DOI: 10.18150/ougf1o
title: Comparing tensor network approaches for discrete optimization against quantum and classical Ising machines

description: This database contains the results from various solvers applied to different instances of optimization problems, categorized by topology (Pegasus, Zephyr), system size (P4, P8, P16, Z3, Z4), problem class (RCO, RAU, CBFM-P), and solver type (D-Wave, Simulated Bifurcation Machine (SBM), Tensor Network (TN)). The purpose of this structure is to allow efficient access to results based on different quantum architectures and problem parameters.Each result file includes the instance ID, the corresponding lowest energy (solution quality), and the state (spin configuration) representing the solution. The spin configurations are represented with the following values:1: Spin up-1: Spin down0: Missing spin------------------------------------------------------------------------System Sizes and Problem Classes------------------------------------------------------------------------Pegasus instances were generated for the D-Wave Advantage_system6.1 machine, and Zephyr instances were generated for the D-Wave Advantage2_prototype1.1 machine.We used a "nice" coordinate system for Pegasus, so some parts of the machine are unused.Size description:P4 - Pegasus 3x3x3 with 216 spins and 1324 couplingsP8 - Pegasus 7x7x3 with 1176 spins and 8107 couplings (1 missing edge compared to "perfect" P8 graph)P16 - Pegasus 15x15x3 with 5 376 spins and 38 615 couplings (24 missing nodes and 341 missing edges compared to the "perfect" P16 graph)Z3 - Zephyr 3x3x4 with 332 spins and 2735 couplings (4 missing nodes and 73 missing edges compared to the "perfect" Z3 graphZ4 - Zephyr 3x3x4 with 563 spins and 4790 couplings (13 missing nodes and 242 missing edges compared to the "perfect" Z4 graph------------------------------------------------------------------------Problem Classes:RCO - Class I - Random Couplings Only: biases are set to 0, and couplings are in the range [-1, 1].RAU - Class II - RAndom Uniform: biases (h) are in the range [-0.1, 0.1], and couplings are in the range [-1, 1].CBFM-P - Class III - Corrupted Biased Ferro-Magnets for Pegasus: The parameter distributions are as follows: P (Jij = 0) = 0.35, P (Jij = −1) = 0.10, P (Jij = 1) = 0.55, ∀(i, j) ∈ Edges of Ising graphP (hi = 0) = 0.15, P (hi = −1) = 0.85, P (hi = 1) = 0, ∀i ∈ Nodes of Ising graph.------------------------------------------------------------------------Directory Structure------------------------------------------------------------------------The database is organized into two main topological structures, Pegasus and Zephyr, with subdirectories representing different system sizes and instance classes.Folder Structure:Database:├── Pegasus│  ├── P4│  │  ├── RCO│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  ├── TN.csv│  │  │  ├── TN16.csv│  │  │  └── TN20.csv│  │  ├── RAU│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  ├── TN.csv│  │  │  ├── TN16.csv│  │  │  └── TN20.csv│  │  ├── CBFM-P│  │      ├── instances│  │      ├── D-Wave.csv│  │      ├── SBM.csv│  │      ├── TN.csv│  │      ├── TN16.csv│  │      └── TN20.csv│  ├── P8│  │  ├── RCO│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  ├── TN.csv│  │  │  ├── TN16.csv│  │  │  └── TN20.csv│  │  ├── RAU│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  ├── TN16.csv│  │  │  └── TN20.csv│  │  ├── CBFM-P│  │      ├── instances│  │      ├── D-Wave.csv│  │      ├── SBM.csv│  │      ├── TN.csv│  │      ├── TN16.csv│  │      └── TN20.csv│  ├── P16│  │  ├── RCO│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  └── TN16.csv│  │  ├── RAU│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  └── TN16.csv│  │  ├── CBFM-P│  │      ├── instances│  │      ├── D-Wave.csv│  │      ├── SBM.csv│  │      └── TN16.csv├── Zephyr│  ├── Z3│  │  ├── RCO│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  ├── TN.csv│  │  │  ├── TN12.csv│  │  │  └── TN14.csv│  │  ├── RAU│  │  │  ├── instances│  │  │  ├── D-Wave.csv│  │  │  ├── SBM.csv│  │  │  ├── TN.csv│  │  │  ├── TN12.csv│  │  │  └── TN14.csv│  ├── Z4│      ├── RCO│      │  ├── instances│      │  ├── D-Wave.csv│      │  ├── SBM.csv│      │  ├── TN.csv│      │  ├── TN12.csv│      │  └── TN14.csv│      ├── RAU│          ├── instances│          ├── D-Wave.csv│          ├── SBM.csv│          ├── TN.csv│          ├── TN12.csv│          └── TN14.csv------------------------------------------------------------------------Explanation of Directory Levels:------------------------------------------------------------------------Top-level folders represent the quantum annealer topologies:Pegasus: D-Wave's Pegasus architecture.Zephyr: D-Wave's Zephyr architecture.Sub-levels (P4, P8, Z3, Z4) represent different system sizes.Further sub-folders (RCO, RAU, CBFM-P) correspond to different problem classes.------------------------------------------------------------------------File Contents------------------------------------------------------------------------Each CSV file (e.g., D-Wave.csv, SBM.csv, TN.csv) contains the results from the corresponding solver.TN12.csv: The best energy results from the tensor network based solver with dimensional reduction of cluster degrees of freedom to 2^12 statesTN14.csv: The best energy results from the tensor network based solver with dimensional reduction of cluster degrees of freedom to 2^14 statesTN16.csv: The best energy results from the tensor network based solver with dimensional reduction of cluster degrees of freedom to 2^16 statesTN20.csv: The best energy results from the tensor network based solver with dimensional reduction of cluster degrees of freedom to 2^20 statesTN.csv: The best energy results from the tensor network based solver without dimensional reduction of cluster degrees of freedomSBM.csv: The best energy results from the Simulated Bifurcation Machine (SBM)D-Wave.csv: The best energy results from the D-Wave quantum annealer----------------------------------------------------------------------------------------------------The CSV files have the following format:Instance, Energy, StateWhere:Instance: The identifier for each problem instance, numbered in ascending order (e.g., 001, 002, 003).Energy: The lowest energy obtained by the solver for the corresponding instance.State: A string of comma-separated spin values (1, -1, 0), representing the spin configuration for that instance's solution. The length of the state vector corresponds to the number of qubits used by the solver. Missing spins (where a particular qubit wasn't used) are represented by 0.Example .csv file:Instance,Energy,State001,-469.0,"1,1,1,-1,1,0,1,-1,1,1,1,1,1,-1,1"002,-492.0,"1,1,-1,1,1,0,-1,1,1,-1,1,1,1,1,1"---------------------------------------------------------------------------------------Instances Folder:Each folder contains a subfolder named instances, which holds the .txt files defining the problem instances for each solver run.-------------------------------------------------------------------------------------This project was supported byThe National Science Center (NCN), Poland, under projects No. 2020/38/E/ST3/00269 (T.S.), 2022/47/B/ST6/02380 (B.G.), 2020/38/E/ST3/00150 (A.D.) and Project 2021/03/Y/ST2/00184 within the QuantERA II Programme that has received funding from the European Union Horizon 2020 research and innovation programme under Grant Agreement No.101017733 (M.M.R.).This work was in part supported by:The Defense Advanced Research Projects Agency (DARPA) under Air Force Research Laboratory (AFRL) contract no. FA8650-23-3-7313 (M.M.).