TY - JOUR

T1 - Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicators

AU - Nakaji, Kouhei

AU - Uno, Shumpei

AU - Suzuki, Yohichi

AU - Raymond, Rudy

AU - Onodera, Tamiya

AU - Tanaka, Tomoki

AU - Tezuka, Hiroyuki

AU - Mitsuda, Naoki

AU - Yamamoto, Naoki

N1 - Publisher Copyright:
© 2022 authors. Published by the American Physical Society.

PY - 2022/6

Y1 - 2022/6

N2 - Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can load only the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement: the standard computational-basis measurement plus the measurement in the Hadamard-transformed basis, introduced in order to handle the sign of the data components. The variational algorithm changes the circuit parameters so as to minimize the sum of two costs corresponding to those two measurement basis, both of which are given by the efficiently computable maximum mean discrepancy. We also consider the problem of constructing the singular value decomposition entropy via the stock market data set to give a financial market indicator; a quantum algorithm (the variational singular value decomposition algorithm) is known to produce a solution faster than classical, which yet requires the sign-dependent amplitude encoding. We demonstrate, with an in-depth numerical analysis, that our algorithm realizes loading of time series of real stock prices on quantum state with small approximation error, and thereby it enables constructing an indicator of the financial market based on the stock prices.

AB - Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can load only the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement: the standard computational-basis measurement plus the measurement in the Hadamard-transformed basis, introduced in order to handle the sign of the data components. The variational algorithm changes the circuit parameters so as to minimize the sum of two costs corresponding to those two measurement basis, both of which are given by the efficiently computable maximum mean discrepancy. We also consider the problem of constructing the singular value decomposition entropy via the stock market data set to give a financial market indicator; a quantum algorithm (the variational singular value decomposition algorithm) is known to produce a solution faster than classical, which yet requires the sign-dependent amplitude encoding. We demonstrate, with an in-depth numerical analysis, that our algorithm realizes loading of time series of real stock prices on quantum state with small approximation error, and thereby it enables constructing an indicator of the financial market based on the stock prices.

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U2 - 10.1103/PhysRevResearch.4.023136

DO - 10.1103/PhysRevResearch.4.023136

M3 - Article

AN - SCOPUS:85132100856

SN - 2643-1564

VL - 4

JO - Physical Review Research

JF - Physical Review Research

IS - 2

M1 - 023136

ER -