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Register a new userMemory-efficient tracking of complex temporal and symbolic dynamics with quantum simulators
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Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of the system than the optimal classical models. We extend these results to general temporal and symbolic dynamics. Our systematic protocol for quantum model construction relies only on an elementary description of the dynamics of the process. This circumvents restrictions on corresponding classical construction protocols, and allows for a broader range of processes to be modelled efficiently. We illustrate our method with an example exhibiting an apparent unbounded memory advantage of the quantum model compared to its optimal classical counterpart.
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The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (pSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol which allows the measurement of SFF and pSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with simulations for Hamiltonian and Floquet many-body spin-systems.
Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of inter-contact durations and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic Susceptible-Infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of inter-contact durations and of the numbers of contacts per link.
A growing body of work has established the modelling of stochastic processes as a promising area of application for quantum techologies; it has been shown that quantum models are able to replicate the future statistics of a stochastic process whilst retaining less information about the past than any classical model must -- even for a purely classical process. Such memory-efficient models open a potential future route to study complex systems in greater detail than ever before, and suggest profound consequences for our notions of structure in their dynamics. Yet, to date methods for constructing these quantum models are based on having a prior knowledge of the optimal classical model. Here, we introduce a protocol for blind inference of the memory structure of quantum models -- tailored to take advantage of quantum features -- direct from time-series data, in the process highlighting the robustness of their structure to noise. This in turn provides a way to construct memory-efficient quantum models of stochastic processes whilst circumventing certain drawbacks that manifest solely as a result of classical information processing in classical inference protocols.
We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in quantum-ness of the theory, or by a scaling the Ising couplings up or down. This behaviour is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimising several increasingly hard two dimensional potentials. For all the potentials we find the general behaviour that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimisation very markedly better than any of these classical techniques. A quantum anneal can be designed so that the system almost never gets trapped in a false minimum, and rapidly and successfully minimises the potentials.
Gauge theories are the cornerstone of our understanding of fundamental interactions among particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers, and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. Here, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a $U(1)$ lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string-breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits, and connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics
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