Advanced Simulation of Quantum Computations

Abstract

Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum computers are in their infancy, a significant amount of research in this domain still relies on simulations of quantum computations on conventional machines. This causes a significant complexity which current state-of-the-art simulators try to tackle with a rather straight forward array-based representation and by applying massive hardware power. There also exist solutions based on decision diagrams (i.e. graph-based approaches) that try to tackle the exponential complexity by exploiting redundancies in quantum states and operations. However, these existing approaches do not fully exploit redundancies that are actually present. In this work, we revisit the basics of quantum computation, investigate how corresponding quantum states and quantum operations can be represented even more compactly, and, eventually, simulated in a more efficient fashion. This leads to a new graph-based simulation approach which outperforms state-of-the-art simulators (array-based as well as graph-based). Experimental evaluations show that the proposed solution is capable of simulating quantum computations for more qubits than before, and in significantly less run-time (several magnitudes faster compared to previously proposed simulators). An implementation of the proposed simulator is publicly available online at http://iic.jku.at/eda/research/quantum_simulation.