Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Preparing matrix product states via fusion: constraints and extensions (2404.16360v2)

Published 25 Apr 2024 in quant-ph and cond-mat.str-el

Abstract: In the era of noisy, intermediate-scale quantum (NISQ) devices, the efficient preparation of many-body resource states is a task of paramount importance. In this paper we focus on the deterministic preparation of matrix-product states (MPS) in constant depth by utilizing measurements and classical communication to fuse smaller states into larger ones. We place strong constraints on the MPS that can be prepared using this method, which we refer to as MPS fusion. Namely, we establish that it is necessary for the MPS to have a flat entanglement spectrum. Using the recently introduced split-index MPS (SIMPS) representation, we then introduce a family of states that belong to interesting phases of matter protected by non-onsite symmetries and serve as resources for long-range quantum teleportation, but which lie beyond the scope of ordinary MPS fusion. It is shown constructively that these states can be prepared in constant depth using a broader class of measurement-assisted protocols, which we dub SIMPS fusion. Even in cases when MPS fusion is possible, using SIMPS fusion can give rise to significantly reduced resource overhead. Our results therefore simultaneously establish the boundaries of conventional MPS fusion and push the envelope of which states can be prepared using measurement-assisted protocols.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (28)
  1. A. Acín, J. I. Cirac, and M. Lewenstein, Entanglement percolation in quantum networks, Nature Physics 3, 256 (2007).
  2. R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
  3. T.-C. Wei, Quantum spin models for measurement-based quantum computation, Advances in Physics: X 3, 1461026 (2018).
  4. L. Piroli, G. Styliaris, and J. I. Cirac, Quantum circuits assisted by local operations and classical communication: Transformations and phases of matter, Phys. Rev. Lett. 127, 220503 (2021).
  5. N. Tantivasadakarn, R. Verresen, and A. Vishwanath, Shortest route to non-Abelian topological order on a quantum processor, Phys. Rev. Lett. 131, 060405 (2023a).
  6. P. Herringer and R. Raussendorf, Classification of measurement-based quantum wire in stabilizer PEPS, Quantum 7, 1041 (2023).
  7. R. Raussendorf, S. Bravyi, and J. Harrington, Long-range quantum entanglement in noisy cluster states, Phys. Rev. A 71, 062313 (2005).
  8. J. C. Hoke et al., Measurement-induced entanglement and teleportation on a noisy quantum processor, Nature 622, 481 (2023).
  9. G. K. Brennen and A. Miyake, Measurement-based quantum computer in the gapped ground state of a two-body hamiltonian, Phys. Rev. Lett. 101, 010502 (2008).
  10. T.-C. Wei, I. Affleck, and R. Raussendorf, Two-dimensional affleck-kennedy-lieb-tasaki state on the honeycomb lattice is a universal resource for quantum computation, Phys. Rev. A 86, 032328 (2012).
  11. D. T. Stephen, Non-onsite symmetries and quantum teleportation in split-index matrix product states (2024), arXiv:2404.15883 [quant-ph] .
  12. S. Bravyi, M. B. Hastings, and F. Verstraete, Lieb-Robinson bounds and the generation of correlations and topological quantum order, Phys. Rev. Lett. 97, 050401 (2006).
  13. Y. Huang and X. Chen, Quantum circuit complexity of one-dimensional topological phases, Phys. Rev. B 91, 195143 (2015).
  14. A. Kapustin, A. Turzillo, and M. You, Topological field theory and matrix product states, Phys. Rev. B 96, 075125 (2017).
  15. C.-F. A. Chen, A. Lucas, and C. Yin, Speed limits and locality in many-body quantum dynamics, Reports on Progress in Physics 86, 116001 (2023).
  16. H. J. Briegel and R. Raussendorf, Persistent entanglement in arrays of interacting particles, Phys. Rev. Lett. 86, 910 (2001).
  17. X. Chen, Z.-X. Liu, and X.-G. Wen, Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations, Phys. Rev. B 84, 235141 (2011).
  18. C. K. Majumdar and D. K. Ghosh, On Next‐Nearest‐Neighbor Interaction in Linear Chain. I, Journal of Mathematical Physics 10, 1388 (1969).
  19. T. Kennedy and H. Tasaki, Hidden Z2subscriptZ2{\mathrm{Z}}_{2}roman_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT×Z2subscriptZ2{\mathrm{Z}}_{2}roman_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT symmetry breaking in haldane-gap antiferromagnets, Phys. Rev. B 45, 304 (1992).
  20. D. V. Else, S. D. Bartlett, and A. C. Doherty, Hidden symmetry-breaking picture of symmetry-protected topological order, Phys. Rev. B 88, 085114 (2013).
  21. N. Seiberg, S. Seifnashri, and S.-H. Shao, Non-invertible symmetries and lsm-type constraints on a tensor product hilbert space (2024), arXiv:2401.12281 [cond-mat.str-el] .
  22. E. O’Brien and P. Fendley, Lattice supersymmetry and order-disorder coexistence in the tricritical ising model, Phys. Rev. Lett. 120, 206403 (2018).
  23. T. B. Wahl, D. Pérez-García, and J. I. Cirac, Matrix product states with long-range localizable entanglement, Phys. Rev. A 86, 062314 (2012).
  24. M. Ippoliti and W. W. Ho, Dynamical purification and the emergence of quantum state designs from the projected ensemble, PRX Quantum 4, 030322 (2023).
  25. A. Lavasani, Z.-X. Luo, and S. Vijay, Monitored quantum dynamics and the kitaev spin liquid, Phys. Rev. B 108, 115135 (2023).
  26. S. J. Garratt, Z. Weinstein, and E. Altman, Measurements conspire nonlocally to restructure critical quantum states, Phys. Rev. X 13, 021026 (2023).
  27. R. Sahay and R. Verresen, Finite-depth preparation of tensor network states from measurement (to appeara).
  28. R. Sahay and R. Verresen, Classifying one-dimensional quantum states prepared by a single round of measurements (to appearb).
Citations (8)

Summary

We haven't generated a summary for this paper yet.