Approximate Simulation of Circuits with Probabilistic Behavior

Various emerging technologies promise advantages with respect to integration density, performance or power consumption, at the cost of approximate or probabilistic behavior. Approximate computing, where limited computational inaccuracies are tolerated at the system or application level is therefore of increasing interest. This paper investigates the use of stochastic computing (SC) as a tool for approximate simulation of probabilistic behavior. SC has the advantage of processing probabilities directly at very low hardware cost. It also allows accuracy to be traded for n.m-time in a natural way (progressive precision). As a target technology to be simulated, we choose quantum computing circuits, whose behavior is inherently probabilistic and cannot be efficiently simulated by conventional (classical) means. We show how complex operations such as superposition and entanglement can be handled by SC. Finally, we report experimental results on software-based simulation of representative quantum circuits, both stand-alone and FPGA-supported. The results show that the SC implementations are orders of magnitude more compact than those based on classical circuits. Accurate results may require very long simulation runs, but run-times can be reduced by exploiting SC's progressive precision property.