Science Advances

Supplementary Materials

This PDF file includes:

  • Section S1. D-Wave embeddings and Jc optimization
  • Section S2. CIM data and post-selection
  • Section S3. C-SDE simulations of CIM
  • Section S4. Optimal–annealing time analysis
  • Section S5. Performance of parallel tempering
  • Fig. S1. D-Wave success probability for SK problems and MAX-CUT problems of edge density 0.5 as a function of problem size N and embedding parameter Jc.
  • Fig. S2. MAX-CUT on graphs with an edge density of 0.5.
  • Fig. S3. Properties of heuristic embeddings for fixed-degree graphs.
  • Fig. S4. Choice of optimal coupling for sparse graphs using the heuristic embedding.
  • Fig. S5. Data filtering and post-selection in NTT CIM.
  • Fig. S6. Comparison of Stanford and NTT CIM performance for SK and dense MAX-CUT problems.
  • Fig. S7. Abstract schematic of measurement-feedback CIM.
  • Fig. S8. Simulated CIM success probability as a function of Fmax for the SK, dense MAXCUT, and cubic MAX-CUT problems in this paper.
  • Fig. S9. Comparison of c-SDE simulations with experimental CIM data.
  • Fig. S10. Simulated CIM success probability and time to solution (in round trips) for SK and MAX-CUT problems.
  • Fig. S11. Time-to-solution analysis for D-Wave at optimal annealing time.
  • Fig. S12. CIM time to solution compared against the parallel tempering algorithm implemented in the Unified Framework for Optimization.
  • Table S1. Seven steps in a single round trip for the measurement-feedback CIM and the appropriate truncated Wigner description.
  • Table S2. Problem-dependent constants α and β used in the relation N0 = α + β log10(T/μs) for the success probability exponential P = e−(N/N0)2.
  • References (6164)

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