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  • Letter
  • Open Access

Nearly optimal time-independent reversal of a spin chain

Aniruddha Bapat1,2,3,*, Eddie Schoute1,4,5,†, Alexey V. Gorshkov1,2,‡, and Andrew M. Childs1,4,5,§

  • 1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 2Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 3Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 4Department of Computer Science, University of Maryland, College Park, Maryland 20742, USA
  • 5Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, USA

  • *ani@lbl.gov
  • †eschoute@umd.edu
  • ‡gorshkov@umd.edu
  • §amchilds@umd.edu
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Phys. Rev. Research 4, L012023 – Published 22 February, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L012023

Abstract

We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, nonuniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using swap gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor 1.502(1+1/N) of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. We give numerical evidence that the fast reversal protocols are more robust to noise than a swap-based reversal. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.

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References (43)

  1. D. P. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48, 771 (2000).
  2. H. J. Kimble, The quantum internet, Nature (London) 453, 1023 (2008).
  3. R. Beals, S. Brierley, O. Gray, A. W. Harrow, S. Kutin, N. Linden, D. Shepherd, and M. Stather, Efficient distributed quantum computing, Proc. R. Soc. London, Ser. A 469, 20120686 (2013).
  4. A. M. Childs, E. Schoute, and C. M. Unsal, Circuit transformations for quantum architectures, in 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019), Leibniz International Proceedings in Informatics (LIPIcs), Vol. 135, edited by W. van Dam and L. Mancinska (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2019), pp. 3:1–3:24.
  5. S. Bose, Quantum communication through spin chain dynamics: An introductory overview, Contemp. Phys. 48, 13 (2007).
  6. E. H. Lieb and D. W. Robinson, The finite group velocity of quantum spin systems, Statistical Mechanics (Springer, New York, 1972), pp. 425–431.
  7. J. Eisert, M. Cramer, and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy,” Rev. Mod. Phys. 82, 277 (2010).
  8. J. Haah, M. Hastings, R. Kothari, and G. H. Low, Quantum algorithm for simulating real time evolution of lattice Hamiltonians, in 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) (IEEE, New York, 2018), pp. 350–360.
  9. W. Dür, G. Vidal, J. I. Cirac, N. Linden, and S. Popescu, Entanglement Capabilities of Nonlocal Hamiltonians, Phys. Rev. Lett. 87, 137901 (2001).
  10. A. M. Childs, D. W. Leung, F. Verstraete, and G. Vidal, Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions, Quantum Inf. Comput. 3, 97 (2003).
  11. A. M. Childs, D. W. Leung, and G. Vidal, Reversible simulation of bipartite product Hamiltonians, IEEE Trans. Inf. Theory 50, 1189 (2004).
  12. C. H. Bennett, A. W. Harrow, D. W. Leung, and J. A. Smolin, On the capacities of bipartite Hamiltonians and unitary gates, IEEE Trans. Inf. Theory 49, 1895 (2003).
  13. S. Bravyi, Upper bounds on entangling rates of bipartite Hamiltonians, Phys. Rev. A 76, 052319 (2007).
  14. K. Van Acoleyen, M. Mariën, and F. Verstraete, Entanglement Rates and Area Laws, Phys. Rev. Lett. 111, 170501 (2013).
  15. K. M. R. Audenaert, Quantum skew divergence, J. Math. Phys. 55, 112202 (2014).
  16. M. Mariën, K. M. R. Audenaert, K. Van Acoleyen, and F. Verstraete, Entanglement rates and the stability of the area law for the entanglement entropy, Commun. Math. Phys. 346, 35 (2016).
  17. S. Bose, Quantum Communication through an Unmodulated Spin Chain, Phys. Rev. Lett. 91, 207901 (2003).
  18. G. Gualdi, V. Kostak, I. Marzoli, and P. Tombesi, Perfect state transfer in long-range interacting spin chains, Phys. Rev. A 78, 022325 (2008).
