Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation (2312.02667v2)
Abstract: Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all virtual bonds in constant time, irrespective of the system size, with controlled accuracy, while it maintains the stability of the wavefunction norm without necessitating sequential renormalization procedures. In addition, we introduce a parallel regauging technique to partially restore the deviated canonical form, thereby improving the accuracy of the simulation in subsequent steps. We further apply this method to simulate unitary quantum dynamics and introduce an improved parallel time-evolving block-decimation (pTEBD) algorithm. We employ the improved pTEBD algorithm for extensive simulations of typical one- and two-dimensional quantum circuits, involving over 1000 qubits. The obtained numerical results unequivocally demonstrate that the improved pTEBD algorithm achieves the same level of simulation precision as the current state-of-the-art MPS algorithm but in polynomially shorter time, exhibiting nearly perfect weak scaling performance on a modern supercomputer.
- C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017), https://www.science.org/doi/pdf/10.1126/science.aal3837 .
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010).
- Y. Zhou, E. M. Stoudenmire, and X. Waintal, What limits the simulation of quantum computers?, Phys. Rev. X 10, 041038 (2020).
- J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018).
- J. Gray and S. Kourtis, Hyper-optimized tensor network contraction, Quantum 5, 410 (2021).
- F. Pan and P. Zhang, Simulation of quantum circuits using the big-batch tensor network method, Phys. Rev. Lett. 128, 030501 (2022).
- H. Collins and C. Nay, Ibm unveils 400 qubit-plus quantum processor and next-generation ibm quantum system two [press release], https://newsroom.ibm.com/2022-11-09-IBM-Unveils-400-Qubit-Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System-Two (2022).
- R. Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of Physics 349, 117 (2014).
- U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96 (2011), january 2011 Special Issue.
- F. Verstraete and J. I. Cirac, Matrix product states represent ground states faithfully, Phys. Rev. B 73, 094423 (2006).
- M. Urbanek and P. Soldán, Parallel implementation of the time-evolving block decimation algorithm for the bose-hubbard model, Computer Physics Communications 199, 170 (2016).
- G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91, 147902 (2003).
- T. Shirakawa, H. Ueda, and S. Yunoki, Automatic quantum circuit encoding of a given arbitrary quantum state, arXiv preprint arXiv:2112.14524 (2021).
- G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93, 040502 (2004).
- R. Orús and G. Vidal, Infinite time-evolving block decimation algorithm beyond unitary evolution, Phys. Rev. B 78, 155117 (2008).
- H. C. Jiang, Z. Y. Weng, and T. Xiang, Accurate determination of tensor network state of quantum lattice models in two dimensions, Phys. Rev. Lett. 101, 090603 (2008).
- R. Alkabetz and I. Arad, Tensor networks contraction and the belief propagation algorithm, Phys. Rev. Res. 3, 023073 (2021).
- S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
- U. Schollwöck, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005).
- M.-D. Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications 10, 285 (1975).
- A. J. Ferris and G. Vidal, Perfect sampling with unitary tensor networks, Phys. Rev. B 85, 165146 (2012).
- D. Adachi, T. Okubo, and S. Todo, Anisotropic tensor renormalization group, Phys. Rev. B 102, 054432 (2020).
- GraceQ/tensor, https://github.com/gracequantum/tensor.
- J. Tindall and M. Fishman, Gauging tensor networks with belief propagation, arXiv preprint arXiv:2306.17837 https://doi.org/10.48550/arXiv.2306.17837 (2023).
- D. Wecker, M. B. Hastings, and M. Troyer, Progress towards practical quantum variational algorithms, Phys. Rev. A 92, 042303 (2015).
- D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
- S. Lloyd, M. Mohseni, and P. Rebentrost, Quantum principal component analysis, Nature Physics 10, 631 (2014).
- H.-K. Lau and M. B. Plenio, Universal quantum computing with arbitrary continuous-variable encoding, Phys. Rev. Lett. 117, 100501 (2016).
- K. Seki, T. Shirakawa, and S. Yunoki, Symmetry-adapted variational quantum eigensolver, Phys. Rev. A 101, 052340 (2020).
- R.-Y. Sun, T. Shirakawa, and S. Yunoki, Efficient variational quantum circuit structure for correlated topological phases, Phys. Rev. B 108, 075127 (2023).
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
