Application of time-series quantum generative model to financial data

TL;DR

A time-series generative model was applied as a quantum generative model to actual financial data and it was observed that fewer parameter values were required compared with the classical method.

Abstract

Despite proposing a quantum generative model for time series that successfully learns correlated series with multiple Brownian motions, the model has not been adapted and evaluated for financial problems. In this study, a time-series generative model was applied as a quantum generative model to actual financial data. Future data for two correlated time series were generated and compared with classical methods such as long short-term memory and vector autoregression. Furthermore, numerical experiments were performed to complete missing values. Based on the results, we evaluated the practical applications of the time-series quantum generation model. It was observed that fewer parameter values were required compared with the classical method. In addition, the quantum time-series generation model was feasible for both stationary and nonstationary data. These results suggest that several parameters can be applied to various types of time-series data.

Figures (6)

• Figure 1: (a) GOOG and IBM stock prices for 2016–2020 ( Close ). GOOG exhibits an increasing trend, whereas IBM exhibits a decreasing trend. (b) Logarithmic difference of (a. The logarithmic difference makes it a stationary time series.
• Figure 2: Quantum circuits for numerical experiments. The discretized states of GOOG and IBM are encoded as bit strings as $\bm{b}_{GOOG}=b^{(1)}_1b^{(1)}_2$ and $\bm{b}_{IBM}=b^{(2)}_1b^{(2)}_2$, respectively. Considering the number of $k$ steps, the state distribution after $k$ steps can be obtained through measurement.
• Figure 5: Variation of loss at 300 steps. (a) and (b) show the time-series quantum generative model and the loss of LSTM. The time-series quantum generative model converges faster than LSTM.
• Figure 6: Accumulation of Manhattan distance at each step. (a) and (b) show the results for GOOGLE and IBM, respectively. Both of these are linearly increasing.
• Figure 7: von Neumann entropy between GOOGLE and the other systems. Statistics were obtained by sampling from all states at $t=1–5$. Here max is the case of maximum entanglement. We confirmed the existence of entanglement in all datasets.