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Circuit Knitting Faces Exponential Sampling Overhead Scaling Bounded by Entanglement Cost (2404.03619v2)

Published 4 Apr 2024 in quant-ph, cs.IT, and math.IT

Abstract: Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even for asymptotic overhead in the parallel cut regime. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication (LOCC), of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we show that the regularized sampling overhead for simulating a general bipartite channel via LOCC is lower bounded by $\kappa$-entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasi-probability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.

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References (70)
  1. Distributed quantum computation over noisy channels. Physical Review A, 59(6):4249, 1999.
  2. John Preskill. Quantum computing in the nisq era and beyond. Quantum, 2:79, 2018.
  3. The path to scalable distributed quantum computing. Computer, 49(9):31–42, 2016.
  4. Quantum algorithms and simulation for parallel and distributed quantum computing. In 2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS), pages 9–19. IEEE, 2021.
  5. Quantum internet: Networking challenges in distributed quantum computing. IEEE Network, 34(1):137–143, 2019.
  6. Trading classical and quantum computational resources. Phys. Rev. X, 6:021043, Jun 2016.
  7. Circuit knitting with classical communication, April 2022.
  8. Cutting circuits with multiple two-qubit unitaries. arXiv preprint arXiv:2312.11638, 2023.
  9. Simulating large quantum circuits on a small quantum computer. Phys. Rev. Lett., 125:150504, Oct 2020.
  10. Doubling the size of quantum simulators by entanglement forging. PRX Quantum, 3:010309, Jan 2022.
  11. Overhead-constrained circuit knitting for variational quantum dynamics. arXiv preprint arXiv:2309.07857, 2023.
  12. Optimal quantum circuit cuts with application to clustered Hamiltonian simulation, March 2024. arXiv:2403.01018 [quant-ph].
  13. Constructing a virtual two-qubit gate by sampling single-qubit operations. New Journal of Physics, 23(2):023021, February 2021.
  14. Overhead for simulating a non-local channel with local channels by quasiprobability sampling. Quantum, 5:388, January 2021.
  15. Quasiprobability decompositions with reduced sampling overhead. npj Quantum Information, 8(1):12, 2022.
  16. Error mitigation for short-depth quantum circuits. Phys. Rev. Lett., 119:180509, Nov 2017.
  17. Practical quantum error mitigation for near-future applications. Phys. Rev. X, 8:031027, Jul 2018.
  18. Error mitigation extends the computational reach of a noisy quantum processor. Nature, 567(7749):491–495, March 2019. Number: 7749 Publisher: Nature Publishing Group.
  19. Error mitigation for universal gates on encoded qubits. Phys. Rev. Lett., 127:200505, Nov 2021.
  20. Experimental demonstration of a high-fidelity virtual two-qubit gate. arXiv preprint arXiv:2307.03232, 2023.
  21. Estimating outcome probabilities of quantum circuits using quasiprobabilities. Phys. Rev. Lett., 115:070501, Aug 2015.
  22. Quantifying quantum speedups: Improved classical simulation from tighter magic monotones. PRX Quantum, 2:010345, Mar 2021.
  23. Application of a resource theory for magic states to fault-tolerant quantum computing. Phys. Rev. Lett., 118:090501, Mar 2017.
  24. Quantifying magic for multi-qubit operations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227):20190251, July 2019. Publisher: Royal Society.
  25. Robustness of Magic and Symmetries of the Stabiliser Polytope. Quantum, 3:132, April 2019. Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften.
  26. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402(6760):390–393, 1999.
  27. Quantum algorithms: entanglement–enhanced information processing. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 356(1743):1769–1782, 1998.
  28. Mixed-state entanglement and quantum error correction. Phys. Rev. A, 54:3824–3851, Nov 1996.
  29. Resource theory of entanglement for bipartite quantum channels. arXiv preprint arXiv:1907.04181, 2019.
  30. Entanglement of a bipartite channel. Physical Review A, 103(6):062422, June 2021.
  31. Dynamical entanglement. Phys. Rev. Lett., 125:180505, Oct 2020.
  32. Amortized entanglement of a quantum channel and approximately teleportation-simulable channels. Journal of Physics A: Mathematical and Theoretical, 51(3):035303, 2017.
