormous practical rewards. Analogue quantum simulation accomplishes this by using the dynamics of a controlled many-body system to mimic those of another system; such a method is feasible on near-term devices. We show that previous theoretical approaches to analogue quantum simulation suffer from fundamental barriers which prohibit scalable experimental implementation. By introducing a new mathematical framework and going beyond the usual toolbox of Hamiltonian complexity theory with an additional resource of engineered dissipation, we show that these barriers can be overcome. This provides a powerful new perspective for the rigorous study of analogue quantum simulators. Analogue quantum simulation has looser experimental requirements than its digital counterpart, but rigorous theoretical results on the capabilities of realisable experiments are scarce. Here, the authors fill this gap by proposing an alternative mathematical framework, and showing how to overcome barriers to scalable implementations using additional resources such as engineered dissipation. [ABSTRACT FROM AUTHOR]

Characterizing the interactions and dynamics of quantum mechanical systems is an essential task in developing quantum technologies. We propose an efficient protocol based on the estimation of the time-derivatives of few qubit observables using polynomial interpolation for characterizing the underlying Hamiltonian dynamics and Markovian noise of a multi-qubit device. For finite range dynamics, our protocol exponentially relaxes the necessary time-resolution of the measurements and quadratically reduces the overall sample complexity compared to previous approaches. Furthermore, we show that our protocol can characterize the dynamics of systems with algebraically decaying interactions. The implementation of the protocol requires only the preparation of product states and single-qubit measurements. Furthermore, we improve a shadow tomography method for quantum channels that is of independent interest and discuss the robustness of the protocol to various errors. This protocol can be used to parallelize the learning of the Hamiltonian, rendering it applicable for the characterization of both current and future quantum devices. Learning Hamiltonians or Lindbladians of quantum systems from experimental data is important for characterization of interactions and noise processes in quantum devices. Here the authors propose an efficient protocol based on estimating time derivatives using multiple temporal sampling points and robust polynomial interpolation. [ABSTRACT FROM AUTHOR]

The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single-particle picture, be supported in the absolutely continuous spectrum of the single-particle Hamiltonian. We show in this note that if a free fermion system on the two-dimensional lattice is gapped in the bulk and has a non-vanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous. [ABSTRACT FROM AUTHOR]

We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen’s theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichotomies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Rényi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing. [ABSTRACT FROM AUTHOR]

Background: The first cases of COVID-19 caused by the SARS-CoV-2 virus were reported in China in December 2019. The disease has since spread globally. Many countries have instated measures to slow the spread of the virus. Information about the spread of the virus in a country can inform the gradual reopening of a country and help to avoid a second wave of infections. Our study focuses on Denmark, which is opening up when this study is performed (end-May 2020) after a lockdown in mid-March. Methods: We perform a phylogenetic analysis of 742 publicly available Danish SARS-CoV-2 genome sequences and put them into context using sequences from other countries. Results: Our findings are consistent with several introductions of the virus to Denmark from independent sources. We identify several chains of mutations that occurred in Denmark. In at least one case we find evidence that the virus spread from Denmark to other countries. A number of the mutations found in Denmark are non-synonymous, and in general there is a considerable variety of strains. The proportions of the most common haplotypes remain stable after lockdown. Conclusion: Employing phylogenetic methods on Danish genome sequences of SARS-CoV-2, we exemplify how genetic data can be used to trace the introduction of a virus to a country. This provides alternative means for verifying existing assumptions. For example, our analysis supports the hypothesis that the virus was brought to Denmark by skiers returning from Ischgl. On the other hand, we identify transmission routes which suggest that Denmark was part of a network of countries among which the virus was being transmitted. This challenges the common narrative that Denmark only got infected from abroad. Our analysis concerning the ratio of haplotypes does not indicate that the major haplotypes appearing in Denmark have a different degree of virality. [ABSTRACT FROM AUTHOR]

A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analog of such a theory. Specifically, we consider local dissipative dynamics preparing an equilibrium steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter.We show that for all such processes, there exist asymptotically stationary symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation. [ABSTRACT FROM AUTHOR]

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

We study a spin-12-particle moving on a one-dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operation is assumed to be deterministic. Each coin is an independent identically distributed random variable with values in the group of two-dimensional unitary matrices. We derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization. Put differently, the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance. Our findings imply that this effect takes place if the coin is chosen at random from the Haar measure, or some measure continuous with respect to it, but also for a class of discrete probability measures which support consists of two coins, one of them being the Hadamard coin. [ABSTRACT FROM AUTHOR]