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Transforming graph states via Bell state measurements

Published 3 May 2024 in quant-ph | (2405.02414v1)

Abstract: Graph states are key resources for measurement-based quantum computing which is particularly promising for photonic systems. Fusions are probabilistic Bell state measurements, measuring pairs of parity operators of two qubits. Fusions can be used to connect/entangle different graph states making them a powerful resource for measurement-based and the related fusion-based quantum computing. There are several different graph structures and types of Bell state measurements, yet the associated graph transformations have only been analyzed for a few specific cases. Here, we provide a full set of such graph transformation rules and we give an intuitive visualization based on Venn diagrams of local neighborhoods of graph nodes. We derive these graph transformations for all fusion types showing that there are five different types of fusion success cases. Finally, we give application examples of the derived graph transformation rules and show that they can be used for constructing graph codes or simulating fusion networks.

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References (53)
  1. “Entanglement in graph states and its applications” (2006). url: arxiv.org/abs/quant-ph/0602096.
  2. “A one-way quantum computer”. Phys. Rev. Lett. 86, 5188–5191 (2001).
  3. “Measurement-based quantum computation on cluster states”. Phys. Rev. A 68, 022312 (2003).
  4. “Fusion-based quantum computation”. Nat. Commun. 14, 912 (2023).
  5. “Resource-efficient linear optical quantum computation”. Phys. Rev. Lett. 95, 010501 (2005).
  6. “Graphical description of the action of local clifford transformations on graph states”. Phys. Rev. A 69, 022316 (2004).
  7. “Multiparty entanglement in graph states”. Phys. Rev. A 69, 062311 (2004).
  8. “Transforming graph states using single-qubit operations”. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, 20170325 (2018).
  9. “Extracting GHZ states from linear cluster states”. Phys. Rev. Res. 6, 013330 (2024).
  10. “Quantum repeaters: The role of imperfect local operations in quantum communication”. Phys. Rev. Lett. 81, 5932–5935 (1998).
  11. “All-photonic quantum repeaters”. Nat. Commun. 6, 6787 (2015).
  12. “Percolation, renormalization, and quantum computing with nondeterministic gates”. Phys. Rev. Lett. 99, 130501 (2007).
  13. “From three-photon Greenberger-Horne-Zeilinger states to ballistic universal quantum computation”. Phys. Rev. Lett. 115, 020502 (2015).
  14. “Loss-tolerant architecture for quantum computing with quantum emitters”. Quantum 8, 1302 (2024).
  15. “Fault-tolerant complexes” (2023). url: arxiv.org/abs/2308.07844.
  16. “Introduction to optical quantum information processing”. Cambridge university press.  (2010).
  17. “Near-deterministic creation of universal cluster states with probabilistic bell measurements and three-qubit resource states”. Phys. Rev. A 91, 042301 (2015).
  18. “Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics”. Quantum 7, 992 (2023).
  19. “Clifford manipulations of stabilizer states: A graphical rule book for clifford unitaries and measurements on cluster states, and application to photonic quantum computing” (2023). url: doi.org/10.48550/arXiv.2312.02377.
  20. “Fast simulation of stabilizer circuits using a graph-state representation”. Phys. Rev. A 73, 022334 (2006).
  21. Dirk Schlingemann. “Stabilizer codes can be realized as graph codes” (2001). url: arxiv.org/abs/quant-ph/0111080.
  22. “Optimal preparation of graph states”. Phys. Rev. A 83, 042314 (2011).
  23. “Mapping graph state orbits under local complementation”. Quantum 4, 305 (2020).
  24. Daniel Gottesman. “The heisenberg representation of quantum computers” (1998). url: arxiv.org/abs/quant-ph/9807006.
  25. “Iso-entangled bases and joint measurements” (2023). url: arxiv.org/abs/2307.06998.
  26. “Optimizing graph codes for measurement-based loss tolerance”. PRX Quantum 4, 020328 (2023).
  27. W. P. Grice. “Arbitrarily complete bell-state measurement using only linear optical elements”. Phys. Rev. A 84, 042331 (2011).
  28. Fabian Ewert and Peter van Loock. “3/4343/43 / 4-efficient bell measurement with passive linear optics and unentangled ancillae”. Phys. Rev. Lett. 113, 140403 (2014).
  29. “Quantum error correction via codes over GF (4)”. IEEE Transactions on Information Theory 44, 1369–1387 (1998).
  30. Matthias C. Löbl et al. “FusionGraphTransformer”. https://github.com/nbi-hyq/FusionGraphTransformer (2023).
  31. “Improved simulation of stabilizer circuits”. Phys. Rev. A 70, 052328 (2004).
  32. “High-threshold universal quantum computation on the surface code”. Phys. Rev. A 80, 052312 (2009).
  33. “Quantum-error-correcting codes using qudit graph states”. Phys. Rev. A 78, 042303 (2008).
  34. “High-threshold quantum computing by fusing one-dimensional cluster states”. Phys. Rev. Lett. 131, 120603 (2023).
  35. “Photonic fusion of entangled resource states from a quantum emitter” (2023). url: arxiv.org/abs/2312.09070.
  36. “Fusion of deterministically generated photonic graph states” (2024). url: arxiv.org/abs/2403.11950.
  37. “Proposal for pulsed on-demand sources of photonic cluster state strings”. Phys. Rev. Lett. 103, 113602 (2009).
  38. “Fidelity of time-bin-entangled multiphoton states from a quantum emitter”. Phys. Rev. A 104, 052604 (2021).
  39. “All-photonic one-way quantum repeaters” (2022). url: arxiv.org/abs/2210.10071.
  40. “Graphical description of the action of clifford operators on stabilizer states”. Phys. Rev. A 77, 042307 (2008).
  41. “Graphical description of pauli measurements on stabilizer states”. Journal of Physics A: Mathematical and Theoretical 43, 025301 (2009).
  42. “Improved graph formalism for quantum circuit simulation”. Phys. Rev. A 105, 022432 (2022).
  43. “Efficient generation of entangled multi-photon graph states from a single atom”. Nature 608, 677–681 (2022).
  44. “High-rate entanglement between a semiconductor spin and indistinguishable photons”. Nat. Photon.Pages 1–6 (2023).
  45. “Deterministic generation of indistinguishable photons in a cluster state”. Nat. Photon. 17, 324–329 (2023).
  46. “Deterministic photon source of genuine three-qubit entanglement” (2023). url: arxiv.org/abs/2310.12038.
  47. “Photonic resource state generation from a minimal number of quantum emitters”. Npj Quantum Inf. 8, 11 (2022).
  48. “Graph-theoretical optimization of fusion-based graph state generation”. Quantum 7, 1212 (2023).
  49. “High photon-loss threshold quantum computing using GHZ-state measurements” (2023). url: arxiv.org/abs/2308.04192.
  50. “Quantum hypergraph states”. New Journal of Physics 15, 113022 (2013).
  51. Mercedes Gimeno-Segovia. “Towards practical linear optical quantum computing”. PhD thesis. Imperial College London.  (2016). url: doi.org/10.25560/43936.
  52. “Efficient inner-product algorithm for stabilizer states” (2012). url: arxiv.org/abs/1210.6646.
  53. “Increasing error tolerance in quantum computers with dynamic bias arrangement” (2023). url: arxiv.org/abs/2303.16122.
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