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where is the thermal di usivity. Its applications are of fundamental importance in most branches of physics and engineering. Black-Scholes NISQ [FJO21; MK22], FTol Num [JLY22b; An+21]. The Black Scholes equation is a PDE which describes the price of the option V (S, t) over time t and price of underlying asset S(t),r is the force of interest , is the annualized drift rate of S, and is the standard deviation of the stock s returns.