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Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization (2307.03884v1)

Published 8 Jul 2023 in quant-ph and cs.LG

Abstract: Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However, these algorithms suffer from classically intractable gradients limiting the scalability. This work addresses the scalability challenge for VQE by proposing a classical gradient computation method which utilizes the parameter shift rule but computes the expected values from the circuits using a tensor ring approximation. The parametrized gates from the circuit transform the tensor ring by contracting the matrix along the free edges of the tensor ring. While the single qubit gates do not alter the ring structure, the state transformations from the two qubit rotations are evaluated by truncating the singular values thereby preserving the structure of the tensor ring and reducing the computational complexity. This variation of the Matrix product state approximation grows linearly in number of qubits and the number of two qubit gates as opposed to the exponential growth in the classical simulations, allowing for a faster evaluation of the gradients on classical simulators.

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References (23)
  1. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM review 41, 303 (1999).
  2. M. A. Continentino, Key Methods and Concepts in Condensed Matter Physics: Green’s functions and real space renormalization group (IOP Publishing, 2021).
  3. P. Deglmann, A. Schäfer, and C. Lennartz, Application of quantum calculations in the chemical industry—an overview, International Journal of Quantum Chemistry 115, 107 (2015).
  4. B. J. Williams-Noonan, E. Yuriev, and D. K. Chalmers, Free energy methods in drug design: prospects of “alchemical perturbation” in medicinal chemistry: miniperspective, Journal of medicinal chemistry 61, 638 (2018).
  5. A. Heifetz, Quantum mechanics in drug discovery (Springer, 2020).
  6. R. Miceli and M. McGuigan, Effective matrix model for nuclear physics on a quantum computer, in 2019 New York Scientific Data Summit (NYSDS) (IEEE, 2019) pp. 1–4.
  7. G. Nannicini, Performance of hybrid quantum-classical variational heuristics for combinatorial optimization, Physical Review E 99, 013304 (2019).
  8. D. S. Abrams and S. Lloyd, Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors, Physical Review Letters 83, 5162 (1999).
  9. A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum algorithm for linear systems of equations, Physical review letters 103, 150502 (2009).
  10. P. Atchade Adelomou, E. Golobardes Ribé, and X. Vilasís Cardona, Using the variational-quantum-eigensolver (vqe) to create an intelligent social workers schedule problem solver, in International Conference on Hybrid Artificial Intelligence Systems (Springer, 2020) pp. 245–260.
  11. G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Physical review letters 91, 147902 (2003).
  12. Y. Zhou, E. M. Stoudenmire, and X. Waintal, What limits the simulation of quantum computers?, Physical Review X 10, 041038 (2020).
  13. I. L. Markov and Y. Shi, Simulating quantum computation by contracting tensor networks, SIAM Journal on Computing 38, 963 (2008).
  14. Y.-Y. Shi, L.-M. Duan, and G. Vidal, Classical simulation of quantum many-body systems with a tree tensor network, Physical review a 74, 022320 (2006).
  15. G. Vidal, Entanglement renormalization, Physical review letters 99, 220405 (2007).
  16. S. Cheng, L. Wang, and P. Zhang, Supervised learning with projected entangled pair states, Physical Review B 103, 125117 (2021).
  17. S. Efthymiou, J. Hidary, and S. Leichenauer, Tensornetwork for machine learning, arXiv preprint arXiv:1906.06329  (2019).
  18. E. Stoudenmire and D. J. Schwab, Supervised learning with tensor networks, Advances in Neural Information Processing Systems 29 (2016).
  19. F. Glover, G. Kochenberger, and Y. Du, A tutorial on formulating and using qubo models, arXiv preprint arXiv:1811.11538  (2018).
  20. A. Lucas, Ising formulations of many np problems, Frontiers in physics , 5 (2014).
  21. W. Wang, V. Aggarwal, and S. Aeron, Efficient low rank tensor ring completion, in Proceedings of the IEEE International Conference on Computer Vision (2017) pp. 5697–5705.
  22. R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of physics 349, 117 (2014).
  23. E. C. Martín, K. Plekhanov, and M. Lubasch, Barren plateaus in quantum tensor network optimization, Quantum 7, 974 (2023).

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