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Applications of the quantum algorithm for Monte Carlo simulation to pricingof financial derivatives have been discussed in previous papers. However, up tonow, the pricing model discussed in such papers is Black-Scholes model, whichis important but simple. Therefore, it is motivating to consider how toimplement more complex models used in practice in financial institutions. Inthis paper, we then consider the local volatility (LV) model, in which thevolatility of the underlying asset price depends on the price and time. Wepresent two types of implementation. One is the register-per-RN way, which isadopted in most of previous papers. In this way, each of random numbers (RNs)required to generate a path of the asset price is generated on a separatedregister, so the required qubit number increases in proportion to the number ofRNs. The other is the PRN-on-a-register way, which is proposed in the author'sprevious work. In this way, a sequence of pseudo-random numbers (PRNs)generated on a register is used to generate paths of the asset price, so therequired qubit number is reduced with a trade-off against circuit depth. Wepresent circuit diagrams for these two implementations in detail and estimaterequired resources: qubit number and T-count.

Quantum Pricing with a Smile: Implementation of Local Volatility Model on Quantum Computer