Built on

K. Heya, K. M. Nakanishi, K. Mitarai, and K. Fujii, “Subspace variational quantum simulator,” arXiv:1904.08566 [quant-ph]
Original
1904
Earlier work this paper cites.
Guillaume Verdon, Michael Broughton, Jarrod R McClean, Kevin J Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, and Masoud Mohseni, “Learning to learn with quantum neural networks via classical neural networks,” arXiv preprint arXiv:1907.05415 (2019b)
Original
1907
Earlier work this paper cites.
X. Xu, J. Sun, S. Endo, Y. Li, S. C. Benjamin, and X. Yuan, “Variational algorithms for linear algebra,” arXiv:1909.03898 [quant-ph]
Original
1909
Earlier work this paper cites.
Guillaume Verdon, Jacob Marks, Sasha Nanda, Stefan Leichenauer, and Jack Hidary, “Quantum hamiltonian-based models and the variational quantum thermalizer algorithm,” arXiv preprint arXiv:1910.02071 (2019a)
Original
1910
Earlier work this paper cites.
P Erdos and A Renyi, “On random graphs i,” Publ. math. debrecen 6
1959
Earlier work this paper cites.
John A Nelder and Roger Mead, “A simplex method for function minimization,” The computer journal 7
1965
Earlier work this paper cites.
Michel X Goemans and David P Williamson, “Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,” Journal of the ACM (JACM) 42
1995
Earlier work this paper cites.
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy, “Proof verification and the hardness of approximation problems,” Journal of the ACM (JACM) 45
1998
Earlier work this paper cites.
Marcel Nooijen, “Can the eigenstates of a many-body hamiltonian be represented exactly using a general two-body cluster expansion?” Physical review letters 84
2000
Earlier work this paper cites.
M Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles, “Cost-function-dependent barren plateaus in shallow quantum neural networks,” arXiv preprint arXiv:2001.00550 (2020d)
Original
2001
Earlier work this paper cites.
Gerardo Ortiz, James E Gubernatis, Emanuel Knill, and Raymond Laflamme, “Quantum algorithms for fermionic simulations,” Physical Review A 64
2001
Earlier work this paper cites.
Johan Håstad, “Some optimal inapproximability results,” Journal of the ACM (JACM) 48
2001
Earlier work this paper cites.
Sergey B Bravyi and Alexei Yu Kitaev, “Fermionic quantum computation,” Annals of Physics 298
2002
Earlier work this paper cites.
M Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J Coles, “Variational quantum state eigensolver,” arXiv preprint arXiv:2004.01372 (2020c)
Original
2004
Earlier work this paper cites.
Andrew Arrasmith, Lukasz Cincio, Rolando D Somma, and Patrick J Coles, “Operator sampling for shot-frugal optimization in variational algorithms,” arXiv preprint arXiv:2004.06252 (2020b)
Original
2004
Earlier work this paper cites.
Frank Arute et al. , “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,” arXiv preprint arXiv:2004.04197 (2020b)
Original
2004
Earlier work this paper cites.
Masanori Ohya and Dénes Petz, Quantum entropy and its use (Springer Science & Business Media, 2004)
2004
Earlier work this paper cites.
Kunal Sharma, M Cerezo, Lukasz Cincio, and Patrick J Coles, “Trainability of dissipative perceptron-based quantum neural networks,” arXiv preprint arXiv:2005.12458 (2020b)
Original
2005
Earlier work this paper cites.
Rodney J Bartlett and Monika Musiał, “Coupled-cluster theory in quantum chemistry,” Reviews of Modern Physics 79
2007
Earlier work this paper cites.
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Michael Broughton, Bob B Buckley, et al. , “Observation of separated dynamics of charge and spin in the fermi-hubbard model,” arXiv preprint arXiv:2010.07965 (2020c)
Original
2010
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010)
2010
Earlier work this paper cites.
Andrew Arrasmith, M. Cerezo, Piotr Czarnik, Lukasz Cincio, and Patrick J Coles, “Effect of barren plateaus on gradient-free optimization,” arXiv preprint arXiv:2011.12245 (2020a)
Original
2011
Earlier work this paper cites.
Bernhard Baumgartner, “An inequality for the trace of matrix products, using absolute values,” arXiv preprint arXiv:1106.6189 (2011)
Original
2011
Earlier work this paper cites.
M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J Coles, “Variational quantum algorithms,” arXiv preprint arXiv:2012.09265 (2020a)
Original
2012
Earlier work this paper cites.
A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5
2014
Earlier work this paper cites.
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, “The quest for a quantum neural network,” Quantum Information Processing 13
2014
Earlier work this paper cites.
Dave Wecker, Matthew B Hastings, and Matthias Troyer, “Progress towards practical quantum variational algorithms,” Physical Review A 92
2015
Earlier work this paper cites.
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, “An introduction to quantum machine learning,” Contemporary Physics 56
2015
Earlier work this paper cites.
Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,” New Journal of Physics 18
2016
Earlier work this paper cites.
Bela Bauer, Dave Wecker, Andrew J Millis, Matthew B Hastings, and Matthias Troyer, “Hybrid quantum-classical approach to correlated materials,” Physical Review X 6
2016
Earlier work this paper cites.
Edward Farhi and Aram W Harrow, “Quantum supremacy through the quantum approximate optimization algorithm,” arXiv preprint arXiv:1602.07674 (2016)
Original
2016
Earlier work this paper cites.
Alexander Müller-Hermes, Daniel Stilck França, and Michael M Wolf, “Relative entropy convergence for depolarizing channels,” Journal of Mathematical Physics 57
Original
2016
Earlier work this paper cites.
Ying Li and Simon C Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Physical Review X 7
2017
Earlier work this paper cites.
Peter D Johnson, Jonathan Romero, Jonathan Olson, Yudong Cao, and Alán Aspuru-Guzik, “QVECTOR: an algorithm for device-tailored quantum error correction,” arXiv:1711.02249 (2017)
Original
2017
Earlier work this paper cites.

