AverageCase Complexity Versus Approximate Simulation of Commuting Quantum Computations
Abstract
We use the class of commuting quantum computations known as IQP (instantaneous quantum polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible averagecase hardness conjectures holds, then IQP computations are hard to simulate classically up to constant additive error. One conjecture relates to the hardness of estimating the complextemperature partition function for random instances of the Ising model; the other concerns approximating the number of zeroes of random lowdegree polynomials. We observe that both conjectures can be shown to be valid in the setting of worstcase complexity. We arrive at these conjectures by deriving spinbased generalizations of the boson sampling problem that avoid the socalled permanent anticoncentration conjecture.
 Publication:

Physical Review Letters
 Pub Date:
 August 2016
 DOI:
 10.1103/PhysRevLett.117.080501
 arXiv:
 arXiv:1504.07999
 Bibcode:
 2016PhRvL.117h0501B
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity
 EPrint:
 This version is arguably easier to read than v1. Trust us, we argued about it. 4+1+5 pages, RevTex 4.1