Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on Quantum Signal Processing (QSP) to encode financial derivative payoffs directly into quantum amplitudes, alleviating the quantum circuits from the burden of costly quantum arithmetic. Compared to current state-of-the-art approaches in the literature, we find that for derivative contracts of practical interest, the application of QSP significantly reduces the required resources across all metrics considered, most notably the total number of T-gates by $\sim 16$x and the number of logical qubits by $\sim 4$x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of $\sim 5$x. Overall, we find that quantum advantage will require $4.7$k logical qubits, and quantum devices that can execute $10^9$ T-gates at a rate of $45$MHz. While in this work we focus specifically on the payoff component of the derivative pricing process where the method we present is most readily applicable, similar techniques can be employed to further reduce the resources in other applications, such as state preparation.

中文翻译：

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使用量子信号处理的衍生品定价

量子计算机上的金融衍生品定价通常包括量子算术组件，这些组件对相应电路所需的量子资源有很大贡献。在这篇手稿中，我们介绍了一种基于量子信号处理（QSP）的方法，将金融衍生品收益直接编码为量子振幅，从而减轻量子电路昂贵的量子算术的负担。与文献中当前最先进的方法相比，我们发现，对于具有实际利益的衍生品合约，QSP 的应用显着减少了所有考虑的指标所需的资源，最显着的是 T-gate 总数减少了 $ \sim 16$x 和逻辑量子位的数量 $\sim 4$x。此外，我们估计量子优势所需的逻辑时钟速率也降低了 $\sim 5$x 倍。总体而言，我们发现量子优势将需要 4.7$k 美元的逻辑量子位，以及能够以 45$MHz 的速率执行 $10^9$ T 门的量子设备。虽然在这项工作中，我们特别关注衍生品定价过程的收益部分，其中我们提出的方法最容易适用，但可以采用类似的技术来进一步减少其他应用程序（例如状态准备）中的资源。