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Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions for one of the paradigmatic models of an integrable quantum field theory: the quantum sine-Gordon (qSG) model in 1+1 space-time dimensions. We analyze the lattice model using the density matrix renormalization group technique and benchmark our numerical results with existing Bethe ansatz computations. Furthermore, we perform analytical form-factor calculations for the two-point correlation function of vertex operators, which closely agree with our numerical computations. Finally, we compute the entanglement spectrum of the qSG model. We compare our results with those obtained using the integrable lattice-regularization based on the quantum XYZ chain and show that the quantum circuit model is less susceptible to corrections to scaling compared to the XYZ chain. We provide numerical evidence that the parameters required to realize the qSG model are accessible with modern-day superconducting circuit technology, thus providing additional credence towards the viability of the latter platform for simulating strongly interacting quantum field theories. 

Motivated by the question of how inflation started, we propose a Euclidean preparation of an asymptotically AdS2 spacetime that contains an inflating dS2 bubble. The setup can be embedded in a four dimensional theory with a Minkowski vacuum and a false vacuum. AdS2 times 2-sphere approximate the near horizon geometry of a 4d near-extremal RN wormhole. Likewise, in the false vacuum the near-horizon geometry of a near-extremal black hole is approximately dS2 times 2-sphere. We interpret the Euclidean solution as describing the decay of an excitation inside the wormhole to a false vacuum bubble. The result is an inflating region inside a non-traversable asymptotically Minkowski wormhole.

Despite decades of theoretical work, the physical realization of topological order, outside of the fractional quantum Hall effect, has proved to be an elusive goal. Even the simplest example of a time-reversal symmetric topological order, as encountered in the paradigmatic toric code, awaits experimental realization. Key challenges include the lack of physically realistic models in these phases, and of ways to probe their defining properties. I will discuss a simple `Rydberg blockade' model, and describe numerical results that point to (i) a ground state with toric code topological order that could potentially be realized in experiment and (ii) ``smoking gun'' signatures of the phase which be accessed using a dynamic protocol. I will also briefly discuss how a topological qubit can be constructed in this platform by tuning boundaries as well as implications for constructing fault-tolerant quantum memories. Time permitting, a different platform for realizing exotic phases, magic-angle graphene and the special features of its band structure will be described, which make it a prime candidate for realizing fractional quantum Hall topological order even in the absence of a magnetic field.

References: arXiv:2011.12310. and arXiv:1912.09634