scholarly journals Quantum amplitude estimation algorithms on IBM quantum devices

2020 ◽  
Author(s):  
Pooja Rao ◽  
Kwangmin Yu ◽  
Hyunkyung Lim ◽  
Dasol Jin ◽  
Deokkyu Choi
Keyword(s):  
Quantum Devices ◽  
Estimation Algorithms ◽  
Amplitude Estimation ◽  
Quantum Amplitude

scholarly journals Amplitude estimation without phase estimation

2020 ◽  
Vol 19 (2) ◽  
Author(s):  
Yohichi Suzuki ◽  
Shumpei Uno ◽  
Rudy Raymond ◽  
Tomoki Tanaka ◽  
Tamiya Onodera ◽  
...  
Keyword(s):  
Measurement Data ◽  
Likelihood Estimation ◽  
Estimation Algorithm ◽  
Quantum Circuits ◽  
Phase Estimation ◽  
Amplitude Estimation ◽  
Quantum Amplitude ◽  
Phase Estimation Algorithm ◽  
Near Term ◽  
Quantum Speedup

AbstractThis 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.

scholarly journals Noisy quantum amplitude estimation without noise estimation

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Tomoki Tanaka ◽  
Shumpei Uno ◽  
Tamiya Onodera ◽  
Naoki Yamamoto ◽  
Yohichi Suzuki
Keyword(s):  
Noise Estimation ◽  
Amplitude Estimation ◽  
Quantum Amplitude

scholarly journals Linear regression by quantum amplitude estimation and its extension to convex optimization

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Kazuya Kaneko ◽  
Koichi Miyamoto ◽  
Naoyuki Takeda ◽  
Kazuyoshi Yoshino
Keyword(s):  
Linear Regression ◽  
Convex Optimization ◽  
Amplitude Estimation ◽  
Quantum Amplitude

scholarly journals Iterative quantum amplitude estimation

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Dmitry Grinko ◽  
Julien Gacon ◽  
Christa Zoufal ◽  
Stefan Woerner
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Empirical Study ◽  
Estimation Accuracy ◽  
Phase Estimation ◽  
Rigorous Analysis ◽  
Logarithmic Factor ◽  
Small Constant ◽  
Amplitude Estimation ◽  
Quantum Amplitude

AbstractWe introduce a variant of Quantum Amplitude Estimation (QAE), called Iterative QAE (IQAE), which does not rely on Quantum Phase Estimation (QPE) but is only based on Grover’s Algorithm, which reduces the required number of qubits and gates. We provide a rigorous analysis of IQAE and prove that it achieves a quadratic speedup up to a double-logarithmic factor compared to classical Monte Carlo simulation with provably small constant overhead. Furthermore, we show with an empirical study that our algorithm outperforms other known QAE variants without QPE, some even by orders of magnitude, i.e., our algorithm requires significantly fewer samples to achieve the same estimation accuracy and confidence level.

scholarly journals Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 566
Author(s):  
Patrick Rall
Keyword(s):  
Quantum Algorithms ◽  
Singular Value ◽  
Query Complexity ◽  
Phase Estimation ◽  
Input State ◽  
Quantum Fourier Transform ◽  
Sorting Network ◽  
Estimation Algorithms ◽  
Amplitude Estimation ◽  
Novel Algorithms

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum estimation algorithms make assumptions that make them unsuitable for this 'coherent' setting, leaving only the textbook approach. We present novel algorithms for phase, energy, and amplitude estimation that are both conceptually and computationally simpler than the textbook method, featuring both a smaller query complexity and ancilla footprint. They do not require a quantum Fourier transform, and they do not require a quantum sorting network to compute the median of several estimates. Instead, they use block-encoding techniques to compute the estimate one bit at a time, performing all amplification via singular value transformation. These improved subroutines accelerate the performance of quantum Metropolis sampling and quantum Bayesian inference.

scholarly journals Faster amplitude estimation

2020 ◽  
Vol 20 (13&14) ◽  
pp. 1109-1123
Author(s):  
Kouhei Nakaji
Keyword(s):  
Upper Bound ◽  
Recent Literature ◽  
Constant Factor ◽  
Query Complexity ◽  
Quantum Computers ◽  
Estimation Task ◽  
Amplitude Estimation ◽  
Quantum Amplitude ◽  
Alternative Approaches ◽  
Near Term

In this paper, we introduce an efficient algorithm for the quantum amplitude estimation task which is tailored for near-term quantum computers. The quantum amplitude estimation is an important problem which has various applications in fields such as quantum chemistry, machine learning, and finance. Because the well-known algorithm for the quantum amplitude estimation using the phase estimation does not work in near-term quantum computers, alternative approaches have been proposed in recent literature. Some of them provide a proof of the upper bound which almost achieves the Heisenberg scaling. However, the constant factor is large and thus the bound is loose. Our contribution in this paper is to provide the algorithm such that the upper bound of query complexity almost achieves the Heisenberg scaling and the constant factor is small.

scholarly journals Modified Grover operator for quantum amplitude estimation

2021 ◽  
Author(s):  
Shumpei Uno ◽  
Yohichi Suzuki ◽  
Keigo Hisanaga ◽  
Rudy Raymond ◽  
Tomoki Tanaka ◽  
...  
Keyword(s):  
Amplitude Estimation ◽  
Quantum Amplitude

An Absolute Phase Estimation Method for Interferometry Imagery

2019 ◽  
Vol 1 (2) ◽  
pp. 14-19
Author(s):  
Sui Ping Lee ◽  
Yee Kit Chan ◽  
Tien Sze Lim
Keyword(s):  
Noise Suppression ◽  
Estimation Method ◽  
Phase Image ◽  
Phase Estimation ◽  
Phase Reconstruction ◽  
Estimation Algorithms ◽  
Absolute Phase ◽  
Filtering Rate ◽  
Interferometric Phase ◽  
Image Performance

Accurate interpretation of interferometric image requires an extremely challenging task based on actual phase reconstruction for incomplete noise observation. In spite of the establishment of comprehensive solutions, until now, a guaranteed means of solution method is yet to exist. The initially observed interferometric image is formed by 2π-periodic phase image that wrapped within (-π, π]. Such inverse problem is further corrupted by noise distortion and leads to the degradation of interferometric image. In order to overcome this, an effective algorithm that enables noise suppression and absolute phase reconstruction of interferometric phase image is proposed. The proposed method incorporates an improved order statistical filter that is able to adjust or vary on its filtering rate by adapting to phase noise level of relevant interferometric image. Performance of proposed method is evaluated and compared with other existing phase estimation algorithms. The comparison is based on a series of computer simulated and real interferometric data images. The experiment results illustrate the effectiveness and competency of the proposed method.

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