  Simulating quantum many-body systems on a classical computer generally
requires a computational cost that grows exponential with the number of
particles. This computational complexity has been the main obstacle to
understanding various fundamental emergent phenomena in condensed matters such
as high-Tc superconductivity and the fractional quantum-Hall effect. The
difficulty arises because even the simplest models that are proposed to capture
those phenomena cannot be simulated on a classical computer. Recognizing this
problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely
new type of machine that exploits quantum superposition and operates by
individually manipulating its constituting quantum particles and their
interactions. Recent advances in various experimental platforms from cold atoms
in optical lattices, trapped ions, to solid-state systems have brought the idea
of Feynman to the realm of reality. Among those, interacting photons in
superconducting circuits has been one of the promising platforms thanks to
their local controllability and long coherence times. Early theoretical
proposals have shown possibilities to realize quantum many-body phenomena of
light using coupled cavity arrays such as Mott to superfluid transitions and
fractional quantum Hall states. Start-of-the-art experiments include
realization of interacting chiral edge states and stroboscopic signatures of
localization of interacting photons in a three-site and a nine-site
superconducting circuit, respectively. Interacting photons also serve as a
natural platform to simulate driven-dissipative quantum many-body phenomena. A
72-site superconducting circuit has also recently been fabricated to study a
dissipative phase transition of light.

Quantum Physics