1Goldman, Sachs & Co., New York, NY
2University of Maryland, College Park, MD
3IBM Quantum, IBM Research – Zurich
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Abstract
We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing – the $textit{re-parameterization method}$ – that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 8k logical qubits and a T-depth of 54 million. We estimate that quantum advantage would require executing this program at the order of a second. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.
Featured image: Loading the probability distribution for derivative pricing with the re-parameterization method takes variationally-trained standard normal gaussians and distributes the probability mass appropriately by re-parameterizing the basis states corresponding to asset prices.
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[2] Alexandru Paler, Oumarou Oumarou, and Robert Basmadjian, “On the realistic worst case analysis of quantum arithmetic circuits”, arXiv:2101.04764.
[3] Prasanth Shyamsundar, “Non-Boolean Quantum Amplitude Amplification and Quantum Mean Estimation”, arXiv:2102.04975.
[4] Andriy Miranskyy, Lei Zhang, and Javad Doliskani, “On Testing and Debugging Quantum Software”, arXiv:2103.09172.
[5] Paula García-Molina, Javier Rodríguez-Mediavilla, and Juan José García-Ripoll, “Solving partial differential equations in quantum computers”, arXiv:2104.02668.
The above citations are from SAO/NASA ADS (last updated successfully 2021-06-01 15:59:31). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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Source: https://quantum-journal.org/papers/q-2021-06-01-463/
