Built on

M. J. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, The computer journal 7
1964
Earlier work this paper cites.
J. A. Nelder and R. Mead, A simplex method for function minimization, The computer journal 7
1965
Earlier work this paper cites.
J. Močkus, in Optimization techniques IFIP technical conference (Springer, 1975) pp. 400–404
1975
Earlier work this paper cites.
R. R. Barton and J. S. Ivey Jr, Modifications of the nelder-mead simplex method for stochastic simulation response optimization, 1991 Winter Simulation Conference Proceedings (1991), 10.1109/WSC.1991.185709
1991
Earlier work this paper cites.
M. J. Powell, in Advances in optimization and numerical analysis (Springer, 1994) pp. 51–67
1994
Earlier work this paper cites.
M. Cerezo, K. Sharma, A. Arrasmith, and P. J. Coles, Variational quantum state eigensolver, arXiv preprint arXiv:2004.01372 (2020b)
Original
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 preprint arXiv:2005.12458 (2020b)
Original
2005
Earlier work this paper cites.
A. W. Harrow and R. A. Low, Random quantum circuits are approximate 2-designs, Communications in Mathematical Physics 291
2009
Earlier work this paper cites.
R. P. Brent, Algorithms for minimization without derivatives (Courier Corporation, 2013)
2013
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
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E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv preprint arXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
M. Schuld, I. Sinayskiy, and F. Petruccione, The quest for a quantum neural network, Quantum Information Processing 13
2014
Earlier work this paper cites.
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
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F. G. Brandao, A. W. Harrow, and M. Horodecki, Local random quantum circuits are approximate polynomial-designs, Communications in Mathematical Physics 346
2016
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J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum autoencoders for efficient compression of quantum data, Quantum Science and Technology 2
2017
Earlier work this paper cites.
G. Verdon, J. Pye, and M. Broughton, A universal training algorithm for quantum deep learning, arXiv preprint arXiv:1806.09729 (2018)
Original
2018
Earlier work this paper cites.
J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature communications 9
2018
Earlier work this paper cites.

Similar

E. Farhi and H. Neven, Classification with quantum neural networks on near term processors, arXiv preprint arXiv:1802.06002 (2018)
Original
2018
Cited alongside, same era.
X. Huang, Robust simplex algorithm for online optimization, Physical Review Accelerators and Beams 21
2018
Cited alongside, same era.
A. Harrow and S. Mehraban, Approximate unitary t t -designs by short random quantum circuits using nearest-neighbor and long-range gates, arXiv preprint arXiv:1809.06957 (2018)
Original
2018
Cited alongside, same era.
S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, Quantum-assisted quantum compiling, Quantum 3
2019
Cited alongside, same era.
R. LaRose, A. Tikku, É. O’Neel-Judy, L. Cincio, and P. J. Coles, Variational quantum state diagonalization, npj Quantum Information 5
2019

Then

C. O. Marrero, M. Kieferová, and N. Wiebe, Entanglement induced barren plateaus, arXiv preprint arXiv:2010.15968 (2020)
Original
2020
Closest in time.
Y. Du, M.-H. Hsieh, T. Liu, S. You, and D. Tao, On the learnability of quantum neural networks, arXiv preprint arXiv:2007.12369 (2020)
Original
2020
Closest in time.
J. M. Kübler, A. Arrasmith, L. Cincio, and P. J. Coles, An adaptive optimizer for measurement-frugal variational algorithms, Quantum 4
2020
Closest in time.
R. Sweke, F. Wilde, J. J. Meyer, M. Schuld, P. K. Fährmann, B. Meynard-Piganeau, and J. Eisert, Stochastic gradient descent for hybrid quantum-classical optimization, Quantum 4
2020
Closest in time.
A. Arrasmith, L. Cincio, R. D. Somma, and P. J. Coles, Operator sampling for shot-frugal optimization in variational algorithms, arXiv preprint arXiv:2004.06252 (2020)

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Reading the bibliography…

2020

Effect of barren plateaus on gradient-free optimization

Arrasmith, Andrew, Cerezo, M., Czarnik, Piotr et al.

Understand

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits.

Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions.
For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus.
However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus.

Built on

M. J. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, The computer journal 7
1964
Earlier work this paper cites.
J. A. Nelder and R. Mead, A simplex method for function minimization, The computer journal 7
1965
Earlier work this paper cites.
J. Močkus, in Optimization techniques IFIP technical conference (Springer, 1975) pp. 400–404
1975
Earlier work this paper cites.
R. R. Barton and J. S. Ivey Jr, Modifications of the nelder-mead simplex method for stochastic simulation response optimization, 1991 Winter Simulation Conference Proceedings (1991), 10.1109/WSC.1991.185709
1991
Earlier work this paper cites.
M. J. Powell, in Advances in optimization and numerical analysis (Springer, 1994) pp. 51–67
1994
Earlier work this paper cites.
M. Cerezo, K. Sharma, A. Arrasmith, and P. J. Coles, Variational quantum state eigensolver, arXiv preprint arXiv:2004.01372 (2020b)
Original
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 preprint arXiv:2005.12458 (2020b)
Original
2005
Earlier work this paper cites.
A. W. Harrow and R. A. Low, Random quantum circuits are approximate 2-designs, Communications in Mathematical Physics 291
2009
Earlier work this paper cites.
R. P. Brent, Algorithms for minimization without derivatives (Courier Corporation, 2013)
2013
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.
E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv preprint arXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
M. Schuld, I. Sinayskiy, and F. Petruccione, The quest for a quantum neural network, Quantum Information Processing 13
2014
Earlier work this paper cites.
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
Earlier work this paper cites.
F. G. Brandao, A. W. Harrow, and M. Horodecki, Local random quantum circuits are approximate polynomial-designs, Communications in Mathematical Physics 346
2016
Earlier work this paper cites.
J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum autoencoders for efficient compression of quantum data, Quantum Science and Technology 2
2017
Earlier work this paper cites.
G. Verdon, J. Pye, and M. Broughton, A universal training algorithm for quantum deep learning, arXiv preprint arXiv:1806.09729 (2018)
Original
2018
Earlier work this paper cites.
J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature communications 9
2018
Earlier work this paper cites.

