Symmetry breaking in geometric quantum machine learning in the presence of noise (2401.10293v1)
Abstract: Geometric quantum machine learning based on equivariant quantum neural networks (EQNN) recently appeared as a promising direction in quantum machine learning. Despite the encouraging progress, the studies are still limited to theory, and the role of hardware noise in EQNN training has never been explored. This work studies the behavior of EQNN models in the presence of noise. We show that certain EQNN models can preserve equivariance under Pauli channels, while this is not possible under the amplitude damping channel. We claim that the symmetry breaking grows linearly in the number of layers and noise strength. We support our claims with numerical data from simulations as well as hardware up to 64 qubits. Furthermore, we provide strategies to enhance the symmetry protection of EQNN models in the presence of noise.
- J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 1 (2018).
- E. R. Anschuetz and B. T. Kiani, Quantum variational algorithms are swamped with traps, Nature Communications 13, 7760 (2022).
- X. You and X. Wu, Exponentially many local minima in quantum neural networks, in Proceedings of the 38th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 139, edited by M. Meila and T. Zhang (PMLR, 2021) pp. 12144–12155.
- T. Volkoff and P. J. Coles, Large gradients via correlation in random parameterized quantum circuits, Quantum Science and Technology 6, 025008 (2021).
- S. Kazi, M. Larocca, and M. Cerezo, On the universality of snsubscript𝑠𝑛s_{n}italic_s start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT-equivariant k𝑘kitalic_k-body gates (2023), arXiv:2303.00728 [quant-ph] .
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2007).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010).
- M. P. Müller, D. Gross, and J. Eisert, Concentration of measure for quantum states with a fixed expectation value, Communications in Mathematical Physics 303, 785 (2011).
- C. Ortiz Marrero, M. Kieferová, and N. Wiebe, Entanglement-Induced Barren Plateaus, PRX Quantum 2, 040316 (2021).
- A. Krampe and S. Kuhnt, Bowker’s test for symmetry and modifications within the algebraic framework, Computational Statistics & Data Analysis 51, 4124 (2007).
- A. P. Bradley, The use of the area under the roc curve in the evaluation of machine learning algorithms, Pattern Recognition 30, 1145 (1997).
- D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, CoRR abs/1412.6980 (2014).
- Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023).
- N. Earnest, C. Tornow, and D. J. Egger, Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware, Phys. Rev. Res. 3, 043088 (2021).
- G. Li, Y. Ding, and Y. Xie, Tackling the qubit mapping problem for nisq-era quantum devices, in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS ’19 (Association for Computing Machinery, 2019) p. 1001–1014.
- L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998).
- Qiskit 0.33 release notes, https://docs.quantum.ibm.com/api/qiskit/release-notes/0.33, accessed: 2024-01-12.
- N. Khaneja and S. J. Glaser, Cartan decomposition of SU(2n) and control of spin systems, Chemical Physics 267, 11 (2001).
Collections
Sign up for free to add this paper to one or more collections.