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P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, M. Martonosi, and F. T. Chong, Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families, (2019) , arXiv:1907.13623
Original
1907
Earlier work this paper cites.
A. F. Izmaylov, T.-C. Yen, R. A. Lang, and V. Verteletskyi, Unitary partitioning approach to the measurement problem in the Variational Quantum Eigensolver method, (2019) , arXiv:1907.09040
Original
1907
Earlier work this paper cites.
G. Verdon, M. Broughton, J. R. McClean, K. J. Sung, R. Babbush, Z. Jiang, H. Neven, and M. Mohseni, Learning to learn with quantum neural networks via classical neural networks, (2019) , arXiv:1907.05415
Original
1907
Earlier work this paper cites.
W. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin Equation: With Applications in Physics, Chemistry and Electrical Engineering (1996)
Original
1996
Earlier work this paper cites.
S. Thrun and L. Pratt, Learning to Learn: Introduction and Overview (1998)
1998
Earlier work this paper cites.
M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks, (2020) , arXiv:2001.00550
Original
2001
Earlier work this paper cites.
P. Dita, Factorization of unitary matrices, Journal of Physics A: Mathematical and General 36
2003
Earlier work this paper cites.
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric informationally complete quantum measurements, Journal of Mathematical Physics 45
2004
Earlier work this paper cites.
K. Sharma, M. Cerezo, L. Cincio, and P. J. Coles, Trainability of dissipative perceptron-based quantum neural networks, arXiv (2020), arXiv:2005.12458
Original
2005
Earlier work this paper cites.
T. Volkoff and P. J. Coles, Large gradients via correlation in random parameterized quantum circuits, (2020) , arXiv:2005.12200
Original
2005
Earlier work this paper cites.
A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib, Layerwise learning for quantum neural networks, (2020) , arXiv:2006.14904
Original
2006
Earlier work this paper cites.
S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, Noise-Induced Barren Plateaus in Variational Quantum Algorithms, (2020) , arXiv:2007.14384
Original
2007
Earlier work this paper cites.
M. J. Bremner, C. Mora, and A. Winter, Are random pure states useful for quantum computation?, Phys. Rev. Lett. 102
2009
Earlier work this paper cites.
D. Gross, S. T. Flammia, and J. Eisert, Most quantum states are too entangled to be useful as computational resources, Phys. Rev. Lett. 102
2009
Earlier work this paper cites.
Z. Holmes, A. Arrasmith, B. Yan, P. J. Coles, A. Albrecht, and A. T. Sornborger, Barren plateaus preclude learning scramblers, (2020) , arXiv:2009.14808
Original
2009
Earlier work this paper cites.

Similar

C. Dankert, R. Cleve, J. Emerson, and E. Livine, Exact and approximate unitary 2-designs and their application to fidelity estimation, Phys. Rev. A 80
2009
Cited alongside, same era.
A. W. Harrow and R. A. Low, Random quantum circuits are approximate 2-designs, Communications in Mathematical Physics 291
2009
Cited alongside, same era.
C. O. Marrero, M. Kieferová, and N. Wiebe, Entanglement Induced Barren Plateaus, (2020) , arXiv:2010.15968
Original
2010
Cited alongside, same era.
E. Campos, A. Nasrallah, and J. Biamonte, Abrupt Transitions in Variational Quantum Circuit Training, (2020) , arXiv:2010.09720
Original
2010
Cited alongside, same era.
A. Uvarov and J. Biamonte, On barren plateaus and cost function locality in variational quantum algorithms, (2020) , arXiv:2011.10530
Original

Then

J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New Journal of Physics 18
2016
Later among the works it cites.
A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware-efficient Quantum Optimizer for Small Molecules and Quantum Magnets, Nature Publishing Group 549
Original
2017
Later among the works it cites.
Z. Puchala and J. Miszczak, Symbolic integration with respect to the haar measure on the unitary groups, Bulletin of the Polish Academy of Sciences: Technical Sciences 65
2017
Later among the works it cites.
J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2
2018
Later among the works it cites.
E. Farhi and H. Neven, Classification with Quantum Neural Networks on Near Term Processors, (2018) , arXiv:1802.06002
Original

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2020

Entanglement Devised Barren Plateau Mitigation

Patti, Taylor L., Najafi, Khadijeh, Gao, Xun et al.

Understand

Hybrid quantum-classical variational algorithms are one of the most propitious implementations of quantum computing on near-term devices, offering classical machine learning support to quantum scale solution spaces.

However, numerous studies have demonstrated that the rate at which this space grows in qubit number could preclude learning in deep quantum circuits, a phenomenon known as barren plateaus.
In this work, we implicate random entanglement as the source of barren plateaus and characterize them in terms of many-body entanglement dynamics, detailing their formation as a function of system size, circuit depth, and circuit connectivity.
Using this comprehension of entanglement, we propose and demonstrate a number of barren plateau ameliorating techniques, including: initial partitioning of cost function and non-cost function registers, meta-learning of low-entanglement circuit initializations, selective inter-register interaction, entanglement regularization, the addition of Langevin noise, and rotation into preferred cost function eigenbases.

