Random Quantum Circuits and Their Simulation Complexity: An Analysis With Statistical Mechanics

Alexander M. Dalzell
Random circuit simulation, the task of replicating the output of a randomly chosen noiseless quantum computation, has been proposed as a path toward achieving quantum advantage: it is believed to be easy for quantum devices, but hard for classical ones. This thesis scrutinizes both sides of this belief. On the one hand, we investigate whether the task is classically hard—we find that, in certain non-trivial cases, it can actually be easy, complicating a potential general...
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