  19. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Perfect State Transfer in Quantum Spin Networks, Phys. Rev. Lett. 92, 187902 (2004).
  20. M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Perfect transfer of arbitrary states in quantum spin networks, Phys. Rev. A 71, 032312 (2005).
  21. L. Campos Venuti, C. Degli Esposti Boschi, and M. Roncaglia, Qubit Teleportation and Transfer Across Antiferromagnetic Spin Chains, Phys. Rev. Lett. 99, 060401 (2007).
  22. L. Banchi, A. Bayat, P. Verrucchi, and S. Bose, Nonperturbative Entangling Gates between Distant Qubits Using Uniform Cold Atom Chains, Phys. Rev. Lett. 106, 140501 (2011).
  23. N. Y. Yao, L. Jiang, A. V. Gorshkov, Z.-X. Gong, A. Zhai, L.-M. Duan, and M. D. Lukin, Robust Quantum State Transfer in Random Unpolarized Spin Chains, Phys. Rev. Lett. 106, 040505 (2011).
  24. C. Di Franco, M. Paternostro, and M. S. Kim, Perfect State Transfer on a Spin Chain without State Initialization, Phys. Rev. Lett. 101, 230502 (2008).
  25. C. Albanese, M. Christandl, N. Datta, and A. Ekert, Mirror Inversion of Quantum States in Linear Registers, Phys. Rev. Lett. 93, 230502 (2004).
  26. T. Shi, Y. Li, Z. Song, and C.-P. Sun, Quantum-state transfer via the ferromagnetic chain in a spatially modulated field, Phys. Rev. A 71, 032309 (2005).
  27. P. Karbach and J. Stolze, Spin chains as perfect quantum state mirrors, Phys. Rev. A 72, 030301(R) (2005).
  28. R. Raussendorf, Quantum computation via translation-invariant operations on a chain of qubits, Phys. Rev. A 72, 052301 (2005).
  29. J. Fitzsimons and J. Twamley, Globally Controlled Quantum Wires for Perfect Qubit Transport, Mirroring, and Computing, Phys. Rev. Lett. 97, 090502 (2006).
  30. P. Kumar and S. Daraeizadeh, Parity-based mirror inversion for efficient quantum state transfer and computation in nearest-neighbor arrays, Phys. Rev. A 91, 042310 (2015).
  31. D. T. Stephen, H. P. Nautrup, J. Bermejo-Vega, J. Eisert, and R. Raussendorf, Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter, Quantum 3, 142 (2019).
  32. T. Devakul and D. J. Williamson, Universal quantum computation using fractal symmetry-protected cluster phases, Phys. Rev. A 98, 022332 (2018).
  33. R. Raussendorf, C. Okay, D.-S. Wang, D. T. Stephen, and H. P. Nautrup, Computationally Universal Phase of Quantum Matter, Phys. Rev. Lett. 122, 090501 (2019).
  34. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L012023 for a generalization of Protocol t1, connections to the time-dependent protocol of [28], and an analysis of the performance of reversal protocols in the presence of disorder.
  35. M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
  36. C. H. Bennett, J. I. Cirac, M. S. Leifer, D. W. Leung, N. Linden, S. Popescu, and G. Vidal, Optimal simulation of two-qubit Hamiltonians using general local operations, Phys. Rev. A 66, 012305 (2002).
  37. G. Vidal, K. Hammerer, and J. I. Cirac, Interaction Cost of Nonlocal Gates, Phys. Rev. Lett. 88, 237902 (2002).
  38. N. Alon, F. R. K. Chung, and R. L. Graham, Routing permutations on graphs via matchings, SIAM J. Discrete Math. 7, 513 (1994).
  39. A. Bapat, A. M. Childs, A. V. Gorshkov, S. King, E. Schoute, and H. Shastri, Quantum routing with fast reversals, Quantum 5, 533 (2021).
  40. H. Yao and S. A. Kivelson, Exact Chiral Spin Liquid with Non-Abelian Anyons, Phys. Rev. Lett. 99, 247203 (2007).
  41. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321, 2 (2006).
  42. Y.-A. Chen, Exact bosonization in arbitrary dimensions, Phys. Rev. Res. 2, 033527 (2020).
  43. N. Y. Yao, C. R. Laumann, A. V. Gorshkov, H. Weimer, L. Jiang, J. I. Cirac, P. Zoller, and M. D. Lukin, Topologically protected quantum state transfer in a chiral spin liquid, Nat. Commun. 4, 1585 (2013).

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Phys. Rev. Research 4, L012023– Published 22 February, 2022
  • Received 5 April 2020
  • Accepted 20 September 2021
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