Quantum Amplitude Estimation in Bayesian Amplitude Estimation
This work delves into Quantum Amplitude Estimation techniques, including classical and quantum solutions, sample averaging, and the use of Grover quantum phase estimation over N samples. It also explores strategies for noisy quantum devices and unlocking new learning rates.
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Bayesian Bayesian Quantum Amplitude Estimation Quantum Amplitude Estimation ReaQCT 2024 Alexandra Ram a This work is financed by National Funds through the Portuguese funding agency, FCT - Funda o para a Ci ncia e a Tecnologia, within project UIDB/50014/2020. DOI 10.54499/UIDB/50014/2020 | https://doi.org/10.54499/uidb/50014/2020
Quantum Amplitude Estimation Quantum Amplitude Estimation (QAE) (QAE) We can prepare the quantum state ? = ? ?1+ 1 ? ?0. . Find Find a a. . 2
Quantum Amplitude Estimation Quantum Amplitude Estimation ? = ? ?1+ 1 ? ?0 Classical solution Quantum solution Sample from Binomial (?) and take averages Apply phase estimation phase estimation to the Grover quantum quantum over N samples. amplitude amplification amplitude amplification operator. G Quantum Phase Estimation 3
Quantum Amplitude Estimation Quantum Amplitude Estimation There is a quadratic quantum speed quadratic quantum speed- -up up for this task. ? ?(? 0.5) estimation error classical quantum ? ?(? 1) cost 4
QAE with Noisy Quantum Devices QAE with Noisy Quantum Devices The circuit is not viable for not viable for today s quantum devices today s quantum devices. Alternative strategies Alternative strategies have been proposed. . in: Grinko, D., Gacon, J., Zoufal, C. et al. Iterative quantum amplitude estimation. npj Quantum Inf 7, 52 (2021). 5
QAE with Noisy Quantum Devices QAE with Noisy Quantum Devices We can sample from ?1?? ? = sin2??? ? ? ? with cost in ?(??). Use this extra freedom to unlock otherwise unachievable learning rates. 6
QAE with Noisy Quantum Devices QAE with Noisy Quantum Devices Learn the hidden parameter of an observable probability distribution Binomial (p ,?? ???). Classical Classical samples: Quantum Quantum- -enhanced enhanced samples: ? ? = ????? ? ? ? = ?????? for ? any odd integer ? ?(? 0.5) ? ?(? 1) 7
QAE with Noisy Quantum Devices QAE with Noisy Quantum Devices We can look at this as a data science problem data science problem. 8
QAE with Noisy Quantum Devices QAE with Noisy Quantum Devices quantum processing ? ? ? ? ? applications of G (i+1)-th experimental control ??+1 i-th experimental outcome classical processing 9
Maximum Likelihood QAE Maximum Likelihood QAE 10
Bayesian Amplitude Estimation Bayesian Amplitude Estimation Bayesian statistics Bayesian statistics offers a natural paradigm for QAE. ? ? ? =? ? ?;? ?(?) ?(?;?) 11
Bayesian Amplitude Estimation Bayesian Amplitude Estimation 12
Bayesian Amplitude Estimation Bayesian Amplitude Estimation 13
Bayesian Amplitude Estimation Bayesian Amplitude Estimation 14
Bayesian Amplitude Estimation Bayesian Amplitude Estimation 15
Bayesian Amplitude Estimation Bayesian Amplitude Estimation ? ? ? =? ? ?;? ?(?) ?(?;?) The use of Bayesian inference does not fully determine the protocol; the optimization optimizationand representation representationmethods employed are determinant for performance. 16
Bayesian Amplitude Estimation Bayesian Amplitude Estimation We combine general, scalable and adaptive-compatible statistical methods statistical methods with problem problem- -tailored heuristics tailored heuristics to keep the problem tractable while retaining the quantum advantage. 17
Comparative Results Comparative Results - ideal case 18
Comparative Results Comparative Results - noisy case 19
Key Takeaways Key Takeaways Our Bayesian amplitude estimation algorithm: Achieves the Heisenberg limit; Is highly adaptable, parallelizable and scalable; Is capable of dealing with noise. 20
Thank you for your attention! Thank you for your attention! Reach me at: alexandra.ramoa@inl.int 21
