2000 character limit reached
Adaptive measurement strategy for noisy quantum amplitude estimation with variational quantum circuits (2405.15174v1)
Published 24 May 2024 in quant-ph
Abstract: In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred to as quantum Cram\'er-Rao bound (QCRB), and to construct an optimal estimator that achieves QCRB. This paper studies the amplitude estimation in the presence of depolarizing noise with unknown intensity. The main difficulty in this problem is that the optimal measurement depends on both the unknown quantum state and the amplitude we aim to estimate. To deal with these issues, we utilize the variational quantum circuits to approximate the (unknown) optimal measurement basis combined with the 2-step adaptive estimation strategy which was proposed in the quantum estimation theory.We numerically show that the proposed method can nearly attain the QCRB.
- A. Montanaro, Quantum speedup of monte carlo methods, Proc. R. Soc. A 471, 20150301 (2015).
- P. Rebentrost, B. Gupt, and T. R. Bromley, Quantum computational finance: Monte carlo pricing of financial derivatives, Phys. Rev. A 98, 022321 (2018).
- S. Woerner and D. J. Egger, Quantum risk analysis, npj Quantum Inf. 5, 15 (2019).
- K. Miyamoto and K. Shiohara, Reduction of qubits in a quantum algorithm for monte carlo simulation by a pseudo-random-number generator, Phys. Rev. A 102, 022424 (2020).
- N. Wiebe, A. Kapoor, and K. M. Svore, Reduction of qubits in a quantum algorithm for monte carlo simulation by a pseudo-random-number generator, Quantum Inf. Comput. 16, 541 (2016).
- E. Knill, G. Ortiz, and R. D. Somma, Optimal quantum measurements of expectation values of observables, Phys. Rev. A 75, 012328 (2007).
- D. Wang, O. Higgott, and S. Brierley, Accelerated variational quantum eigensolve, Phys. Rev. Lett. 122, 140504 (2019).
- L. Lin and Y. Tong, Near-optimal ground state preparation, Quantum 4, 372 (2020).
- Y. Dong, L. Lin, and Y. Tong, Ground-state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices, PRX Quantum 3, 040305 (2022).
- K. Nakaji, Faster amplitude estimation, Quantum Inf. Computat. 20, 1109 (2020).
- S. Herbert, R. Guichard, and D. Ng, Noise-aware quantum amplitude estimation, arXiv preprint arXiv:2109.04840 .
- C. M. Helstrom, Quantum Detection and Estimation Theory, Vol. 123 (Mathematics in Science and Engineering, New York, 1976).
- A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, Vol. 1 (Springer Science & Business Media, New York, 2011).
- C. M. Helstrom, The minimum variance of estimates in quantum signal detection, IEEE Trans. Inf. Theory 14, 234 (1968).
- S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
- M. G. A. Paris, Quantum estimation for quantum technology, Int. J. Quantum Inform. 07, 125 (2009).
- K. Wada, K. Fukuchi, and N. Yamamoto, Quantum-enhanced mean value estimation via adaptive measurement, arXiv preprint arXiv:2210.15624 (2022).
- V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2005).
- M. Hayashi and K. Matsumoto, Statistical model with measurement degree of freedom and quantum physics, Surikaiseki Kenkyusho Kokyuroku 1055, 96 (1998).
- O. E. Barndorff-Nielsen and R. D. Gill, Fisher information in quantum statistics, J. Phys. A: Math. Gen. 33, 4481 (2000).
- J. J. Meyer, J. Borregaard, and J. Eisert, A variational toolbox for quantum multi-parameter estimation, npj Quantum Inf. 7, 89 (2021).
- C. R. Rao, Linear Statistical Inference and its Applications, Vol. 2 (Wiley, New York, 1973).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
- J. Suzuki, Y. Yang, and M. Hayashi, Quantum state estimation with nuisance parameters, J. Phys. A: Math. Theor. 53, 453001 (2020b).
- H. Nagaoka, On the parameter estimation problem for quantum statistical models, in Proceeding of 12th Symposium on Information Theory and Its Applications(unpublised) , 125 (1989).
- A. Fujiwara, Strong consistency and asymptotic efficiency for adaptive quantum estimation problems, J. Phys. A 39, 12489 (2006), [Corrigendum: 44, 079501(2011)].
- A. Callison and D. E. Browne, Improved maximum-likelihood quantum amplitude estimation, arXiv preprint arXiv:2209.03321 .