Built on

A. Harrow and J. Napp, Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms, Physical Review Letters 126
Original
1901
Earlier work this paper cites.
J. Knoblauch, J. Jewson, and T. Damoulas, Generalized Variational Inference: Three arguments for deriving new Posteriors (2019), arXiv:1904.02063
Original
1904
Earlier work this paper cites.
A. W. Harrow and A. Y. Wei, Adaptive quantum simulated annealing for Bayesian inference and estimating partition functions, in Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA) (2020) pp. 193–212, arXiv:1907.09965
Original
1907
Earlier work this paper cites.
Y. Nesterov, A method for solving the convex programming problem with convergence rate o ⁡ ( 1 / k 2 ) o(1/k^{2}) , Proceedings of the USSR Academy of Sciences 269
1983
Earlier work this paper cites.
A. J. Izenman and C. J. Sommer, Philatelic mixtures and multimodal densities, Journal of the American Statistical Association 83
1988
Earlier work this paper cites.
R. R. Tucci, Quantum Bayesian nets, International Journal of Modern Physics B 09
1995
Earlier work this paper cites.
P. M. Williams, Bayesian regularization and pruning using a Laplace prior, Neural computation 7
1995
Earlier work this paper cites.
R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological) 58
1996
Earlier work this paper cites.
K. V. Mardia, P. E. Jupp, and K. Mardia, Directional statistics , Vol. 2 (Wiley Online Library, 2000)
2000
Earlier work this paper cites.
J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. S. Allman, C. H. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer, C. Ryan-Anderson, and B. Neyenhuis, Demonstration of the trapped-ion quantum CCD computer architecture, Nature 592
Original
2003
Earlier work this paper cites.
S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, t | | ket ⟩ \rangle : A retargetable compiler for NISQ devices, Quantum Science and Technology 6
Original
2003
Earlier work this paper cites.
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Modeling & Simulation 4
2005
Earlier work this paper cites.
H. Ishwaran and J. S. Rao, Spike and slab variable selection: Frequentist and Bayesian strategies, The Annals of Statistics 33
2005
Earlier work this paper cites.
T. Volkoff and P. J. Coles, Large gradients via correlation in random parameterized quantum circuits, Quantum Science and Technology 6
Original
2005
Earlier work this paper cites.
A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib, Layerwise learning for quantum neural networks, Quantum Machine Intelligence 3
Original
2006
Earlier work this paper cites.
M. Leifer and D. Poulin, Quantum Graphical Models and Belief Propagation, Annals of Physics 323
Original
2008
Earlier work this paper cites.
C. M. Carvalho, N. G. Polson, and J. G. Scott, Handling sparsity via the horseshoe, in Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics , Proceedings of Machine Learning Research, Vol. 5, edited by D. van Dyk and M. Welling (PMLR, Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA, 2009) pp. 73–80
2009
Earlier work this paper cites.
C. Andrieu and G. O. Roberts, The pseudo-marginal approach for efficient Monte Carlo computations, The Annals of Statistics 37
2009
Earlier work this paper cites.
S. Brooks, A. Gelman, G. Jones, and X.-L. Meng, Handbook of Markov Chain Monte Carlo (CRC press, 2011)
2011
Earlier work this paper cites.
M. Welling and Y. W. Teh, Bayesian learning via stochastic gradient Langevin dynamics, in Proceedings of the 28th international conference on machine learning (ICML-11) (2011) pp. 681–688
2011
Earlier work this paper cites.
S. Sachdev, Quantum Phase Transitions , 2nd ed. (Cambridge University Press, Cambridge, UK, 2011)
2011
Earlier work this paper cites.
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, Nature Reviews Physics 3
Original
2012
Earlier work this paper cites.
A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. Smola, A kernel two-sample test, Journal of Machine Learning Research 13
2012
Earlier work this paper cites.

