Built on

Daniel Gottesman, “Theory of fault-tolerant quantum computation,” Phys. Rev. A 57
1998
Earlier work this paper cites.
M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information , Cambridge Series on Information and the Natural Sciences (Cambridge University Press, 2000)
2000
Earlier work this paper cites.
Leslie G. Valiant, “Quantum computers that can be simulated classically in polynomial time,” Sym. Theo. Comp. 33
2001
Earlier work this paper cites.
A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303
2003
Earlier work this paper cites.
Dorit Aharonov and Amnon Ta-Shma, “Adiabatic quantum state generation and statistical zero knowledge,” ArXiv:quant-ph/0301023 (2003)
2003
Earlier work this paper cites.
Google AI Quantum and Collaborators, “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,” ArXiv:2004.04197 (2020a)
Original
2004
Earlier work this paper cites.
Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders, “Efficient quantum algorithms for simulating sparse hamiltonians,” Comm. Math. Phys. 270
2007
Earlier work this paper cites.
B. L. Higgins, D. W. Berry, S. D. Bartlett, M. W. Mitchell, H. M. Wiseman, and G. J. Pryde., “Demonstrating heisenberg-limited unambiguous phase estimation without adaptive measurements.” New J. Phys. 11
Original
2009
Earlier work this paper cites.
James D. Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik, “Simulation of electronic structure hamiltonians using quantum computers,” Mol. Phys. 109
Original
2011
Earlier work this paper cites.
Easwar Magesan, J. M. Gambetta, , and Joseph Emerson, “Scalable and robust randomized benchmarking of quantum processes,” Phys. Rev. Lett. 106
Original
2011
Earlier work this paper cites.
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A 86
Original
2012
Earlier work this paper cites.
Krysta M. Svore, Matthew B. Hastings, and Michael Freedman, “Faster phase estimation,” Quant. Inf. Comp. 14
Original
2013
Earlier work this paper cites.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, “A quantum approximate optimization algorithm,” ArXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
Nathan Wiebe, Christopher Granade, Christopher Ferrie, and D. G. Cory, “Hamiltonian learning and certification using quantum resources,” Phys. Rev. Lett. 112
Original
2014
Earlier work this paper cites.
Shelby Kimmel, Guang Hao Low, and Theodore J. Yoder, “Robust calibration of a universal single-qubit gate-set via robust phase estimation,” Phys. Rev. A 92
Original
2015
Earlier work this paper cites.
D. Wecker, M. B. Hastings, and M. Troyer, “Towards practical quantum variational algorithms,” Phys. Rev. A 92
Original
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 J. Phys. 18
2016
Earlier work this paper cites.
Adenilton J. da Silva, Teresa B. Ludermir, and Wilson R. de Oliveira, “Quantum perceptron over a field and neural network architecture selection in a quantum computer,” Neu. Net. 76
Original
2016
Earlier work this paper cites.
Nathan Wiebe and Chris Granade, “Efficient bayesian phase estimation,” Phys. Rev. Lett. 117
Original
2016
Earlier work this paper cites.
Joel J Wallman and Joseph Emerson, “Noise tailoring for scalable quantum computation via randomized compiling,” Physical Review A 94
2016
Earlier work this paper cites.

Similar

Ilia Zintchenko and Nathan Wiebe, “Randomized gap and amplitude estimation,” Phys. Rev. A 93
2016
Cited alongside, same era.
P.J.J. O’Malley, R. Babbush, I.D. Kivlichan, J. Romero, J.R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A.G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J.Y. Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T.C. White, P.V. Coveney, P.J. Love, H. Neven, A. Aspuru-Guzik, and J.M. Martinis, “Scalable quantum simulation of molecular energies,” Phys. Rev. X 6
2016
Cited alongside, same era.
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
Cited alongside, same era.
J. S. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, M. Block, B. Bloom, S. Caldwell, N. Didier, E. Schuyler Fried, S. Hong, P. Karalekas, C. B. Osborn, A. Papageorge, E. C. Peterson, G. Prawiroatmodjo, N. Rubin, Colm A. Ryan, D. Scarabelli, M. Scheer, E. A. Sete, P. Sivarajah, Robert S. Smith, A. Staley, N. Tezak, W. J. Zeng, A. Hudson, Blake R. Johnson, M. Reagor, M. P. da Silva, and C. Rigetti, “Unsupervised machine learning on a hybrid quantum computer,” ArXiv:1712.05771 (2017)

