Built on

B. Ghorbani, S. Krishnan, and Y. Xiao, “An investigation into neural net optimization via hessian eigenvalue density,” arXiv:1901.10159 [cs.LG]
Original
1901
Earlier work this paper cites.
S. Fort and S. Ganguli, “Emergent properties of the local geometry of neural loss landscapes,” arXiv:1910.05929 [cs.LG]
Original
1910
Earlier work this paper cites.
C. Liu, L. Zhu, and M. Belkin, “Loss landscapes and optimization in over-parameterized non-linear systems and neural networks,” arXiv:2003.00307 [cs.LG]
Original
2003
Earlier work this paper cites.
T. Hubregtsen, J. Pichlmeier, P. Stecher, and K. Bertels, “Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility and entangling capability,” arXiv:2003.09887 [quant-ph]
Original
2003
Earlier work this paper cites.
M. Broughton, G. Verdon, T. McCourt, A. J. Martinez, J. H. Yoo, S. V. Isakov, P. Massey, M. Y. Niu, R. Halavati, E. Peters, M. Leib, A. Skolik, M. Streif, D. V. Dollen, J. R. McClean, S. Boixo, D. Bacon, A. K. Ho, H. Neven, and M. Mohseni, “TensorFlow Quantum: A Software Framework for Quantum Machine Learning,” arXiv:2003.02989 [quant-ph]
Original
2003
Earlier work this paper cites.
B. Collins and P. Śniady, “Integration with respect to the haar measure on unitary, orthogonal and symplectic group,” Communications in Mathematical Physics
2006
Earlier work this paper cites.
M. B. Hastings, “An area law for one-dimensional quantum systems,” Journal of Statistical Mechanics: Theory and Experiment
2007
Earlier work this paper cites.
M. Cerezo and P. J. Coles, “Impact of barren plateaus on the hessian and higher order derivatives,” arXiv:2008.07454 [quant-ph]
Original
2008
Earlier work this paper cites.

Similar

J. Eisert, M. Cramer, and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy,” Reviews of Modern Physics
2010
Cited alongside, same era.
C. O. Marrero, M. Kieferová, and N. Wiebe, “Entanglement induced barren plateaus,” arXiv:2010.15968 [quant-ph]
Original
2010
Cited alongside, same era.
G. S. Barron and C. J. Wood, “Measurement error mitigation for variational quantum algorithms,” arXiv:2010.08520 [quant-ph]
Original
2010
Cited alongside, same era.
J. Zeng, Z. Wu, C. Cao, C. Zhang, S. Hou, P. Xu, and B. Zeng, “Simulating noisy variational quantum eigensolver with local noise models,” arXiv:2010.14821 [quant-ph]
Original
2010
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,” arXiv:2011.08763 [quant-ph]

Then

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
2017
Later among the works it cites.
J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,” Nature Communications
2018
Later among the works it cites.
S. Sim, P. D. Johnson, and A. Aspuru‐Guzik, “Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum‐classical algorithms,” Advanced Quantum Technologies
2019
Later among the works it cites.
S. E. Rasmussen, N. J. S. Loft, T. Bækkegaard, M. Kues, and N. T. Zinner, “Reducing the amount of single‐qubit rotations in vqe and related algorithms,” Advanced Quantum Technologies
2020
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…

2021

Quantum Energy Landscape and VQA Optimization

Kim, Joonho, Oz, Yaron

Understand

We study the effects of entanglement and control parameters on the energy landscape and optimization performance of the variational quantum circuit.

Through a systematic analysis of the Hessian spectrum, we characterize the local geometry of the energy landscape at a random point and along an optimization trajectory.
We argue that decreasing the entangling capability and increasing the number of circuit parameters have the same qualitative effect on the Hessian eigenspectrum.
Both the low-entangling capability and the abundance of control parameters increase the curvature of non-flat directions, contributing to the efficient search of area-law entangled ground states as to the optimization accuracy and the convergence speed.