Similar

G. H. Low, T. J. Yoder, and I. L. Chuang, Quantum inference on Bayesian networks, Phys. Rev. A 89
Original
2014
Cited alongside, same era.
N. Parikh and S. Boyd, Proximal algorithms, Found. Trends Optim. 1
2014
Cited alongside, same era.
T. Chen, E. Fox, and C. Guestrin, Stochastic gradient Hamiltonian Monte Carlo, in Proceedings of the 31st International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 32, edited by E. P. Xing and T. Jebara (PMLR, Bejing, China, 2014) pp. 1683–1691
2014
Cited alongside, same era.
N. G. Polson, J. G. Scott, and B. T. Willard, Proximal algorithms in statistics and machine learning, Statistical Science 30
Original
2015
Cited alongside, same era.
Y.-A. Ma, T. Chen, and E. Fox, A Complete Recipe for Stochastic Gradient MCMC, in Advances in Neural Information Processing Systems , Vol. 28, edited by C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett (Curran Associates, Inc., 2015) arXiv:1506.04696

Then

B. T. Gard, L. Zhu, G. S. Barron, N. J. Mayhall, S. E. Economou, and E. Barnes, Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm, npj Quantum Information 6
2020
Later among the works it cites.
Y. Du, M.-H. Hsieh, T. Liu, and D. Tao, Expressive power of parametrized quantum circuits, Phys. Rev. Research 2
2020
Later among the works it cites.
R. Sweke, F. Wilde, J. Meyer, M. Schuld, P. K. Faehrmann, B. Meynard-Piganeau, and J. Eisert, Stochastic gradient descent for hybrid quantum-classical optimization, Quantum 4
2020
Later among the works it cites.
N. Chopin and O. Papaspiliopoulos, Introduction to Sequential Monte Carlo (Springer International Publishing, 2020)
2020
Later among the works it cites.
A. G. Wilson and P. Izmailov, Bayesian deep learning and a probabilistic perspective of generalization, in Proceedings of the 34th International Conference on Neural Information Processing Systems , NIPS’20 (Curran Associates Inc., Red Hook, NY, USA, 2020)

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2022

Bayesian Learning of Parameterised Quantum Circuits

Duffield, Samuel, Benedetti, Marcello, Rosenkranz, Matthias

Understand

Currently available quantum computers suffer from constraints including hardware noise and a limited number of qubits.

As such, variational quantum algorithms that utilise a classical optimiser in order to train a parameterised quantum circuit have drawn significant attention for near-term practical applications of quantum technology.
In this work, we take a probabilistic point of view and reformulate the classical optimisation as an approximation of a Bayesian posterior.
The posterior is induced by combining the cost function to be minimised with a prior distribution over the parameters of the quantum circuit.

