Quantum Reservoir Parameter Estimation via Fisher Information

Year 2022, , 388 - 396, 30.04.2022

Ufuk Korkmaz Deniz Türkpençe

https://doi.org/10.16984/saufenbilder.1018716

Abstract

In this study, we show that as a result of weak interaction of different information environments structured with a single probe qubit, these environments can perform binary classification of the information they contain. In this way, we refer to these environments as quantum information baths because they consist of sequences of identical qubits in certain pure quantum states. A micro-maser like master equation has been developed to clearly describe the system dynamics analytically and the quantum states of different information reservoirs. The model can also be treated as a quantum neuron, due to the single-qubit probe that makes a binary decision depending on the reservoir parameters in its steady state. The numerical results of the repeated interaction process based on the divisibility and additivity of the quantum dynamic maps are compared with the analytical results. Besides being a single quantum classifier, the model we present can also serve as a basic unit of a quantum neural network within the framework of the dissipative model of quantum computing.

Keywords

Binary classification, information reservoir, collision model, quantum Fisher information

Project Number

120F353

References

• [1] P. Rebentrost, M. Mohseni, and S. Lloyd, ‘Quantum Support Vector Machine for Big Data Classification’, Phys. Rev. Lett., vol. 113, no. 13, p. 130503, Sep. 2014.
• [2] M. Schuld, I. Sinayskiy, and F. Petruccione, ‘Simulating a perceptron on a quantum computer’, Physics Letters A, vol. 379, no. 7, pp. 660–663, Mar. 2015.
• [3] L. Banchi, N. Pancotti, and S. Bose, ‘Quantum gate learning in qubit networks: Toffoli gate without time-dependent control’, npj Quantum Information, vol. 2, no. 1, 2016.
• [4] S. Lu et al., ‘Separability-entanglement classifier via machine learning’, Phys. Rev. A, vol. 98, no. 1, p. 012315, Jul. 2018.
• [5] S. Lloyd and C. Weedbrook, ‘Quantum Generative Adversarial Learning’, Phys. Rev. Lett., vol. 121, no. 4, p. 040502, Jul. 2018.
• [6] A. Y. Yamamoto, K. M. Sundqvist, P. Li, and H. R. Harris, ‘Simulation of a Multidimensional Input Quantum Perceptron’, Quantum Inf Process, vol. 17, no. 6, p. 128, Apr. 2018.
• [7] D. Türkpençe, T. Ç. Akıncı, and S. Şeker, ‘A steady state quantum classifier’, Physics Letters A, vol. 383, no. 13, pp. 1410–1418, Apr. 2019.
• [8] R. Blume-Kohout and W. H. Zurek, ‘A Simple Example of “Quantum Darwinism”: Redundant Information Storage in Many-Spin Environments’, Found Phys, vol. 35, no. 11, pp. 1857–1876, Nov. 2005.
• [9] M. Zwolak and W. H. Zurek, ‘Redundancy of einselected information in quantum Darwinism: The irrelevance of irrelevant environment bits’, Phys. Rev. A, vol. 95, no. 3, p. 030101, Mar. 2017.
• [10] S. Deffner, ‘Information-driven current in a quantum Maxwell demon’, Phys. Rev. E, vol. 88, no. 6, p. 062128, Dec. 2013.
• [11] S. Deffner, ‘Information-driven current in a quantum Maxwell demon’, Physical Review E, vol. 88, no. 6, p. 062128, Dec. 2013.
• [12] J. F. Poyatos, J. I. Cirac, and P. Zoller, ‘Quantum Reservoir Engineering with Laser Cooled Trapped Ions’, Phys. Rev. Lett., vol. 77, no. 23, pp. 4728–4731, Dec. 1996.
• [13] H.-P. Breuer, P. I. H.-P. Breuer, F. Petruccione, and S. of P. and A. P. F. Petruccione, The Theory of Open Quantum Systems. Oxford University Press, 2002.
• [14] M. Siomau and S. Fritzsche, ‘Quantum computing with mixed states’, Eur. Phys. J. D, vol. 62, no. 3, p. 449, May 2011.
• [15] F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, ‘Quantum computation and quantum-state engineering driven by dissipation’, Nature Phys, vol. 5, no. 9, pp. 633–636, Sep. 2009.
