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K. Sharma, S. Khatri, M. Cerezo, and P. J. Coles, “Noise resilience of variational quantum compiling,” arXiv:1908.04416 [quant-ph]
Original
1908
Earlier work this paper cites.
H. Rabitz, M. Hsieh, and C. Rosenthal, “Quantum optimally controlled transition landscapes,” Science 303
2004
Earlier work this paper cites.
N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, “Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms,” Journal of Magnetic Resonance 172
2005
Earlier work this paper cites.
H. Rabitz, M. Hsieh, and C. Rosenthal, “Landscape for optimal control of quantum-mechanical unitary transformations,” Physical Review A 72
2005
Earlier work this paper cites.
H. Rabitz, T.-S. Ho, M. Hsieh, R. Kosut, and M. Demiralp, “Topology of optimally controlled quantum mechanical transition probability landscapes,” Physical Review A 74
2006
Earlier work this paper cites.
R. Chakrabarti and H. Rabitz, “Quantum control landscapes,” International Reviews in Physical Chemistry 26
2007
Earlier work this paper cites.
K. Moore, M. Hsieh, and H. Rabitz, “On the relationship between quantum control landscape structure and optimization complexity,” The Journal of chemical physics 128
2008
Earlier work this paper cites.
T.-S. Ho, J. Dominy, and H. Rabitz, “Landscape of unitary transformations in controlled quantum dynamics,” Physical Review A 79
2009
Earlier work this paper cites.
C. Brif, R. Chakrabarti, and H. Rabitz, “Control of quantum phenomena: past, present and future,” New Journal of Physics 12
2010
Earlier work this paper cites.

Similar

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. O’brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature communications 5
2014
Cited alongside, same era.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 3rd International Conference on Learning Representations, ICLR 2015 , arXiv:1412.6980 (2014)
Original
2014
Cited alongside, same era.
G. Riviello, K. M. Tibbetts, C. Brif, R. Long, R.-B. Wu, T.-S. Ho, and H. Rabitz, “Searching for quantum optimal controls under severe constraints,” Physical Review A 91
2015
Cited alongside, same era.
E. Farhi and A. W. Harrow, “Quantum supremacy through the quantum approximate optimization algorithm,” arXiv:1602.07674 (2016)
Original
2016
Cited alongside, same era.

Then

S. Lloyd, “Quantum approximate optimization is computationally universal,” arXiv:1812.11075 (2018)
Original
2018
Later among the works it cites.
L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices,” arXiv:1812.01041 (2018)
Original
2018
Later among the works it cites.
M. Zaheer, S. Reddi, D. Sachan, S. Kale, and S. Kumar, “Adaptive methods for nonconvex optimization,” in Advances in Neural Information Processing Systems (2018) pp. 9793–9803
2018
Later among the works it cites.
S. Lloyd and R. Maity, “Efficient implementation of unitary transformations,” arXiv:1901.03431 (2019)
Original
2019
Later among the works it cites.

Beyond the bibliography

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2020

Learning Unitaries by Gradient Descent

Kiani, Bobak Toussi, Lloyd, Seth, Maity, Reevu

Understand

We study the hardness of learning unitary transformations in $U(d)$ via gradient descent on time parameters of alternating operator sequences.

We provide numerical evidence that, despite the non-convex nature of the loss landscape, gradient descent always converges to the target unitary when the sequence contains $d^2$ or more parameters.
Rates of convergence indicate a "computational phase transition." With less than $d^2$ parameters, gradient descent converges to a sub-optimal solution, whereas with more than $d^2$ parameters, gradient descent converges exponentially to an optimal solution.