Built on

A. Harrow and J. Napp, Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms, Physical Review Letters 126
Original
1901
Earlier work this paper cites.
J. Knoblauch, J. Jewson, and T. Damoulas, Generalized Variational Inference: Three arguments for deriving new Posteriors (2019), arXiv:1904.02063
Original
1904
Earlier work this paper cites.
A. W. Harrow and A. Y. Wei, Adaptive quantum simulated annealing for Bayesian inference and estimating partition functions, in Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA) (2020) pp. 193–212, arXiv:1907.09965
Original
1907
Earlier work this paper cites.
Y. Nesterov, A method for solving the convex programming problem with convergence rate o ⁡ ( 1 / k 2 ) o(1/k^{2}) , Proceedings of the USSR Academy of Sciences 269
1983
Earlier work this paper cites.
A. J. Izenman and C. J. Sommer, Philatelic mixtures and multimodal densities, Journal of the American Statistical Association 83
1988
Earlier work this paper cites.
R. R. Tucci, Quantum Bayesian nets, International Journal of Modern Physics B 09
1995
Earlier work this paper cites.
P. M. Williams, Bayesian regularization and pruning using a Laplace prior, Neural computation 7
1995
Earlier work this paper cites.
R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological) 58
1996
Earlier work this paper cites.
K. V. Mardia, P. E. Jupp, and K. Mardia, Directional statistics , Vol. 2 (Wiley Online Library, 2000)
2000
Earlier work this paper cites.
J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. S. Allman, C. H. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer, C. Ryan-Anderson, and B. Neyenhuis, Demonstration of the trapped-ion quantum CCD computer architecture, Nature 592
Original
2003
Earlier work this paper cites.
S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, t | | ket ⟩ \rangle : A retargetable compiler for NISQ devices, Quantum Science and Technology 6
Original
2003
Earlier work this paper cites.
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Modeling & Simulation 4
2005
Earlier work this paper cites.
H. Ishwaran and J. S. Rao, Spike and slab variable selection: Frequentist and Bayesian strategies, The Annals of Statistics 33
2005
Earlier work this paper cites.
T. Volkoff and P. J. Coles, Large gradients via correlation in random parameterized quantum circuits, Quantum Science and Technology 6
Original
2005
Earlier work this paper cites.
A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib, Layerwise learning for quantum neural networks, Quantum Machine Intelligence 3
Original
2006
Earlier work this paper cites.
M. Leifer and D. Poulin, Quantum Graphical Models and Belief Propagation, Annals of Physics 323
Original
2008
Earlier work this paper cites.
C. M. Carvalho, N. G. Polson, and J. G. Scott, Handling sparsity via the horseshoe, in Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics , Proceedings of Machine Learning Research, Vol. 5, edited by D. van Dyk and M. Welling (PMLR, Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA, 2009) pp. 73–80
2009
Earlier work this paper cites.
C. Andrieu and G. O. Roberts, The pseudo-marginal approach for efficient Monte Carlo computations, The Annals of Statistics 37
2009
Earlier work this paper cites.
S. Brooks, A. Gelman, G. Jones, and X.-L. Meng, Handbook of Markov Chain Monte Carlo (CRC press, 2011)
2011
Earlier work this paper cites.
M. Welling and Y. W. Teh, Bayesian learning via stochastic gradient Langevin dynamics, in Proceedings of the 28th international conference on machine learning (ICML-11) (2011) pp. 681–688
2011
Earlier work this paper cites.
S. Sachdev, Quantum Phase Transitions , 2nd ed. (Cambridge University Press, Cambridge, UK, 2011)
2011
Earlier work this paper cites.
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, Nature Reviews Physics 3
Original
2012
Earlier work this paper cites.
A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. Smola, A kernel two-sample test, Journal of Machine Learning Research 13
2012
Earlier work this paper cites.

Similar

G. H. Low, T. J. Yoder, and I. L. Chuang, Quantum inference on Bayesian networks, Phys. Rev. A 89
Original
2014
Cited alongside, same era.
N. Parikh and S. Boyd, Proximal algorithms, Found. Trends Optim. 1
2014
Cited alongside, same era.
T. Chen, E. Fox, and C. Guestrin, Stochastic gradient Hamiltonian Monte Carlo, in Proceedings of the 31st International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 32, edited by E. P. Xing and T. Jebara (PMLR, Bejing, China, 2014) pp. 1683–1691
2014
Cited alongside, same era.
N. G. Polson, J. G. Scott, and B. T. Willard, Proximal algorithms in statistics and machine learning, Statistical Science 30
Original
2015
Cited alongside, same era.
Y.-A. Ma, T. Chen, and E. Fox, A Complete Recipe for Stochastic Gradient MCMC, in Advances in Neural Information Processing Systems , Vol. 28, edited by C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett (Curran Associates, Inc., 2015) arXiv:1506.04696

Then

B. T. Gard, L. Zhu, G. S. Barron, N. J. Mayhall, S. E. Economou, and E. Barnes, Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm, npj Quantum Information 6
2020
Later among the works it cites.
Y. Du, M.-H. Hsieh, T. Liu, and D. Tao, Expressive power of parametrized quantum circuits, Phys. Rev. Research 2
2020
Later among the works it cites.
R. Sweke, F. Wilde, J. Meyer, M. Schuld, P. K. Faehrmann, B. Meynard-Piganeau, and J. Eisert, Stochastic gradient descent for hybrid quantum-classical optimization, Quantum 4
2020
Later among the works it cites.
N. Chopin and O. Papaspiliopoulos, Introduction to Sequential Monte Carlo (Springer International Publishing, 2020)
2020
Later among the works it cites.
A. G. Wilson and P. Izmailov, Bayesian deep learning and a probabilistic perspective of generalization, in Proceedings of the 34th International Conference on Neural Information Processing Systems , NIPS’20 (Curran Associates Inc., Red Hook, NY, USA, 2020)