Then

Earl Campbell, Ankur Khurana, and Ashley Montanaro, “Applying quantum algorithms to constraint satisfaction problems,” Quantum 3
2019
Later among the works it cites.
Sergey Bravyi, David Gosset, and Ramis Movassagh, “Classical algorithms for quantum mean values,” ArXiv:1909.11485 (2019)
Original
2019
Later among the works it cites.
R. Sagastizabal, X. Bonet-Monroig, M. Singh, M.A. Rol, C.C. Bultink, X. Fu, C.H. Price, V.P. Ostroukh, N. Muthusubramanian, A. Bruno, M. Beekman, N. Haider, T.E. O’Brien, and L. DiCarlo, “Error mitigation by symmetry verification on a variational quantum eigensolver,” Phys. Rev. A 100
Original
2019
Later among the works it cites.
Abhinav Kandala, Kristan Temme, Antonio D. Córcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta, “Error mitigation extends the computational reach of a noisy quantum processor,” Nature 567
2019
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…

2020

Error mitigation via verified phase estimation

O'Brien, Thomas E., Polla, Stefano, Rubin, Nicholas C. et al.

Understand

The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts.

We do not expect to be able to afford the overhead required for quantum error correction in the next decade, so in the meantime we must rely on low-cost, unscalable error mitigation techniques to bring quantum computing to its full potential.
This paper presents a new error mitigation technique based on quantum phase estimation that can also reduce errors in expectation value estimation (e.g., for variational algorithms).
The general idea is to apply phase estimation while effectively post-selecting for the system register to be in the starting state, which allows us to catch and discard errors which knock us away from there.

Built on

Daniel Gottesman, “Theory of fault-tolerant quantum computation,” Phys. Rev. A 57
1998
Earlier work this paper cites.
M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information , Cambridge Series on Information and the Natural Sciences (Cambridge University Press, 2000)
2000
Earlier work this paper cites.
Leslie G. Valiant, “Quantum computers that can be simulated classically in polynomial time,” Sym. Theo. Comp. 33
2001
Earlier work this paper cites.
A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303
2003
Earlier work this paper cites.
Dorit Aharonov and Amnon Ta-Shma, “Adiabatic quantum state generation and statistical zero knowledge,” ArXiv:quant-ph/0301023 (2003)
2003
Earlier work this paper cites.
Google AI Quantum and Collaborators, “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,” ArXiv:2004.04197 (2020a)
Original
2004
Earlier work this paper cites.
Dominic W. Berry, Graeme Ahokas, Richard Cleve, and Barry C. Sanders, “Efficient quantum algorithms for simulating sparse hamiltonians,” Comm. Math. Phys. 270
2007
Earlier work this paper cites.
B. L. Higgins, D. W. Berry, S. D. Bartlett, M. W. Mitchell, H. M. Wiseman, and G. J. Pryde., “Demonstrating heisenberg-limited unambiguous phase estimation without adaptive measurements.” New J. Phys. 11
Original
2009
Earlier work this paper cites.
James D. Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik, “Simulation of electronic structure hamiltonians using quantum computers,” Mol. Phys. 109
Original
2011
Earlier work this paper cites.
Easwar Magesan, J. M. Gambetta, , and Joseph Emerson, “Scalable and robust randomized benchmarking of quantum processes,” Phys. Rev. Lett. 106
Original
2011
Earlier work this paper cites.
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A 86
Original
2012
Earlier work this paper cites.
Krysta M. Svore, Matthew B. Hastings, and Michael Freedman, “Faster phase estimation,” Quant. Inf. Comp. 14
Original
2013
Earlier work this paper cites.
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, “A quantum approximate optimization algorithm,” ArXiv:1411.4028 (2014)
Original
2014
Earlier work this paper cites.
Nathan Wiebe, Christopher Granade, Christopher Ferrie, and D. G. Cory, “Hamiltonian learning and certification using quantum resources,” Phys. Rev. Lett. 112
Original
2014
Earlier work this paper cites.
Shelby Kimmel, Guang Hao Low, and Theodore J. Yoder, “Robust calibration of a universal single-qubit gate-set via robust phase estimation,” Phys. Rev. A 92
Original
2015
Earlier work this paper cites.
D. Wecker, M. B. Hastings, and M. Troyer, “Towards practical quantum variational algorithms,” Phys. Rev. A 92
Original
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 J. Phys. 18
2016
Earlier work this paper cites.
Adenilton J. da Silva, Teresa B. Ludermir, and Wilson R. de Oliveira, “Quantum perceptron over a field and neural network architecture selection in a quantum computer,” Neu. Net. 76
Original
2016
Earlier work this paper cites.
Nathan Wiebe and Chris Granade, “Efficient bayesian phase estimation,” Phys. Rev. Lett. 117
Original
2016
Earlier work this paper cites.
Joel J Wallman and Joseph Emerson, “Noise tailoring for scalable quantum computation via randomized compiling,” Physical Review A 94
2016
Earlier work this paper cites.

