title: Average-Case 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 average-case 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 complex-temperature partition function for random instances of the Ising model; the other concerns approximating the number of zeroes of random low-degree polynomials. We observe that both conjectures can be shown to be valid in the setting of worst-case complexity. We arrive at these conjectures by deriving spin-based generalizations of the boson sampling problem that avoid the so-called permanent anticoncentration conjecture.
authors: Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW 2007, Australia.
authors: Michael J
authors: MJ
authors: Bremner
authors: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.
authors: Ashley
authors: A
authors: Montanaro
authors: CESG, Hubble Road, Cheltenham GL51 0EX, United Kingdom.
authors: Dan J
authors: DJ
authors: Shepherd