Fetching the paper…

Reading the bibliography…

Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation · Around

2020

Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation

Commeau, Benjamin, Cerezo, M., Holmes, Zoë et al.

Original
PDF
Post on X

Understand

Dynamical quantum simulation may be one of the first applications to see quantum advantage.

However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers.
This has led to recent proposals for variational approaches to dynamical simulation.
In this work, we aim to make variational dynamical simulation even more practical and near-term.

Built on

Seth Lloyd, “Universal quantum simulators,” Science , 1073–1078 (1996)
1996
Earlier work this paper cites.
Daniel S Abrams and Seth Lloyd, “Simulation of many-body fermi systems on a universal quantum computer,” Physical Review Letters 79
1997
Earlier work this paper cites.
Richard P Feynman, “Simulating physics with computers,” Int. J. Theor. Phys 21
1999
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.
Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,” Physical Review A 60
1999
Earlier work this paper cites.
M Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles, “Cost-function-dependent barren plateaus in shallow quantum neural networks,” arXiv preprint arXiv:2001.00550 (2020c)
Original
2001
Earlier work this paper cites.
Michael A Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Physics Letters A 303
2002
Earlier work this paper cites.
M Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J Coles, “Variational quantum state eigensolver,” arXiv preprint arXiv:2004.01372 (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 (2020a)
Original
2005
Earlier work this paper cites.
D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, “Efficient quantum algorithms for simulating sparse Hamiltonians,” Commun. Math. Phys. 270
2007
Earlier work this paper cites.
Subir Sachdev, “Quantum phase transitions,” Handbook of Magnetism and Advanced Magnetic Materials (2007)
2007
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 (2020b)
Original
2007
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.
Jonathan Welch, Daniel Greenbaum, Sarah Mostame, and Alán Aspuru-Guzik, “Efficient quantum circuits for diagonal unitaries without ancillas,” New Journal of Physics 16
2014
Earlier work this paper cites.

Similar

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
Cited alongside, same era.
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
Cited alongside, same era.
J. Romero, J. P. Olson, and A. Aspuru-Guzik, “Quantum autoencoders for efficient compression of quantum data,” Quantum Science and Technology 2
2017
Cited alongside, same era.
Ying Li and Simon C Benjamin, “Efficient variational quantum simulator incorporating active error minimization,” Physical Review X 7
2017
Cited alongside, same era.
Yosi Atia and Dorit Aharonov, “Fast-forwarding of hamiltonians and exponentially precise measurements,” Nature communications 8

Then

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.
Carlos Bravo-Prieto, Ryan LaRose, M. Cerezo, Yigit Subasi, Lukasz Cincio, and Patrick J. Coles, “Variational quantum linear solver: A hybrid algorithm for linear systems,” arXiv:1909.05820 (2019)
Original
2019
Later among the works it cites.
Kentaro Heya, Ken M Nakanishi, Kosuke Mitarai, and Keisuke Fujii, “Subspace variational quantum simulator,” arXiv preprint arXiv:1904.08566 (2019)
Original
2019
Later among the works it cites.
Cristina Cirstoiu, Zoe Holmes, Joseph Iosue, Lukasz Cincio, Patrick J Coles, and Andrew Sornborger, “Variational fast forwarding for quantum simulation beyond the coherence time,” arXiv preprint arXiv:1910.04292 (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…

2017

Cited alongside, same era.

T. Loke and J. B. Wang, “Efficient quantum circuits for continuous-time quantum walks on composite graphs,” Journal of Physics A: Mathematical and Theoretical 50

2017

Cited alongside, same era.

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 549

2017

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

2018

Cited alongside, same era.

Suguru Endo, Ying Li, Simon Benjamin, and Xiao Yuan, “Variational quantum simulation of general processes,” arXiv preprint arXiv:1812.08778 (2018)

2018

Cited alongside, same era.

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.

Guanyu Zhu, Yiğit Subaşı, James D Whitfield, and Mohammad Hafezi, “Hardware-efficient fermionic simulation with a cavity–qed system,” npj Quantum Information 4

2018

Cited alongside, same era.

K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, “Quantum circuit learning,” Phys. Rev. A 98

2018

Cited alongside, same era.

Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, and Simon C Benjamin, “Theory of variational quantum simulation,” Quantum 3

2019

Later among the works it cites.

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

2019

Later among the works it cites.

Guillaume Verdon, Michael Broughton, Jarrod R McClean, Kevin J Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, and Masoud Mohseni, “Learning to learn with quantum neural networks via classical neural networks,” arXiv preprint arXiv:1907.05415 (2019)

2019

Later among the works it cites.

Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran, “Evaluating analytic gradients on quantum hardware,” Physical Review A 99

2019

Later among the works it cites.

Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin Chan, “Quantum algorithms for quantum chemistry and quantum materials science,” arXiv preprint arXiv:2001.03685 (2020)

2020

Closest in time.

Thi Ha Kyaw, Tim Menke, Sukin Sim, Nicolas PD Sawaya, William D Oliver, Gian Giacomo Guerreschi, and Alán Aspuru-Guzik, “Quantum computer-aided design: digital quantum simulation of quantum processors,” arXiv preprint arXiv:2006.03070 (2020)

2020

Closest in time.

M Cerezo and Patrick J Coles, “Impact of barren plateaus on the hessian and higher order derivatives,” arXiv preprint arXiv:2008.07454 (2020)

2020

Closest in time.

Samson Wang, Enrico Fontana, M Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles, “Noise-induced barren plateaus in variational quantum algorithms,” arXiv preprint arXiv:2007.14384 (2020)

2020

Closest in time.

Tyler Volkoff and Patrick J Coles, “Large gradients via correlation in random parameterized quantum circuits,” arXiv preprint arXiv:2005.12200 (2020)

2020

Closest in time.

Alexey Uvarov, Jacob Biamonte, and Dmitry Yudin, “Variational quantum eigensolver for frustrated quantum systems,” arXiv preprint arXiv:2005.00544 (2020)

2020

Closest in time.