Published February 3, 2023
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Real quantum amplitude estimation
Authors/Creators
- 1. Universidade da Coruña
- 2. CESGA
- 3. Universidad de Oviedo
Description
We introduce the Real Quantum Amplitude Estimation (RQAE) algorithm, an extension of Quantum Amplitude Estimation (QAE) which is sensitive to the sign of the amplitude. RQAE is an iterative algorithm which offers explicit control over the amplification policy through an adjustable parameter. We provide a rigorous analysis of the RQAE performance and prove that it achieves a quadratic speedup, modulo logarithmic corrections, with respect to unamplified sampling. Besides, we corroborate the theoretical analysis with a set of numerical experiments.
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References
- Knill E, Ortiz G, Somma RD. Optimal quantum measurements of expectation values of observables. Phys Rev A. 2007;75(1):012328.
- Kassal I et al.. Polynomial-time quantum algorithm for the simulation of chemical dynamics. Proc Natl Acad Sci. 2008;105(48):18681–6.
- Rebentrost P, Gupt B, Bromley TR. Quantum computational finance: Monte Carlo pricing of financial derivatives. Phys Rev A. 2018;98(2):022321.
- Woerner S, Egger DJ. Quantum risk analysis. npj Quantum Inf. 2019;5(1):1–8.
- Gómez A et al.. A survey on quantum computational finance for derivatives pricing and VaR. In: Archives of computational methods in engineering. 2022.
- Wiebe N, Kapoor A, Svore K. Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. Quantum Inf Comput. 2015;15(3):318–58.
- Wiebe N, Kapoor A, Svore K. Quantum Perceptron Models. In: Proceedings of the 30th International Conference on Neural Information Processing Systems. 2016. p. 4006–14.
- Brassard G et al.. Quantum amplitude amplification and estimation. In: Quantum computation and information. 2002. p. 53–74.
- Nielsen MA, Chuang IL. Quantum computation and quantum information. Phys Today. 2001;54:2.
- Grover LK. A fast quantum mechanical algorithm for database search. In: Proceedings of the twenty-eighth annual ACM symposium on theory of computing. 1996. p. 212–9.
- Suzuki Y et al.. Amplitude estimation without phase estimation. Quantum Inf Process. 2020;19:2.
- Wie CR. Simpler quantum counting. Quantum Inf Comput. 2019;19:11–2.
- Kitaev AY. Quantum measurements and the Abelian Stabilizer Problem. Electron. Colloq. Comput. Complex.. 1995;TR96.
- Grinko D et al.. Iterative quantum amplitude estimation. npj Quantum Inf. 2021;7:1.
- Aaronson S, Rall P. Quantum approximate counting, simplified. In: Symposium on simplicity in algorithms. 2020. p. 24–32.
- Abrams DS, Williams CP. Fast quantum algorithms for numerical integrals and stochastic processes (1999).
- Shimada NH, Hachisuka T. Quantum coin method for numerical integration. Comput Graph Forum. 2020;39:243–57.
- Manzano A et al.. A modular framework for generic quantum algorithms. Mathematics. 2022;10:785.
- Hoeffding W. Probability inequalities for sums of bounded random variables. J Am Stat Assoc. 1963;58(301):13–30.
- Clopper CJ, Pearson ES. The use of confidence of fiducial limits illustrated in the case of the binomial. Biometrika. 1934;26(4):404–13.