Asynchronous Operations on Qubits in Distributed Simulation Environments using QooSim

Operations on a pair of entangled qubits are conventionally presented as the application of the tensor product of operations. The tensor product is linearly extended to act synchronously across the entire entangled system. When simulating an entangled system, the conventional approach is possible and practical if both parts of the entangled system exist within the same physical simulator. However, if we wish to simulate an entangled system across a distributed network, sending half of the entangled pair to another simulator on another computer system, the synchronous approach becomes difficult. In the first part of this paper, we demonstrate a method of simulating operations on entangled states in a distributed environment which is equivalent to the conventional approach. The advantage to our approach is that we can simulate distributed quantum systems on physically distributed hardware. Such a system advances the possibilities of demonstrating distributed quantum algorithms for research, teaching, and learning. Further, the security of quantum key exchange depends on successfully detecting the presence of an eavesdropper. In most cases this is done by comparing the errors introduced by an eavesdropper with the channel error rate. In other words, the communicating parties must tolerate some errors without losing a significant amount of key information. In the second part of this paper, we characterize the effects of amplitude damping errors on quantum key distribution protocols and explore allowable tolerances. Through simulations we observe that the effect of these errors, in some cases, is highly dependent on where the eavesdropper is located on the channel. In this paper, we also briefly describe the development of a new quantum simulation library called QooSim.