Built on

P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, M. Martonosi, and F. T. Chong, Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families, (2019) , arXiv:1907.13623
Original
1907
Earlier work this paper cites.
A. F. Izmaylov, T.-C. Yen, R. A. Lang, and V. Verteletskyi, Unitary partitioning approach to the measurement problem in the Variational Quantum Eigensolver method, (2019) , arXiv:1907.09040
Original
1907
Earlier work this paper cites.
G. Verdon, M. Broughton, J. R. McClean, K. J. Sung, R. Babbush, Z. Jiang, H. Neven, and M. Mohseni, Learning to learn with quantum neural networks via classical neural networks, (2019) , arXiv:1907.05415
Original
1907
Earlier work this paper cites.
W. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin Equation: With Applications in Physics, Chemistry and Electrical Engineering (1996)
Original
1996
Earlier work this paper cites.
S. Thrun and L. Pratt, Learning to Learn: Introduction and Overview (1998)
1998
Earlier work this paper cites.
M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks, (2020) , arXiv:2001.00550
Original
2001
Earlier work this paper cites.
P. Dita, Factorization of unitary matrices, Journal of Physics A: Mathematical and General 36
2003
Earlier work this paper cites.
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric informationally complete quantum measurements, Journal of Mathematical Physics 45
2004
Earlier work this paper cites.
K. Sharma, M. Cerezo, L. Cincio, and P. J. Coles, Trainability of dissipative perceptron-based quantum neural networks, arXiv (2020), arXiv:2005.12458
Original
2005
Earlier work this paper cites.
T. Volkoff and P. J. Coles, Large gradients via correlation in random parameterized quantum circuits, (2020) , arXiv:2005.12200
Original
2005
Earlier work this paper cites.
A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib, Layerwise learning for quantum neural networks, (2020) , arXiv:2006.14904
Original
2006
Earlier work this paper cites.
S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, Noise-Induced Barren Plateaus in Variational Quantum Algorithms, (2020) , arXiv:2007.14384
Original
2007
Earlier work this paper cites.
M. J. Bremner, C. Mora, and A. Winter, Are random pure states useful for quantum computation?, Phys. Rev. Lett. 102
2009
Earlier work this paper cites.
D. Gross, S. T. Flammia, and J. Eisert, Most quantum states are too entangled to be useful as computational resources, Phys. Rev. Lett. 102
2009
Earlier work this paper cites.
Z. Holmes, A. Arrasmith, B. Yan, P. J. Coles, A. Albrecht, and A. T. Sornborger, Barren plateaus preclude learning scramblers, (2020) , arXiv:2009.14808
Original
2009
Earlier work this paper cites.

Similar

C. Dankert, R. Cleve, J. Emerson, and E. Livine, Exact and approximate unitary 2-designs and their application to fidelity estimation, Phys. Rev. A 80
2009
Cited alongside, same era.
A. W. Harrow and R. A. Low, Random quantum circuits are approximate 2-designs, Communications in Mathematical Physics 291
2009
Cited alongside, same era.
C. O. Marrero, M. Kieferová, and N. Wiebe, Entanglement Induced Barren Plateaus, (2020) , arXiv:2010.15968
Original
2010
Cited alongside, same era.
E. Campos, A. Nasrallah, and J. Biamonte, Abrupt Transitions in Variational Quantum Circuit Training, (2020) , arXiv:2010.09720
Original
2010
Cited alongside, same era.
A. Uvarov and J. Biamonte, On barren plateaus and cost function locality in variational quantum algorithms, (2020) , arXiv:2011.10530
Original

Then

J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantum-classical algorithms, New Journal of Physics 18
2016
Later among the works it cites.
A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware-efficient Quantum Optimizer for Small Molecules and Quantum Magnets, Nature Publishing Group 549
Original
2017
Later among the works it cites.
Z. Puchala and J. Miszczak, Symbolic integration with respect to the haar measure on the unitary groups, Bulletin of the Polish Academy of Sciences: Technical Sciences 65
2017
Later among the works it cites.
J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2
2018
Later among the works it cites.
E. Farhi and H. Neven, Classification with Quantum Neural Networks on Near Term Processors, (2018) , arXiv:1802.06002
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2011

Cited alongside, same era.

A. Arrasmith, M. Cerezo, P. Czarnik, L. Cincio, and P. J. Coles, Effect of barren plateaus on gradient-free optimization, (2020) , arXiv:2011.12245

Original

2011

Cited alongside, same era.

E. Fontana, M. Cerezo, A. Arrasmith, I. Rungger, and P. J. Coles, Optimizing parametrized quantum circuits via noise-induced breaking of symmetries, (2020) , arXiv:2011.08763

Original

2011

Cited alongside, same era.

A. Pesah, M. Cerezo, S. Wang, T. Volkoff, A. T. Sornborger, and P. J. Coles, Absence of Barren Plateaus in Quantum Convolutional Neural Networks, (2020) , arXiv:2011.02966

Original

2011

Cited alongside, same era.

M. Welling and Y. W. Teh, Bayesian learning via stochastic gradient langevin dynamics, Proceedings of the 28th International Conference on International Conference on Machine Learning (2011)

2011

Cited alongside, same era.

A. Anand, M. Degroote, and A. Aspuru-Guzik, Natural Evolutionary Strategies for Variational Quantum Computation, (2020) , arXiv:2012.00101

Original

2012

Cited alongside, same era.

E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv (2014), arXiv:1411.4028

Original

2014

Cited alongside, same era.

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

Cited alongside, same era.

2018