Similar

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
Cited alongside, same era.
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549
2017
Cited alongside, same era.
Zhang Jiang, Eleanor G Rieffel, and Zhihui Wang, “Near-optimal quantum circuit for grover’s unstructured search using a transverse field,” Physical Review A 95
2017
Cited alongside, same era.
Jun Li, Xiaodong Yang, Xinhua Peng, and Chang-Pu Sun, “Hybrid quantum-classical approach to quantum optimal control,” Physical Review Letters 118
2017
Cited alongside, same era.
Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz, “Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography,” Nature communications 8

Then

Taylor L Patti, Khadijeh Najafi, Xun Gao, and Susanne F Yelin, “Entanglement devised barren plateau mitigation,” arXiv preprint arXiv:2012.12658 (2020)
Original
2020
Closest in time.
Alexey Uvarov and Jacob Biamonte, “On barren plateaus and cost function locality in variational quantum algorithms,” arXiv preprint arXiv:2011.10530 (2020)
Original
2020
Closest in time.
Andrea Skolik, Jarrod R McClean, Masoud Mohseni, Patrick van der Smagt, and Martin Leib, “Layerwise learning for quantum neural networks,” arXiv preprint arXiv:2006.14904 (2020)
Original
2020
Closest in time.
Jeffrey Marshall, Filip Wudarski, Stuart Hadfield, and Tad Hogg, “Characterizing local noise in QAOA circuits,” IOP SciNotes 1
2020
Closest in time.
Laura Gentini, Alessandro Cuccoli, Stefano Pirandola, Paola Verrucchi, and Leonardo Banchi, “Noise-resilient variational hybrid quantum-classical optimization,” Physical Review A 102

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2020

Noise-Induced Barren Plateaus in Variational Quantum Algorithms

Wang, Samson, Fontana, Enrico, Cerezo, M. et al.

Understand

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers.

A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance.
We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient).
Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits $n$ if the depth of the ansatz grows linearly with $n$.