• [16] D. Turkpence, G. B. Akguc, A. Bek, and M. E. Tasgin, ‘Engineering nonlinear response of nanomaterials using Fano resonances’, J. Opt., vol. 16, no. 10, p. 105009, Sep. 2014.
• [17] D. Türkpençe and Ö. E. Müstecaplıoğlu, ‘Quantum fuel with multilevel atomic coherence for ultrahigh specific work in a photonic Carnot engine’, Phys. Rev. E, vol. 93, no. 1, p. 012145, Jan. 2016.
• [18] D. Türkpençe, F. Altintas, M. Paternostro, and Ö. E. Müstecaplioğlu, ‘A photonic Carnot engine powered by a spin-star network’, EPL (Europhysics Letters), vol. 117, no. 5, p. 50002, Mar. 2017.
• [19] J. Kołodyński, J. B. Brask, M. Perarnau-Llobet, and B. Bylicka, ‘Adding dynamical generators in quantum master equations’, Phys. Rev. A, vol. 97, no. 6, p. 062124, Jun. 2018.
• [20] M. M. Wolf and J. I. Cirac, ‘Dividing Quantum Channels’, Commun. Math. Phys., vol. 279, no. 1, pp. 147–168, Apr. 2008.
• [21] S. N. Filippov, J. Piilo, S. Maniscalco, and M. Ziman, ‘Divisibility of quantum dynamical maps and collision models’, Phys. Rev. A, vol. 96, no. 3, p. 032111, Sep. 2017.
• [22] U. Korkmaz, D. Türkpençe, T. Ç. Akinci, and S. Şeker, ‘A thermal quantum classifier’, Quantum Information and Computation, vol. 20, no. 11–12, pp. 969–986, 2020.
• [23] R. Hecht-Nielsen, ‘Neurocomputing: picking the human brain’, IEEE Spectrum, vol. 25, no. 3, pp. 36–41, Mar. 1988.
• [24] M. Schuld and F. Petruccione, ‘Quantum ensembles of quantum classifiers’, Sci Rep, vol. 8, no. 1, p. 2772, Feb. 2018.
• [25] M. T. Mitchison and M. B. Plenio, ‘Non-additive dissipation in open quantum networks out of equilibrium’, New J. Phys., vol. 20, no. 3, p. 033005, Mar. 2018.
• [26] J. Kołodyński, J. B. Brask, M. Perarnau-Llobet, and B. Bylicka, ‘Adding dynamical generators in quantum master equations’, Physical Review A, vol. 97, no. 6, p. 062124, Jun. 2018.
• [27] L. Bruneau, A. Joye, and M. Merkli, ‘Repeated interactions in open quantum systems’, J. Math. Phys., vol. 55, no. 7, p. 075204, Jul. 2014.
• [28] V. Scarani, M. Ziman, P. Štelmachovič, N. Gisin, and V. Bužek, ‘Thermalizing Quantum Machines: Dissipation and Entanglement’, Phys. Rev. Lett., vol. 88, no. 9, p. 097905, Feb. 2002.
• [29] A. Manatuly, W. Niedenzu, R. Román-Ancheyta, B. Çakmak, Ö. E. Müstecaplıoğlu, and G. Kurizki, ‘Collectively enhanced thermalization via multiqubit collisions’, Phys. Rev. E, vol. 99, no. 4, p. 042145, Apr. 2019.
• [30] J. D. Cresser, ‘Quantum-field model of the injected atomic beam in the micromaser’, Phys. Rev. A, vol. 46, no. 9, pp. 5913–5931, Nov. 1992.
• [31] J.-Q. Liao, H. Dong, and C. P. Sun, ‘Single-particle machine for quantum thermalization’, Phys. Rev. A, vol. 81, no. 5, p. 052121, May 2010.
• [32] C. W. Helstrom, ‘Quantum detection and estimation theory’, J Stat Phys, vol. 1, no. 2, pp. 231–252, Jun. 1969.
• [33] J. Dittmann, ‘Explicit formulae for the Bures metric’, J. Phys. A: Math. Gen., vol. 32, no. 14, pp. 2663–2670, Jan. 1999.
• [34] W. Zhong, Z. Sun, J. Ma, X. Wang, and F. Nori, ‘Fisher information under decoherence in Bloch representation’, Phys. Rev. A, vol. 87, no. 2, p. 022337, Feb. 2013.
• [35] J. R. Johansson, P. D. Nation, and F. Nori, ‘QuTiP: An open-source Python framework for the dynamics of open quantum systems’, Computer Physics Communications, vol. 183, no. 8, pp. 1760–1772, Aug. 2012.
• [36] S. Filipp et al., ‘Multimode mediated qubit-qubit coupling and dark-state symmetries in circuit quantum electrodynamics’, Phys. Rev. A, vol. 83, no. 6, p. 063827, Jun. 2011.
• [37] X.-H. Deng, E. Barnes, and S. E. Economou, ‘Robustness of error-suppressing entangling gates in cavity-coupled transmon qubits’, Phys. Rev. B, vol. 96, no. 3, p. 035441, Jul. 2017.
• [38] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, ‘Circuit quantum electrodynamics’, Rev. Mod. Phys., vol. 93, no. 2, p. 025005, May 2021.