That would be very surprising. They show in this work that their problem is complete for the complexity class BQP. That means that if you can solve it on a classical computer (analog or not) in polynomial time you get (for free) classical polynomial-time algorithms for solving a bunch of problems we don't currently have classical poly-time algorithms for.
Most surpisingly this would include the hidden subgroup problem and hence give you a classical poly-time algorithm for integer factorization.
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I suspect an analog computer would work just as well for modeling coupled harmonic oscillators.
That would be very surprising. They show in this work that their problem is complete for the complexity class BQP. That means that if you can solve it on a classical computer (analog or not) in polynomial time you get (for free) classical polynomial-time algorithms for solving a bunch of problems we don't currently have classical poly-time algorithms for.
Most surpisingly this would include the hidden subgroup problem and hence give you a classical poly-time algorithm for integer factorization.