Built on

K. Heya, K. M. Nakanishi, K. Mitarai, and K. Fujii, “Subspace variational quantum simulator,” arXiv:1904.08566 [quant-ph]
Original
1904
Earlier work this paper cites.
Guillaume Verdon, Michael Broughton, Jarrod R McClean, Kevin J Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, and Masoud Mohseni, “Learning to learn with quantum neural networks via classical neural networks,” arXiv preprint arXiv:1907.05415 (2019b)
Original
1907
Earlier work this paper cites.
X. Xu, J. Sun, S. Endo, Y. Li, S. C. Benjamin, and X. Yuan, “Variational algorithms for linear algebra,” arXiv:1909.03898 [quant-ph]
Original
1909
Earlier work this paper cites.
Guillaume Verdon, Jacob Marks, Sasha Nanda, Stefan Leichenauer, and Jack Hidary, “Quantum hamiltonian-based models and the variational quantum thermalizer algorithm,” arXiv preprint arXiv:1910.02071 (2019a)
Original
1910
Earlier work this paper cites.
P Erdos and A Renyi, “On random graphs i,” Publ. math. debrecen 6
1959
Earlier work this paper cites.
John A Nelder and Roger Mead, “A simplex method for function minimization,” The computer journal 7
1965
Earlier work this paper cites.
Michel X Goemans and David P Williamson, “Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,” Journal of the ACM (JACM) 42
1995
Earlier work this paper cites.
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy, “Proof verification and the hardness of approximation problems,” Journal of the ACM (JACM) 45
1998
Earlier work this paper cites.
Marcel Nooijen, “Can the eigenstates of a many-body hamiltonian be represented exactly using a general two-body cluster expansion?” Physical review letters 84
2000
Earlier work this paper cites.
M Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles, “Cost-function-dependent barren plateaus in shallow quantum neural networks,” arXiv preprint arXiv:2001.00550 (2020d)
Original
2001
Earlier work this paper cites.
Gerardo Ortiz, James E Gubernatis, Emanuel Knill, and Raymond Laflamme, “Quantum algorithms for fermionic simulations,” Physical Review A 64
2001
Earlier work this paper cites.
Johan Håstad, “Some optimal inapproximability results,” Journal of the ACM (JACM) 48
2001
Earlier work this paper cites.
Sergey B Bravyi and Alexei Yu Kitaev, “Fermionic quantum computation,” Annals of Physics 298
2002
Earlier work this paper cites.
M Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J Coles, “Variational quantum state eigensolver,” arXiv preprint arXiv:2004.01372 (2020c)
Original
2004
Earlier work this paper cites.
Andrew Arrasmith, Lukasz Cincio, Rolando D Somma, and Patrick J Coles, “Operator sampling for shot-frugal optimization in variational algorithms,” arXiv preprint arXiv:2004.06252 (2020b)
Original
2004
Earlier work this paper cites.
Frank Arute et al. , “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,” arXiv preprint arXiv:2004.04197 (2020b)
Original
2004
Earlier work this paper cites.
Masanori Ohya and Dénes Petz, Quantum entropy and its use (Springer Science & Business Media, 2004)
2004
Earlier work this paper cites.
Kunal Sharma, M Cerezo, Lukasz Cincio, and Patrick J Coles, “Trainability of dissipative perceptron-based quantum neural networks,” arXiv preprint arXiv:2005.12458 (2020b)
Original
2005
Earlier work this paper cites.
Rodney J Bartlett and Monika Musiał, “Coupled-cluster theory in quantum chemistry,” Reviews of Modern Physics 79
2007
Earlier work this paper cites.
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Michael Broughton, Bob B Buckley, et al. , “Observation of separated dynamics of charge and spin in the fermi-hubbard model,” arXiv preprint arXiv:2010.07965 (2020c)
Original
2010
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010)
2010
Earlier work this paper cites.
Andrew Arrasmith, M. Cerezo, Piotr Czarnik, Lukasz Cincio, and Patrick J Coles, “Effect of barren plateaus on gradient-free optimization,” arXiv preprint arXiv:2011.12245 (2020a)
Original
2011
Earlier work this paper cites.
Bernhard Baumgartner, “An inequality for the trace of matrix products, using absolute values,” arXiv preprint arXiv:1106.6189 (2011)
Original
2011
Earlier work this paper cites.
M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J Coles, “Variational quantum algorithms,” arXiv preprint arXiv:2012.09265 (2020a)
Original
2012
Earlier work this paper cites.
A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5
2014
Earlier work this paper cites.
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, “The quest for a quantum neural network,” Quantum Information Processing 13
2014
Earlier work this paper cites.
Dave Wecker, Matthew B Hastings, and Matthias Troyer, “Progress towards practical quantum variational algorithms,” Physical Review A 92
2015
Earlier work this paper cites.
Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione, “An introduction to quantum machine learning,” Contemporary Physics 56
2015
Earlier work this paper cites.
Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,” New Journal of Physics 18
2016
Earlier work this paper cites.
Bela Bauer, Dave Wecker, Andrew J Millis, Matthew B Hastings, and Matthias Troyer, “Hybrid quantum-classical approach to correlated materials,” Physical Review X 6
2016
Earlier work this paper cites.
Edward Farhi and Aram W Harrow, “Quantum supremacy through the quantum approximate optimization algorithm,” arXiv preprint arXiv:1602.07674 (2016)
Original
2016
Earlier work this paper cites.
Alexander Müller-Hermes, Daniel Stilck França, and Michael M Wolf, “Relative entropy convergence for depolarizing channels,” Journal of Mathematical Physics 57
Original
2016
Earlier work this paper cites.
Ying Li and Simon C Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Physical Review X 7
2017
Earlier work this paper cites.
Peter D Johnson, Jonathan Romero, Jonathan Olson, Yudong Cao, and Alán Aspuru-Guzik, “QVECTOR: an algorithm for device-tailored quantum error correction,” arXiv:1711.02249 (2017)
Original
2017
Earlier work this paper cites.

