Built on

Rolando D. Somma, “Quantum eigenvalue estimation via time series analysis,” (2020), arXiv:1907.11748 [quant-ph]
Original
1907
Earlier work this paper cites.
AN Krylov, “On the numerical solution of equation by which are determined in technical problems the frequencies of small vibrations of material systems,” News Acad. Sci. USSR 7
1931
Earlier work this paper cites.
Elliott Lieb, Theodore Schultz, and Daniel Mattis, “Two soluble models of an antiferromagnetic chain,” Annals of Physics 16
1961
Earlier work this paper cites.
Masuo Suzuki, “Generalized trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems,” Communications in Mathematical Physics 51
1976
Earlier work this paper cites.
Seth Lloyd, “Universal quantum simulators,” Science , 1073–1078 (1996)
1996
Earlier work this paper cites.
AT Sornborger and Ewan D Stewart, “Higher-order methods for simulations on quantum computers,” Physical Review A 60
1999
Earlier work this paper cites.
Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)
2000
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.
Kunal Sharma, M. Cerezo, Lukasz Cincio, and Patrick J Coles, “Trainability of dissipative perceptron-based quantum neural networks,” arXiv preprint arXiv:2005.12458 (2020c)
Original
2005
Earlier work this paper cites.
Kunal Sharma, M. Cerezo, Zoë Holmes, Lukasz Cincio, Andrew Sornborger, and Patrick J Coles, “Reformulation of the no-free-lunch theorem for entangled data sets,” arXiv preprint arXiv:2007.04900 (2020a)
Original
2007
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.
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.
Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature communications 5
2014
Earlier work this paper cites.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, “A quantum approximate optimization algorithm,” arXiv preprint arXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma, “Simulating hamiltonian dynamics with a truncated taylor series,” Physical Review Letters 114
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.
Y. Li and S. C. Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Phys. Rev. X 7
2017
Earlier work this paper cites.
Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
Earlier work this paper cites.
Colin J Trout, Muyuan Li, Mauricio Gutiérrez, Yukai Wu, Sheng-Tao Wang, Luming Duan, and Kenneth R Brown, “Simulating the performance of a distance-3 surface code in a linear ion trap,” New Journal of Physics 20
2018
Earlier work this paper cites.

Similar

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.
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, et al. , “Quantum supremacy using a programmable superconducting processor,” Nature 574
2019
Cited alongside, same era.
Guang Hao Low and Isaac L Chuang, “Hamiltonian simulation by qubitization,” Quantum 3
2019
Cited alongside, same era.
Sumeet Khatri, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T Sornborger, and Patrick J Coles, “Quantum-assisted quantum compiling,” Quantum 3
2019
Cited alongside, same era.
Ryan LaRose, Arkin Tikku, Étude O’Neel-Judy, Lukasz Cincio, and Patrick J Coles, “Variational quantum state diagonalization,” npj Quantum Information 5
2019

Then

Burak Sahinoglu and Rolando D Somma, “Hamiltonian simulation in the low energy subspace,” arXiv preprint arXiv:2006.02660 (2020)
Original
2020
Later among the works it cites.
Zoë Holmes, Andrew Arrasmith, Bin Yan, Patrick J Coles, Andreas Albrecht, and Andrew T Sornborger, “Barren plateaus preclude learning scramblers,” arXiv preprint arXiv:2009.14808 (2020)
Original
2020
Later among the works it cites.
Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T Sornborger, and Patrick J Coles, “Absence of barren plateaus in quantum convolutional neural networks,” arXiv preprint arXiv:2011.02966 (2020)
Original
2020
Later among the works it cites.
Alexey Uvarov and Jacob Biamonte, “On barren plateaus and cost function locality in variational quantum algorithms,” arXiv preprint arXiv:2011.10530 (2020)
Original
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…

Reading the bibliography…

2021

Long-time simulations with high fidelity on quantum hardware

Gibbs, Joe, Gili, Kaitlin, Holmes, Zoë et al.

Understand

Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems.

However, while rapidly improving, these devices have short coherence times, limiting the depth of algorithms that may be successfully implemented.
Here we demonstrate that, despite these limitations, it is possible to implement long-time, high fidelity simulations on current hardware.
Specifically, we simulate an XY-model spin chain on the Rigetti and IBM quantum computers, maintaining a fidelity of at least 0.9 for over 600 time steps.