Similar

E. Farhi and H. Neven, Classification with quantum neural networks on near term processors, arXiv preprint arXiv:1802.06002 (2018)
Original
2018
Cited alongside, same era.
X. Huang, Robust simplex algorithm for online optimization, Physical Review Accelerators and Beams 21
2018
Cited alongside, same era.
A. Harrow and S. Mehraban, Approximate unitary t t -designs by short random quantum circuits using nearest-neighbor and long-range gates, arXiv preprint arXiv:1809.06957 (2018)
Original
2018
Cited alongside, same era.
S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, Quantum-assisted quantum compiling, Quantum 3
2019
Cited alongside, same era.
R. LaRose, A. Tikku, É. O’Neel-Judy, L. Cincio, and P. J. Coles, Variational quantum state diagonalization, npj Quantum Information 5
2019

Then

C. O. Marrero, M. Kieferová, and N. Wiebe, Entanglement induced barren plateaus, arXiv preprint arXiv:2010.15968 (2020)
Original
2020
Closest in time.
Y. Du, M.-H. Hsieh, T. Liu, S. You, and D. Tao, On the learnability of quantum neural networks, arXiv preprint arXiv:2007.12369 (2020)
Original
2020
Closest in time.
J. M. Kübler, A. Arrasmith, L. Cincio, and P. J. Coles, An adaptive optimizer for measurement-frugal variational algorithms, Quantum 4
2020
Closest in time.
R. Sweke, F. Wilde, J. J. Meyer, M. Schuld, P. K. Fährmann, B. Meynard-Piganeau, and J. Eisert, Stochastic gradient descent for hybrid quantum-classical optimization, Quantum 4
2020
Closest in time.
A. Arrasmith, L. Cincio, R. D. Somma, and P. J. Coles, Operator sampling for shot-frugal optimization in variational algorithms, arXiv preprint arXiv:2004.06252 (2020)

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

A. Arrasmith, L. Cincio, A. T. Sornborger, W. H. Zurek, and P. J. Coles, Variational consistent histories as a hybrid algorithm for quantum foundations, Nature communications 10

2019

Cited alongside, same era.

C. Bravo-Prieto, R. LaRose, M. Cerezo, Y. Subasi, L. Cincio, and P. Coles, Variational quantum linear solver, arXiv preprint arXiv:1909.05820 (2019)

Original

2019

Cited alongside, same era.

I. Cong, S. Choi, and M. D. Lukin, Quantum convolutional neural networks, Nature Physics 15

2019

Cited alongside, same era.

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, arXiv preprint arXiv:1907.05415 (2019)

Original

2019

Cited alongside, same era.

E. Grant, L. Wossnig, M. Ostaszewski, and M. Benedetti, An initialization strategy for addressing barren plateaus in parametrized quantum circuits, Quantum 3

2019

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N. Killoran, T. R. Bromley, J. M. Arrazola, M. Schuld, N. Quesada, and S. Lloyd, Continuous-variable quantum neural networks, Physical Review Research 1

2019

Cited alongside, same era.

C. Cirstoiu, Z. Holmes, J. Iosue, L. Cincio, P. J. Coles, and A. Sornborger, Variational fast forwarding for quantum simulation beyond the coherence time, npj Quantum Information 6

2020

Cited alongside, same era.

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2020

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J. Stokes, J. Izaac, N. Killoran, and G. Carleo, Quantum natural gradient, Quantum 4

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K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, Noisy intermediate-scale quantum (nisq) algorithms, arXiv preprint arXiv:2101.08448 (2021)

Original

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M. Cerezo and P. J. Coles, Higher order derivatives of quantum neural networks with barren plateaus, Quantum Science and Technology 6

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A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and S. Woerner, The power of quantum neural networks, Nature Computational Science 1

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T. L. Patti, K. Najafi, X. Gao, and S. F. Yelin, Entanglement devised barren plateau mitigation, Physical Review Research 3

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A. Uvarov and J. D. Biamonte, On barren plateaus and cost function locality in variational quantum algorithms, Journal of Physics A: Mathematical and Theoretical 54

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A. Arrasmith, Z. Holmes, M. Cerezo, and P. J. Coles, Equivalence of quantum barren plateaus to cost concentration and narrow gorges, arXiv preprint arXiv:2104.05868 (2021)

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T. Volkoff and P. J. Coles, Large gradients via correlation in random parameterized quantum circuits, Quantum Science and Technology 6

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A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib, Layerwise learning for quantum neural networks, Quantum Machine Intelligence 3

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