Built on

B. Ghorbani, S. Krishnan, and Y. Xiao, “An investigation into neural net optimization via hessian eigenvalue density,” arXiv:1901.10159 [cs.LG]
Original
1901
Earlier work this paper cites.
S. Fort and S. Ganguli, “Emergent properties of the local geometry of neural loss landscapes,” arXiv:1910.05929 [cs.LG]
Original
1910
Earlier work this paper cites.
C. Liu, L. Zhu, and M. Belkin, “Loss landscapes and optimization in over-parameterized non-linear systems and neural networks,” arXiv:2003.00307 [cs.LG]
Original
2003
Earlier work this paper cites.
T. Hubregtsen, J. Pichlmeier, P. Stecher, and K. Bertels, “Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility and entangling capability,” arXiv:2003.09887 [quant-ph]
Original
2003
Earlier work this paper cites.
M. Broughton, G. Verdon, T. McCourt, A. J. Martinez, J. H. Yoo, S. V. Isakov, P. Massey, M. Y. Niu, R. Halavati, E. Peters, M. Leib, A. Skolik, M. Streif, D. V. Dollen, J. R. McClean, S. Boixo, D. Bacon, A. K. Ho, H. Neven, and M. Mohseni, “TensorFlow Quantum: A Software Framework for Quantum Machine Learning,” arXiv:2003.02989 [quant-ph]
Original
2003
Earlier work this paper cites.
B. Collins and P. Śniady, “Integration with respect to the haar measure on unitary, orthogonal and symplectic group,” Communications in Mathematical Physics
2006
Earlier work this paper cites.
M. B. Hastings, “An area law for one-dimensional quantum systems,” Journal of Statistical Mechanics: Theory and Experiment
2007
Earlier work this paper cites.
M. Cerezo and P. J. Coles, “Impact of barren plateaus on the hessian and higher order derivatives,” arXiv:2008.07454 [quant-ph]
Original
2008
Earlier work this paper cites.

Similar

J. Eisert, M. Cramer, and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy,” Reviews of Modern Physics
2010
Cited alongside, same era.
C. O. Marrero, M. Kieferová, and N. Wiebe, “Entanglement induced barren plateaus,” arXiv:2010.15968 [quant-ph]
Original
2010
Cited alongside, same era.
G. S. Barron and C. J. Wood, “Measurement error mitigation for variational quantum algorithms,” arXiv:2010.08520 [quant-ph]
Original
2010
Cited alongside, same era.
J. Zeng, Z. Wu, C. Cao, C. Zhang, S. Hou, P. Xu, and B. Zeng, “Simulating noisy variational quantum eigensolver with local noise models,” arXiv:2010.14821 [quant-ph]
Original
2010
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,” arXiv:2011.08763 [quant-ph]

Then

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
2017
Later among the works it cites.
J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,” Nature Communications
2018
Later among the works it cites.
S. Sim, P. D. Johnson, and A. Aspuru‐Guzik, “Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum‐classical algorithms,” Advanced Quantum Technologies
2019
Later among the works it cites.
S. E. Rasmussen, N. J. S. Loft, T. Bækkegaard, M. Kues, and N. T. Zinner, “Reducing the amount of single‐qubit rotations in vqe and related algorithms,” Advanced Quantum Technologies
2020
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…

Original

2011

Cited alongside, same era.

M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, “Variational quantum algorithms,” arXiv:2012.09265 [quant-ph]

Original

2012

Cited alongside, same era.

D. Kunin, J. Sagastuy-Breña, S. Ganguli, D. L. K. Yamins, and H. Tanaka, “Neural mechanics: Symmetry and broken conservation laws in deep learning dynamics,” CoRR

Original

2012

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

2014

Cited alongside, same era.

E. Farhi, J. Goldstone, and S. Gutmann, “A Quantum Approximate Optimization Algorithm,” arXiv:1411.4028 [quant-ph]

Original

Cited in the paper.

Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, “Connecting ansatz expressibility to gradient magnitudes and barren plateaus,” arXiv:2101.02138 [quant-ph]

Original

Cited in the paper.

J. Kim and Y. Oz, “Entanglement Diagnostics for Efficient Quantum Computation,” arXiv:2102.12534 [quant-ph]

Original

Cited in the paper.

A. Arrasmith, Z. Holmes, M. Cerezo, and P. J. Coles, “Equivalence of quantum barren plateaus to cost concentration and narrow gorges,” arXiv:2104.05868 [quant-ph]

Original

Cited in the paper.

S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, “Hybrid quantum-classical algorithms and quantum error mitigation,” Journal of the Physical Society of Japan

2021

Closest in time.

J. Kim, J. Kim, and D. Rosa, “Universal effectiveness of high-depth circuits in variational eigenproblems,” Physical Review Research

2021

Closest in time.

L. Funcke, T. Hartung, K. Jansen, S. Kühn, and P. Stornati, “Dimensional expressivity analysis of parametric quantum circuits,” Quantum

2021

Closest in time.

P. Huembeli and A. Dauphin, “Characterizing the loss landscape of variational quantum circuits,” Quantum Science and Technology

2058

Closest in time.