Built on

Rolando D. Somma, “Quantum eigenvalue estimation via time series analysis,” (2020), arXiv:1907.11748 [quant-ph]
Original
1907
Earlier work this paper cites.
AN Krylov, “On the numerical solution of equation by which are determined in technical problems the frequencies of small vibrations of material systems,” News Acad. Sci. USSR 7
1931
Earlier work this paper cites.
Elliott Lieb, Theodore Schultz, and Daniel Mattis, “Two soluble models of an antiferromagnetic chain,” Annals of Physics 16
1961
Earlier work this paper cites.
Masuo Suzuki, “Generalized trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems,” Communications in Mathematical Physics 51
1976
Earlier work this paper cites.
Seth Lloyd, “Universal quantum simulators,” Science , 1073–1078 (1996)
1996
Earlier work this paper cites.
AT Sornborger and Ewan D Stewart, “Higher-order methods for simulations on quantum computers,” Physical Review A 60
1999
Earlier work this paper cites.
Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)
2000
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.
Kunal Sharma, M. Cerezo, Lukasz Cincio, and Patrick J Coles, “Trainability of dissipative perceptron-based quantum neural networks,” arXiv preprint arXiv:2005.12458 (2020c)
Original
2005
Earlier work this paper cites.
Kunal Sharma, M. Cerezo, Zoë Holmes, Lukasz Cincio, Andrew Sornborger, and Patrick J Coles, “Reformulation of the no-free-lunch theorem for entangled data sets,” arXiv preprint arXiv:2007.04900 (2020a)
Original
2007
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.
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.
Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature communications 5
2014
Earlier work this paper cites.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, “A quantum approximate optimization algorithm,” arXiv preprint arXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma, “Simulating hamiltonian dynamics with a truncated taylor series,” Physical Review Letters 114
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.
Y. Li and S. C. Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Phys. Rev. X 7
2017
Earlier work this paper cites.
Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
Earlier work this paper cites.
Colin J Trout, Muyuan Li, Mauricio Gutiérrez, Yukai Wu, Sheng-Tao Wang, Luming Duan, and Kenneth R Brown, “Simulating the performance of a distance-3 surface code in a linear ion trap,” New Journal of Physics 20
2018
Earlier work this paper cites.

Similar

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.
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, et al. , “Quantum supremacy using a programmable superconducting processor,” Nature 574
2019
Cited alongside, same era.
Guang Hao Low and Isaac L Chuang, “Hamiltonian simulation by qubitization,” Quantum 3
2019
Cited alongside, same era.
Sumeet Khatri, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T Sornborger, and Patrick J Coles, “Quantum-assisted quantum compiling,” Quantum 3
2019
Cited alongside, same era.
Ryan LaRose, Arkin Tikku, Étude O’Neel-Judy, Lukasz Cincio, and Patrick J Coles, “Variational quantum state diagonalization,” npj Quantum Information 5
2019

Then

Burak Sahinoglu and Rolando D Somma, “Hamiltonian simulation in the low energy subspace,” arXiv preprint arXiv:2006.02660 (2020)
Original
2020
Later among the works it cites.
Zoë Holmes, Andrew Arrasmith, Bin Yan, Patrick J Coles, Andreas Albrecht, and Andrew T Sornborger, “Barren plateaus preclude learning scramblers,” arXiv preprint arXiv:2009.14808 (2020)
Original
2020
Later among the works it cites.
Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T Sornborger, and Patrick J Coles, “Absence of barren plateaus in quantum convolutional neural networks,” arXiv preprint arXiv:2011.02966 (2020)
Original
2020
Later among the works it cites.
Alexey Uvarov and Jacob Biamonte, “On barren plateaus and cost function locality in variational quantum algorithms,” arXiv preprint arXiv:2011.10530 (2020)
Original
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…

Cited alongside, same era.

Andrew Arrasmith, Lukasz Cincio, Andrew T Sornborger, Wojciech H Zurek, and Patrick J Coles, “Variational consistent histories as a hybrid algorithm for quantum foundations,” Nature communications 10

2019

Cited alongside, same era.

Kentaro Heya, Ken M Nakanishi, Kosuke Mitarai, and Keisuke Fujii, “Subspace variational quantum simulator,” arXiv preprint arXiv:1904.08566 (2019)

Original

2019

Cited alongside, same era.

Sukin Sim, Peter D. Johnson, and Alán Aspuru-Guzik, “Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms,” Advanced Quantum Technologies 2

2019

Cited alongside, same era.

Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, and Marcello Benedetti, “An initialization strategy for addressing barren plateaus in parametrized quantum circuits,” Quantum 3

2019

Cited alongside, same era.

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 (2020)

Original

2020

Cited alongside, same era.

Suguru Endo, Jinzhao Sun, Ying Li, Simon C Benjamin, and Xiao Yuan, “Variational quantum simulation of general processes,” Physical Review Letters 125

Original

2020

Cited alongside, same era.

Yong-Xin Yao, Niladri Gomes, Feng Zhang, Thomas Iadecola, Cai-Zhuang Wang, Kai-Ming Ho, and Peter P Orth, “Adaptive variational quantum dynamics simulations,” arXiv preprint arXiv:2011.00622 (2020)

Original

2020

Cited alongside, same era.

Carlos Ortiz Marrero, Mária Kieferová, and Nathan Wiebe, “Entanglement induced barren plateaus,” arXiv preprint arXiv:2010.15968 (2020)

Original

2020