  33. Entanglement cost of quantum channels. IEEE Transactions on Information Theory, 59(10):6779–6795, 2013.
  34. Mark M. Wilde. Entanglement cost and quantum channel simulation. Physical Review A, 98(4):042338, oct 2018.
  35. Quantum circuit architecture. Physical review letters, 101(6):060401, 2008.
  36. Irreversibility of asymptotic entanglement manipulation under quantum operations completely preserving positivity of partial transpose. Physical Review Letters, 119(18):180506, 2017.
  37. Exact entanglement cost of quantum states and channels under PPT-preserving operations. Physical Review A, 107(1):012429, 2023. arXiv:1809.09592 [quant-ph].
  38. No second law of entanglement manipulation after all. Nature Physics, 19(2):184–189, 2023.
  39. Fundamental limits on the capacities of bipartite quantum interactions. Phys. Rev. Lett., 121:250504, Dec 2018.
  40. Robert R. Tucci. An introduction to cartan’s kak decomposition for qc programmers, July 2005.
  41. Mixed-state entanglement and distillation: Is there a “bound” entanglement in nature? Physical Review Letters, 80(24):5239, 1998.
  42. Bound entanglement can be activated. Physical review letters, 82(5):1056, 1999.
  43. Seven definitions of bipartite bound entanglement. Journal of Physics A: Mathematical and Theoretical, 56(38):385302, 2023.
  44. Mark M Wilde. Quantum information theory. Cambridge university press, 2013.
  45. Power of quantum measurement in simulating unphysical operations. arXiv preprint arXiv:2309.09963, 2023.
  46. Alexei Y. Kitaev. Quantum computations: algorithms and error correction. Russian Mathematical Surveys, 52:1191–1249, 1997.
  47. Variational quantum algorithms. Nature Reviews Physics, 3(9):625–644, 2021.
  48. Robustness of entanglement. Physical Review A, 59(1):141–155, January 1999.
  49. Fundamental limitations on distillation of quantum channel resources. Nature Communications, 12(1):4411, 2021.
  50. Cost of Quantum Entanglement Simplified. Physical Review Letters, 125(4):040502, jul 2020.
  51. α𝛼\alphaitalic_α-logarithmic negativity. Phys. Rev. A, 102:032416, Sep 2020.
  52. Violations additivity Eκsubscript𝐸𝜅E_{\kappa}italic_E start_POSTSUBSCRIPT italic_κ end_POSTSUBSCRIPT. Private email communication on July 27, 2023, 2023.
  53. Non-additivity of kappa-entanglement and bounds on exact PPT entanglement cost. in preparation, 2024.
  54. Semidefinite programming converse bounds for quantum communication. IEEE Transactions on Information Theory, 65(4):2583–2592, 2019. arXiv:1709.00200 [quant-ph].
  55. Complete family of separability criteria. Physical Review A, 69(2):022308, 2004.
  56. Entanglement manipulation and distillability beyond locc. arXiv preprint arXiv:1711.03835, 2017.
  57. Architecture for a large-scale ion-trap quantum computer. Nature, 417(6890):709–711, 2002.
  58. Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys. Rev. Lett., 70:1895–1899, Mar 1993.
  59. Quantum computation and quantum information. Cambridge university press, 2010.
  60. E. M. Rains. Bound on distillable entanglement. Phys. Rev. A, 60:179–184, Jul 1999.
  61. V. Vedral and M. B. Plenio. Entanglement measures and purification procedures. Phys. Rev. A, 57:1619–1633, Mar 1998.
  62. Hand-waving and interpretive dance: an introductory course on tensor networks. Journal of Physics A: Mathematical and Theoretical, 50(22):223001, May 2017.
  63. Quantum-channel capacity of very noisy channels. Physical Review A, 57(2):830, 1998.
  64. Bounding the quantum capacity with flagged extensions. Quantum, 6:647, 2022. arXiv:2008.02461 [quant-ph].
  65. How to quantify a dynamical quantum resource. Phys. Rev. Lett., 123:150401, Oct 2019.
  66. On the capacities of bipartite hamiltonians and unitary gates. IEEE Transactions on Information Theory, 49(8):1895–1911, 2003.
  67. Semidefinite programming converse bounds for quantum communication. IEEE Transactions on Information Theory, 65(4):2583–2592, 2018.
  68. Practical quantum error mitigation for near-future applications. Physical Review X, 8(3):031027, 2018.
  69. Nilanjana Datta. Max-relative entropy of entanglement, alias log robustness. International Journal of Quantum Information, 7(02):475–491, 2009.
  70. A reversible theory of entanglement and its relation to the second law. Communications in Mathematical Physics, 295:829–851, 2010.
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