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Nikitas Stamatopoulos, Daniel J. Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner, “Option pricing using quantum computers,” (2019), arXiv:1905.02666 [quant-ph]
Original
1905
Earlier work this paper cites.
Daniel J. Egger, Ricardo Gacía Gutiérrez, Jordi Cahué Mestre, and Stefan Woerner, “Credit risk analysis using quantum computers,” (2019), arXiv:1907.03044 [quant-ph]
Original
1907
Earlier work this paper cites.
Dmitry Grinko, Julien Gacon, Christa Zoufal, and Stefan Woerner, “Iterative quantum amplitude estimation,” (2019), arXiv:1912.05559 [quant-ph]
Original
1912
Earlier work this paper cites.
Lov K. Grover, “A fast quantum mechanical algorithm for database search,” (1996), arXiv:quant-ph/9605043 [quant-ph]
1996
Earlier work this paper cites.
Lov K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79
1997
Earlier work this paper cites.
E. Knill and R. Laflamme, “Power of one bit of quantum information,” Phys. Rev. Lett. 81
1998
Earlier work this paper cites.
Peter W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Review 41
1999
Earlier work this paper cites.
Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp, “Quantum amplitude amplification and estimation,” (2000), arXiv:quant-ph/0005055 [quant-ph]
2000
Earlier work this paper cites.
Kouhei Nakaji, “Faster amplitude estimation,” (2020), arXiv:2003.02417 [quant-ph]
Original
2003
Earlier work this paper cites.
Guoming Wang, Dax Enshan Koh, Peter D. Johnson, and Yudong Cao, “Bayesian inference with engineered likelihood functions for robust amplitude estimation,” (2020), arXiv:2006.09350 [quant-ph]
Original
2006
Earlier work this paper cites.

Similar

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Original
2013
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Then

Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549
2017
Later among the works it cites.
Ilya G. Ryabinkin, Tzu-Ching Yen, Scott N. Genin, and Artur F. Izmaylov, “Qubit coupled-cluster method: A systematic approach to quantum chemistry on a quantum computer,” (2018), arXiv:1809.03827 [quant-ph]
Original
2018
Later among the works it cites.
John Preskill, “Quantum computing in the nisq era and beyond,” Quantum 2
2018
Later among the works it cites.
Patrick Rebentrost, Brajesh Gupt, and Thomas R. Bromley, “Quantum computational finance: Monte carlo pricing of financial derivatives,” Physical Review A 98
2018
Later among the works it cites.
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2019
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

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Reading the bibliography…

2020

Quantum Amplitude Estimation in the Presence of Noise

Brown, Eric G., Goktas, Oktay, Tham, W. K.

Understand

Quantum Amplitude Estimation (QAE) -- a technique by which the amplitude of a given quantum state can be estimated with quadratically fewer queries than by standard sampling -- is a key sub-routine in several important quantum algorithms, including Grover search and Quantum Monte-Carlo methods.

An obstacle to implementing QAE in near-term noisy intermediate-scale quantum (NISQ) devices has been the need to perform Quantum Phase Estimation (QPE) -- a costly procedure -- as a sub-routine.
This impediment was lifted with various QPE-free methods of QAE, wherein Grover queries of varying depths / powers (often according to a "schedule") are followed immediately by measurements and classical post-processing techniques like maximum likelihood estimation (MLE).
Existing analyses as to the optimality of various query schedules in these QPE-free QAE schemes have hitherto assumed noise-free systems.