Similar

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
Cited alongside, same era.
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549
2017
Cited alongside, same era.
Zhang Jiang, Eleanor G Rieffel, and Zhihui Wang, “Near-optimal quantum circuit for grover’s unstructured search using a transverse field,” Physical Review A 95
2017
Cited alongside, same era.
Jun Li, Xiaodong Yang, Xinhua Peng, and Chang-Pu Sun, “Hybrid quantum-classical approach to quantum optimal control,” Physical Review Letters 118
2017
Cited alongside, same era.
Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz, “Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography,” Nature communications 8

Then

Taylor L Patti, Khadijeh Najafi, Xun Gao, and Susanne F Yelin, “Entanglement devised barren plateau mitigation,” arXiv preprint arXiv:2012.12658 (2020)
Original
2020
Closest in time.
Alexey Uvarov and Jacob Biamonte, “On barren plateaus and cost function locality in variational quantum algorithms,” arXiv preprint arXiv:2011.10530 (2020)
Original
2020
Closest in time.
Andrea Skolik, Jarrod R McClean, Masoud Mohseni, Patrick van der Smagt, and Martin Leib, “Layerwise learning for quantum neural networks,” arXiv preprint arXiv:2006.14904 (2020)
Original
2020
Closest in time.
Jeffrey Marshall, Filip Wudarski, Stuart Hadfield, and Tad Hogg, “Characterizing local noise in QAOA circuits,” IOP SciNotes 1
2020
Closest in time.
Laura Gentini, Alessandro Cuccoli, Stefano Pirandola, Paola Verrucchi, and Leonardo Banchi, “Noise-resilient variational hybrid quantum-classical optimization,” Physical Review A 102

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2017

Cited alongside, same era.

M. M. Wilde, Quantum Information Theory , 2nd ed. (Cambridge University Press, 2017)

2017

Cited alongside, same era.

J. Preskill, “Quantum computing in the NISQ era and beyond,” Quantum 2

2018

Cited alongside, same era.

Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven, “Barren plateaus in quantum neural network training landscapes,” Nature communications 9

2018

Cited alongside, same era.

Joonho Lee, William J Huggins, Martin Head-Gordon, and K Birgitta Whaley, “Generalized unitary coupled cluster wave functions for quantum computation,” Journal of chemical theory and computation 15

2018

Cited alongside, same era.

Jonathan Romero, Ryan Babbush, Jarrod R McClean, Cornelius Hempel, Peter J Love, and Alán Aspuru-Guzik, “Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz,” Quantum Science and Technology 4

2018

Cited alongside, same era.

L. Cincio, Y. Subaşı, A. T. Sornborger, and P. J. Coles, “Learning the quantum algorithm for state overlap,” New Journal of Physics 20

2018

Cited alongside, same era.

Tyson Jones, Suguru Endo, Sam McArdle, Xiao Yuan, and Simon C Benjamin, “Variational quantum algorithms for discovering hamiltonian spectra,” Physical Review A 99

2019

Cited alongside, same era.