High-Speed Algorithm for Quantum Monte Carlo Simulation

Mihail Marcu, Jürgen Müller, Franz-Karl Schmatzer

Gen Chen, Lin Wang

Since the beginning of the 21st century, the scale and complexity of financial derivatives have increased significantly. Meanwhile, the pricing models of derivatives have become increasingly complex, and have involved larger-scale data, posing unprecedented challenges to algorithms and computing speed. Although classical computing can still solve the pricing problem of some complex derivatives by adopting the big data simulation algorithms, its speed has become more and more difficult to meet the needs of real-time computing. In recent years, the emerging quantum computing makes full use of the advantages of quantum superposition to improve the computing speed and accuracy. It has been proven to be an efficient computing mode in big data simulation. This paper takes the pricing of European options and defaultable bonds as examples to explore the application of Quantum Monte Carlo Simulation of complicated derivative pricing in big data. The innovative comprehensive method of pricing derivatives by Quantum Monte Carlo Simulation provides new development for the application of quantum computing in the pricing of complicated financial derivatives (taking defaultable bond as example) with big data simulation. In the case of defaultable bond pricing, the Quantum Amplitude Estimation has been employed to speed up the Monte Carlo Simulation and the price of it has been successfully obtained with at least the same accuracy, which demonstrates that the Quantum Monte Carlo Simulation is a prospective approach to price the complicated derivatives based on the big data since the quantum bits has dramatically increased.

Ye Luo, Jeongnim Kim, Paul R. C. Kent

For quantum Monte Carlo simulations of molecular systems or supercells with thousands of electrons, matrix operations related to Slater determinants lead the computational cost. McDaniel et al. [ J. Chem. Phys. 2017, 147, 174107] proposed a delayed update algorithm to increase computational efficiency by using matrix–matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman–Morrison–Woodbury formula remained a bottleneck. In this work, we introduce an improved algorithm for CPUs and GPUs that (1) reduces this bottleneck by iteratively updating the intermediate matrices and (2) is efficient at any acceptance ratio, with no cost for rejected moves on CPUs and minimal cost on GPUs. We show the full scheme of integrating the delayed update algorithm into a single-electron move. The high efficiency of our algorithm is demonstrated on CPUs and GPUs for a 512 atom/6144 valence electron calculation, with 12× and 2× overall speed-up compared to traditional rank-1 update schemes in diffusion quantum Monte Carlo, respectively.

Matthias Troyer, Philipp Werner, Adolfo Avella +1 more

Yutaka Okabe, Macoto Kikuchi

We implement a high-speed algorithm for Monte Carlo simulation of the quantum spin system using the Suzuki-Trotter formula. The calculation is fully vectorized by decomposing into appropriate sublattices. We introduce a ``plaquette'' spin representation using logical commands. In order to check the efficiency of our algorithm, we study the one-dimensional XY model for the Trotter number m\ensuremath{\le}32. Excellent agreement with the exact solution is obtained.

Hyeonseong Jung, Shiho Kim