Built on

Nikitas Stamatopoulos, Daniel J. Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner, “Option pricing using quantum computers,” (2019), arXiv:1905.02666 [quant-ph]
Original
1905
Earlier work this paper cites.
Daniel J. Egger, Ricardo Gacía Gutiérrez, Jordi Cahué Mestre, and Stefan Woerner, “Credit risk analysis using quantum computers,” (2019), arXiv:1907.03044 [quant-ph]
Original
1907
Earlier work this paper cites.
Dmitry Grinko, Julien Gacon, Christa Zoufal, and Stefan Woerner, “Iterative quantum amplitude estimation,” (2019), arXiv:1912.05559 [quant-ph]
Original
1912
Earlier work this paper cites.
Lov K. Grover, “A fast quantum mechanical algorithm for database search,” (1996), arXiv:quant-ph/9605043 [quant-ph]
1996
Earlier work this paper cites.
Lov K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79
1997
Earlier work this paper cites.
E. Knill and R. Laflamme, “Power of one bit of quantum information,” Phys. Rev. Lett. 81
1998
Earlier work this paper cites.
Peter W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Review 41
1999
Earlier work this paper cites.
Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp, “Quantum amplitude amplification and estimation,” (2000), arXiv:quant-ph/0005055 [quant-ph]
2000
Earlier work this paper cites.
Kouhei Nakaji, “Faster amplitude estimation,” (2020), arXiv:2003.02417 [quant-ph]
Original
2003
Earlier work this paper cites.
Guoming Wang, Dax Enshan Koh, Peter D. Johnson, and Yudong Cao, “Bayesian inference with engineered likelihood functions for robust amplitude estimation,” (2020), arXiv:2006.09350 [quant-ph]
Original
2006
Earlier work this paper cites.

Similar

D. Petz and C. Ghinea, “Introduction to quantum fisher information,” Quantum Probability and Related Topics (2011)
2011
Cited alongside, same era.
Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition , 10th ed. (Cambridge University Press, USA, 2011)
2011
Cited alongside, same era.
Seth T. Merkel, Jay M. Gambetta, John A. Smolin, Stefano Poletto, Antonio D. Córcoles, Blake R. Johnson, Colm A. Ryan, and Matthias Steffen, “Self-consistent quantum process tomography,” Physical Review A 87
2013
Cited alongside, same era.
Robin Blume-Kohout, John King Gamble, Erik Nielsen, Jonathan Mizrahi, Jonathan D. Sterk, and Peter Maunz, “Robust, self-consistent, closed-form tomography of quantum logic gates on a trapped ion qubit,” (2013), arXiv:1310.4492 [quant-ph]
Original
2013
Cited alongside, same era.

Then

Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549
2017
Later among the works it cites.
Ilya G. Ryabinkin, Tzu-Ching Yen, Scott N. Genin, and Artur F. Izmaylov, “Qubit coupled-cluster method: A systematic approach to quantum chemistry on a quantum computer,” (2018), arXiv:1809.03827 [quant-ph]
Original
2018
Later among the works it cites.
John Preskill, “Quantum computing in the nisq era and beyond,” Quantum 2
2018
Later among the works it cites.
Patrick Rebentrost, Brajesh Gupt, and Thomas R. Bromley, “Quantum computational finance: Monte carlo pricing of financial derivatives,” Physical Review A 98
2018
Later among the works it cites.
Stefan Woerner and Daniel J. Egger, “Quantum risk analysis,” npj Quantum Information 5
2019
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5

2014

Cited alongside, same era.

Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, “A Quantum Approximate Optimization Algorithm,” (2014) , arXiv:1411.4028

Original

2014

Cited alongside, same era.

Ashley Montanaro, “Quantum speedup of monte carlo methods,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471

2015

Cited alongside, same era.

Edward Farhi and Aram W Harrow, “Quantum Supremacy through the Quantum Approximate Optimization Algorithm,” (2016) , arXiv:1602.07674

Original

2016

Cited alongside, same era.

Nathan Wiebe and Chris Granade, “Efficient bayesian phase estimation,” Physical Review Letters 117

2016

Cited alongside, same era.

Vedran Dunjko and Hans J. Briegel, “Machine learning & artificial intelligence in the quantum domain,” (2017), arXiv:1709.02779 [quant-ph]

Original

2017

Cited alongside, same era.

T. Tanaka, S. Uno, Y. Suzuki, and R. Raymond, “Amplitude estimation without quantum fourier transform and controlled grover operators,” https://github.com/qiskit-community/qiskit-community-tutorials/blob/master/algorithms/SimpleIntegral_AEwoPE.ipynb (2019)

2019

Later among the works it cites.

Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, “Quantum computational chemistry,” Rev. Mod. Phys. 92

2020

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Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto, “Amplitude estimation without phase estimation,” Quantum Information Processing 19

2020

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Scott Aaronson and Patrick Rall, “Quantum approximate counting, simplified,” Symposium on Simplicity in Algorithms , 24–32 (2020)

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