Efficient classical simulation of a variant of cluster state quantum computation

Abstract

Quantum computers are known for their ability to solve some computational problems faster than classical computers. There is a race to build quantum computers because it is believed they might be better than classical; but it remains unknown whether quantum computers are in fact better than conventional computers. To understand this problem, we develop a new method of classically simulating certain types of quantum system that are previously unknown to be efficiently simulatable on classical computers. We adjust a part of cluster state quantum computation to study the computational power and we demonstrate that there is a finite region of pure states j i around the Z-eigenstates for which the setup can be efficiently simulated classically, given that the measurements are limited to Z and X - Y plane measurements. This classical simulation works by considering alternative local state spaces that we called "cylinders" and different notion of entanglement to normal quantum entanglement. Then, we work out similar regions for states created using other diagonal gates instead of the CZ. These diagonal gates are represented by V (θ) = |0><0⊗I+|1><1|⊗ Zθ where Zθ = |0><0| + eiθ|1><1|. It turns out that almost all inputs are classically simulatable when θ is small. In addition, we nd that classical simulation also works by considering new type of non-quantum state spaces other than cylinders and maintaining non-entangled representation by growing the size of these state spaces. We search over some state spaces to try optimize our classical simulation and it turns out that, among the state spaces that we searched through, the cylinder is the most optimal state space. And finally, we will look at a coarse graining version of construction which increases the efficiently simulatable region.