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The interplay of quantum fluctuations and interactions can yield novel quantum phases of matter with fascinating properties. Understanding the physics of such systems is a very challenging problem as it requires to solve quantum many body problems—which are generically exponentially hard to solve on classical computers. In this context, universal quantum computers are potentially an ideal setting for simulating the emergent quantum many-body physics. In this talk, I will discuss two different classes of quantum phases: First, we consider symmetry protected topological (SPT) phases and show that a topological phase transitions can be simulated using shallow circuits. We then utilize quantum convolutional neural networks (QCNNs) as classifiers and introduce an efficient framework to train them. Second, we focus on the realization of topological ordered phases and simulate the braiding of anyons. Taking into account additional symmetries, we then investigate phase transitions between different symmetry enriched topological (SET) phases.

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Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

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Topological strings are well understood in perturbation theory, but their non-perturbative structure has been the subject of much work and speculation. A useful approach to this problem is to unveil the non-perturbative sectors of the theory by looking at the large order behavior of the perturbative series. This approach can be formulated in a mathematically rigorous way by using the theory of resurgence. In this talk I review the basic ideas behind this approach and I show that it can be successfully applied to topological string theory on arbitrary Calabi-Yau threefolds. Thsee methods lead, not only to explicit non-perturbative topological string amplitudes, but also to a conjecture relating the “invariants” of the theory of resurgence (also known as Stokes constants) to BPS invariants. Physically, this conjecture implies that the large order behavior of the topological string perturbative series contains information about the spectrum of stable D-brane sectors.

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Besides providing a possible explanation to the strong CP problem and dark matter, the QCD axion possesses a rich cosmology. For example, if PQ breaking occurs after inflation, then axion cosmic strings form. Near the QCD phase transition, every axion string become attached to a domain wall which pull on the strings and cause the string-wall network to decay. While every string becomes attached to a domain wall, it is possible, though rare, to form an enclosed domain wall that is not attached to any axion string. These enclosed domain walls collapse under their own self tension, compressing a large amount of energy into a small volume and thereby potentially forming a primordial black hole. In this talk, I will discuss the abundance of enclosed domain walls, their dynamics of collapse, the efficiency of black hole formation, and their relic abundance. For sufficiently large axion decay constants, there may be an observable gravitational lensing signal at future lensing telescopes, especially in models with axion-like-particles.

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