As a newbie to Quantum, I was reading some of the articles and ran into a no-fast-forwarding theorem, which is described "Simulating the dynamics of a quantum system for time T typically requires Ω(T) gates so that a generic Hamiltonian evolution cannot be achieved in sublinear time. This result is known as the “no fast-forwarding theorem”, and holds both for a typical unknown Hamiltonian and for the query model setting"

Does this mean that "there won't be any shorter-time algorithm than the required T? I don't think I fully appreciate the implication or practical meaning of this.

Any help would be appreciated

  • 4
    $\begingroup$ There may be special classes of Hamiltonians that can be simulated by shorter time algorithms. For example, see this paper (arxiv.org/abs/1610.09619). But, as this paper proves, if all generic physically realizable Hamiltonians can be fast-forwarded, then BQP=PSPACE, which is thought to be highly unlikely. $\endgroup$
    – BlackHat18
    Jul 13, 2021 at 4:54

1 Answer 1


In simple words, it means you can't simulate a quantum system faster than time evolves it. However, if you have an analytical solution to the system, you can get the answer faster in theory. As an example consider a simple pendulum that you want to simulate for $t= 5$ sec. If you do it physically with an actual pendulum you have to wait for $5$ sec to get the results. But we already know its analytical solution and can predict its evolution with certainty using mathematical equations. So we can simulate the same on a computer in less than a sec. However, for most natural processes this is not the case, specifically complicated Hamiltonians.


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