Abstract
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.
Highlights
Quantum computers are expected to allow us to perform high-speed computations over classical computations for problems in a wide range of scientific and technological fields
We focus on the amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications, e.g., in chemistry [7,8], finance [9,10], and machine learning [11,12,13,14]
We proposed a quantum amplitude estimation algorithm achieving quantum speedup by reducing controlled gates with maximum likelihood (ML) estimation
Summary
Quantum computers are expected to allow us to perform high-speed computations over classical computations for problems in a wide range of scientific and technological fields. Owing to the ubiquitous nature of the eigenvalue estimation problem, some versions of the phase estimation algorithm suitable for NISQ devices [18,19,20,21,22] have been proposed (with the last one appeared slightly after ours), and they all rely on classical post-processing statistics such as the Bayes method. These modified phase estimation algorithms as well as the original scheme [17] still involve many controlled operations The paper Ref. [25] gave an amplitude estimation scheme that employs a Bayes rule together with applying random Unitary operations (subjected to the Haar measure) to ideally realize the quadratic speedup, without a controlled Unitary operation; this scheme is applicable to low-dimensional quantum circuits, due to the hardness to implement the random Unitaries
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