Investigation of strongly interacting quantum field theories (QFTs) remains one of the outstanding challenges of modern physics. Quantum simulation has the potential to be a crucial technique towards solving this problem. By harnessing the power of quantum information processing, quantum simulation can potentially perform tasks deemed intractable by the classical information processing paradigm. In this talk, I will describe analog quantum simulators for strongly interacting QFTs using mesoscopic quantum electronic circuit lattices. The tunable, robust and dispersive Josephson nonlinearity gives rise to the nonlinear interactions in these QFTs. I will concentrate on the quantum sine- Gordon model and its nontrivial generalizations. In particular, I will show that a two-field generalization, the double sine-Gordon model, is realizable with quantum circuits. In contrast to the sine-Gordon QFT, this model can be purely quantum-integrable, when it does not admit a semiclassical description – a property that is generic to many multifield QFTs. In addition to being experimentally viable with modern-day superconducting circuit technology, the quantum circuits provide lattice-regularized models of these QFTs amenable for numerical simulations. I will present a density matrix renormalization group and exact Bethe ansatz computation results on the thermodynamic properties of the aforementioned QFTs.