Built on

K. Sharma, S. Khatri, M. Cerezo, and P. J. Coles, “Noise resilience of variational quantum compiling,” arXiv:1908.04416 [quant-ph]
Original
1908
Earlier work this paper cites.
H. Rabitz, M. Hsieh, and C. Rosenthal, “Quantum optimally controlled transition landscapes,” Science 303
2004
Earlier work this paper cites.
N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, “Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms,” Journal of Magnetic Resonance 172
2005
Earlier work this paper cites.
H. Rabitz, M. Hsieh, and C. Rosenthal, “Landscape for optimal control of quantum-mechanical unitary transformations,” Physical Review A 72
2005
Earlier work this paper cites.
H. Rabitz, T.-S. Ho, M. Hsieh, R. Kosut, and M. Demiralp, “Topology of optimally controlled quantum mechanical transition probability landscapes,” Physical Review A 74
2006
Earlier work this paper cites.
R. Chakrabarti and H. Rabitz, “Quantum control landscapes,” International Reviews in Physical Chemistry 26
2007
Earlier work this paper cites.
K. Moore, M. Hsieh, and H. Rabitz, “On the relationship between quantum control landscape structure and optimization complexity,” The Journal of chemical physics 128
2008
Earlier work this paper cites.
T.-S. Ho, J. Dominy, and H. Rabitz, “Landscape of unitary transformations in controlled quantum dynamics,” Physical Review A 79
2009
Earlier work this paper cites.
C. Brif, R. Chakrabarti, and H. Rabitz, “Control of quantum phenomena: past, present and future,” New Journal of Physics 12
2010
Earlier work this paper cites.

Similar

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. O’brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature communications 5
2014
Cited alongside, same era.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 3rd International Conference on Learning Representations, ICLR 2015 , arXiv:1412.6980 (2014)
Original
2014
Cited alongside, same era.
G. Riviello, K. M. Tibbetts, C. Brif, R. Long, R.-B. Wu, T.-S. Ho, and H. Rabitz, “Searching for quantum optimal controls under severe constraints,” Physical Review A 91
2015
Cited alongside, same era.
E. Farhi and A. W. Harrow, “Quantum supremacy through the quantum approximate optimization algorithm,” arXiv:1602.07674 (2016)
Original
2016
Cited alongside, same era.

Then

S. Lloyd, “Quantum approximate optimization is computationally universal,” arXiv:1812.11075 (2018)
Original
2018
Later among the works it cites.
L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices,” arXiv:1812.01041 (2018)
Original
2018
Later among the works it cites.
M. Zaheer, S. Reddi, D. Sachan, S. Kale, and S. Kumar, “Adaptive methods for nonconvex optimization,” in Advances in Neural Information Processing Systems (2018) pp. 9793–9803
2018
Later among the works it cites.
S. Lloyd and R. Maity, “Efficient implementation of unitary transformations,” arXiv:1901.03431 (2019)
Original
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…

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

Cited alongside, same era.

G. Riviello, R.-B. Wu, Q. Sun, and H. Rabitz, “Searching for an optimal control in the presence of saddles on the quantum-mechanical observable landscape,” Physical Review A 95

2017

Cited alongside, same era.

B. Russell, H. Rabitz, and R.-B. Wu, “Quantum control landscapes are almost always trap free,” Journal of Physics A: Mathematical and Theoretical 50

2017

Cited alongside, same era.

Z. Jiang, E. Rieffel, and Z. Wang, “A QAOA-inspired circuit for Grover’s unstructured search using a transverse field,” arXiv:1702.0257 (2017)

Original

2017

Cited alongside, same era.

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

Original

Cited in the paper.

E. Farhi, J. Goldstone, and S. Gutmann, “A quantum approximate optimization algorithm applied to a bounded occurrence constraint problem,” arXiv:1412.6062 (2014b)

Original

Cited in the paper.

A. Gilyén, S. Arunachalam, and N. Wiebe, “Optimizing quantum optimization algorithms via faster quantum gradient computation,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SIAM, 2019) pp. 1425–1444

2019

Later among the works it cites.

S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, “Quantum-assisted quantum compiling,” Quantum 3

2019

Later among the works it cites.

A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, et al. , “Pytorch: An imperative style, high-performance deep learning library,” in Advances in Neural Information Processing Systems 32 (2019) pp. 8024–8035

Original

2019

Later among the works it cites.

J. Carolan, M. Mohseni, J. P. Olson, M. Prabhu, C. Chen, D. Bunandar, M. Y. Niu, N. C. Harris, F. Wong, M. Hochberg, et al. , “Variational quantum unsampling on a quantum photonic processor,” Nature Physics , 1–6 (2020)

2020

Closest in time.