Similar

Ilia Zintchenko and Nathan Wiebe, “Randomized gap and amplitude estimation,” Phys. Rev. A 93
2016
Cited alongside, same era.
P.J.J. O’Malley, R. Babbush, I.D. Kivlichan, J. Romero, J.R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A.G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J.Y. Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T.C. White, P.V. Coveney, P.J. Love, H. Neven, A. Aspuru-Guzik, and J.M. Martinis, “Scalable quantum simulation of molecular energies,” Phys. Rev. X 6
2016
Cited alongside, same era.
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
Cited alongside, same era.
J. S. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, M. Block, B. Bloom, S. Caldwell, N. Didier, E. Schuyler Fried, S. Hong, P. Karalekas, C. B. Osborn, A. Papageorge, E. C. Peterson, G. Prawiroatmodjo, N. Rubin, Colm A. Ryan, D. Scarabelli, M. Scheer, E. A. Sete, P. Sivarajah, Robert S. Smith, A. Staley, N. Tezak, W. J. Zeng, A. Hudson, Blake R. Johnson, M. Reagor, M. P. da Silva, and C. Rigetti, “Unsupervised machine learning on a hybrid quantum computer,” ArXiv:1712.05771 (2017)

Then

Earl Campbell, Ankur Khurana, and Ashley Montanaro, “Applying quantum algorithms to constraint satisfaction problems,” Quantum 3
2019
Later among the works it cites.
Sergey Bravyi, David Gosset, and Ramis Movassagh, “Classical algorithms for quantum mean values,” ArXiv:1909.11485 (2019)
Original
2019
Later among the works it cites.
R. Sagastizabal, X. Bonet-Monroig, M. Singh, M.A. Rol, C.C. Bultink, X. Fu, C.H. Price, V.P. Ostroukh, N. Muthusubramanian, A. Bruno, M. Beekman, N. Haider, T.E. O’Brien, and L. DiCarlo, “Error mitigation by symmetry verification on a variational quantum eigensolver,” Phys. Rev. A 100
Original
2019
Later among the works it cites.
Abhinav Kandala, Kristan Temme, Antonio D. Córcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta, “Error mitigation extends the computational reach of a noisy quantum processor,” Nature 567
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…

Original

2017

Cited alongside, same era.

Jarrod R. McClean, Mollie E. Schwartz, Jonathan Carter, and Wibe A. de Jong, “Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states,” Phys. Rev. A 95

Original

2017

Cited alongside, same era.

Kristan Temme, Sergey Bravyi, and Jay M. Gambetta, “Error mitigation for short-depth quantum circuits,” Phys. Rev. Lett. 119

Original

2017

Cited alongside, same era.

Yosi Atia and Dorit Aharonov, “Fast-forwarding of hamiltonians and exponentially precise measurements,” Nat. Comm. 8

2017

Cited alongside, same era.

Cornelius Hempel, Christine Maier, Jonathan Romero, Jarrod McClean, Thomas Monz, Heng Shen, Petar Jurcevic, Ben Lanyon, Peter Love, Ryan Babbush, Alan Aspuru-Guzik, Rainer Blatt, and Christian Roos, “Quantum chemistry calculations on a trapped-ion quantum simulator,” Phys. Rev. X 8

2018

Cited alongside, same era.

John Preskill, “Quantum computing in the nisq era and beyond,” Quantum 2

2018

Cited alongside, same era.

Hongxiang Chen, Leonard Wossnig, Simone Severini, Hartmut Neven, and Masoud Mohseni, “Universal discriminative quantum neural networks,” ArXiv:1805.08654 (2018)

Original

2018

Cited alongside, same era.

Suguru Endo, Simon C. Benjamin, and Ying Li, “Practical quantum error mitigation for near-future applications,” Phys. Rev. X 8

2018

Cited alongside, same era.

Nicholas C. Rubin, Ryan Babbush, and Jarrod McClean, “Application of fermionic marginal constraints to hybrid quantum algorithms,” New J. Phys. 20

2018

Cited alongside, same era.

Sam McArdle, Xiao Yuan, and Simon Benjamin, “Error-mitigated digital quantum simulation,” Phys. Rev. Lett. 122

Original

2019