Michael Bremner: Average-case Complexity Vs. Approx. Simulation of Commuting Quantum Computations
0Michael Bremner (University of Technology, Sydney)
Average-case Complexity Versus Approximate Simulation of Commuting Quantum Computations
QuICS Workshop on the Frontiers of Quantum Information and Computer Science (September 30, 2015)
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, while 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 generalisations of the Boson Sampling problem that avoid the so-called permanent anticoncentration conjecture.