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The Exclusive-OR Sum-of-Product (ESOP) minimization problem has long been of interest to the research community because of its importance in classical logic design (including low-power design and design for test), reversible logic synthesis, and knowledge discovery, among other applications. However, no exact minimal minimization method has been presented for more than seven variables on arbitrary functions. This paper presents a novel quantum-classical hybrid algorithm for the exact minimal ESOP minimization of incompletely specified Boolean functions. This algorithm constructs oracles from sets of constraints and leverages the quantum speedup offered by Grover's algorithm to find solutions to these oracles, thereby improving over classical algorithms. Improved encoding of ESOP expressions results in substantially fewer decision variables compared to many existing algorithms for many classes of Boolean functions. This paper also extends the idea of exact minimal ESOP minimization to additionally minimize the cost of realizing an ESOP expression as a quantum circuit. To the extent of the authors' knowledge, such a method has never been published. This algorithm was tested on completely and incompletely specified Boolean functions via quantum simulation. |
