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Article
Quantum Science & Technology
Kazuya Kaneko et al.
Summary: This paper explores quantum algorithms for pricing financial derivatives and focuses on implementing more complex models, specifically the local volatility (LV) model. The authors compare two state preparation methods, amplitude encoding (AE) and pseudo-random number (PRN), and provide detailed circuit diagrams and resource estimations.
EPJ QUANTUM TECHNOLOGY
(2022)
Article
Physics, Multidisciplinary
Tudor Giurgica-Tiron et al.
Article
Quantum Science & Technology
Shouvanik Chakrabarti et al.
Summary: This study provides an upper bound on the resources needed for valuable quantum advantage in pricing derivatives, introducing a new method for quantum derivative pricing. While the current systems fall short of meeting these requirements, the estimates hope to guide future improvements in algorithms, implementations, and hardware architectures.
Article
Quantum Science & Technology
Dong An et al.
Summary: Inspired by recent progress in quantum algorithms for differential equations, this study focuses on stochastic differential equations (SDEs) and provides a quantum algorithm that improves the efficiency of multilevel Monte Carlo methods. Applications include computing expectation values of SDEs with increased precision in mathematical finance models, such as Black-Scholes and Local Volatility, using the same quantum algorithm for binomial option pricing models with improved performance.
Article
Computer Science, Hardware & Architecture
Daniel J. Egger et al.
Summary: This study introduces a quantum algorithm for efficiently estimating credit risk, particularly the economic capital requirement. By implementing and analyzing the scaling of the problem to a realistic size, estimates of the total number of required qubits, expected circuit depth, and runtime on future fault-tolerant quantum hardware are provided.
IEEE TRANSACTIONS ON COMPUTERS
(2021)
Article
Quantum Science & Technology
Dmitry Grinko et al.
Summary: The Iterative Quantum Amplitude Estimation (IQAE) is a new quantum algorithm that achieves quadratic speedup compared to classical Monte Carlo simulation and performs significantly better than other known QAE variants without Quantum Phase Estimation (QPE).
NPJ QUANTUM INFORMATION
(2021)
Article
Quantum Science & Technology
Carsten Blank et al.
Summary: Discrete stochastic processes (DSP) are widely used in modeling the dynamics of probabilistic systems, often analyzed using Monte-Carlo methods. A quantum algorithm for calculating the characteristic function of a DSP has been proposed, which grows linearly with the number of time steps and guarantees optimal variance without the need for importance sampling.
NPJ QUANTUM INFORMATION
(2021)
Article
Optics
Kenji Kubo et al.
Summary: A quantum-classical hybrid algorithm is proposed to solve Stochastic Differential Equations (SDEs) by approximating the target SDE with a trinomial tree structure and formulating it as the time-evolution of a quantum state embedding the probability distributions of the SDE variables. This approach enables the construction of simple quantum circuits for simulating the time evolution of the state for general SDEs, potentially achieving quantum speedup for expectation-value evaluations of the SDE variables.
Article
Quantum Science & Technology
Yohichi Suzuki et al.
QUANTUM INFORMATION PROCESSING
(2020)
Article
Quantum Science & Technology
Nikitas Stamatopoulos et al.
Article
Quantum Science & Technology
Niel de Beaudrap et al.
Article
Optics
Koichi Miyamoto et al.
Article
Quantum Science & Technology
Stefan Woerner et al.
NPJ QUANTUM INFORMATION
(2019)
Article
Quantum Science & Technology
John Preskill
Article
Multidisciplinary Sciences
Ashley Montanaro
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2015)
