Data set for 'Role of Nonstabilizerness in Quantum Optimization'

This archive contains the complete raw data necessary to reproduce all results presented in the associated article. The folder structure is organized as follows: The main directory contains three subfolders: annealing/ qubits/ qutrits/ Each folder corresponds to a different part of the study. 1.annealing/ folder: This folder contains three data files corresponding to annealing simulations for: 16 qubits 32 qubits 64 qubits Each file contains three columns: Annealing parameter λ (x-axis) SRE (Shannon Rényi Entropy) values (y-axis) Error bars on SRE These data reproduce Figure 4(b) of the paper. 2. qubits/ folder: This folder contains all QAOA simulation results and SRE calculations for qubit systems. 2.1 System Sizes There are three subfolders: 4-Q/ 6-Q/ 8-Q/ Each corresponds to simulations for 4, 6, and 8 qubits, respectively. 2.2 Depth Structure Inside each system-size folder, there are: Multiple folders named depth_X/ (where X is the circuit depth) One folder named exact/ One file named: SK-[2, ... , 2]_in_DEPTH_.json 2.3 Data Inside Each depth_X/ Folder Each depth_X/ folder contains data for 50 independent disorder realizations of the Sherrington–Kirkpatrick (SK) model. For each realization, there is one JSON file containing the full information required to reconstruct the QAOA optimization and the underlying Hamiltonian. (A) Realization JSON File Structure Each realization file contains the following fields: "dims"Dimension of the single-site Hilbert subspace. For qubits: [2]*Number of qubits For qutrits: [3]*Number of qutrits "SK"Dictionary describing the Sherrington–Kirkpatrick Hamiltonian: "graph" : List of all interacting pairs (fully connected SK graph). "weights" : List of coupling strengths associated with each interaction pair. "external field operator"Dictionary describing the additional external field term added to the SK couplings: "external_field_type": "Z" : A longitudinal Z-type external field is included. "coefficients" : Coefficients of the external field acting on each site. "energies"List of the energy values obtained at each optimization step during the QAOA parameter update. "initial_params"Initial QAOA parameters: List of initial γ (gamma) and initial β (beta) values "parameters"Full list of optimized QAOA parameters at every optimization step.This allows reconstruction of the complete optimization trajectory and all intermediate circuits. (b) magic/ Subfolder This folder contains 50 JSON files (one per realization), each storing the magic quantifiers evaluated during the optimization. Each magic file contains: "step magic calculation" : List of optimization steps at which the magic quantifier was computed(magic is not necessarily evaluated at every optimization step). "magic type":"SRE"(Stabilizer Rényi Entropy) "magic values" : List of SRE values corresponding to the steps specified above. "magic type 2" : null for qubit simulations / "MANA" for qutrit simulations "magic values 2": Empty list [] for qubits / List of corresponding MANA values for qutrit systems 2.4 Exact Diagonalization (exact/) Each system-size folder contains a subdirectory named exact/, which includes 50 JSON files, corresponding to the same 50 disorder realizations described in Section 2.3. For each realization, the file contains the same system data as the optimization files described in Section 2.3 (i.e., "dims", "SK" with "graph"and "weights", and the "external field operator" with its "external_field_type" and "coefficients"), ensuring that the exact diagonalization corresponds to the identical Hamiltonian instance used in the associated QAOA simulation. In addition, each file contains: "eigenvalues" — complete spectrum of the Hamiltonian "eigenvectors" — corresponding eigenvectors 2.5 Aggregated Depth File The file: SK-[2, ... , 2]_in_DEPTH.json (and analogously SK-[3, 3, 3, 3]_in_DEPTH.json for qutrits) contains the aggregated performance metrics for all disorder realizations and circuit depths. The file has the following top-level structure: {"normalized energy": { ... },"fidelity": { ... },"sre": { ... }}Each of these three entries is a dictionary indexed by the QAOA circuit depth. Structure for a Fixed Depth For a given depth d, each metric ("normalized energy", "fidelity", or "sre") contains a list of 50 elements, one for each disorder realization. (for example : dict["fidelity"]["4"] returns the list of 50 entries corresponding to the fidelity of the N-qubit (or N-qutrit) system optimized with a QAOA circuit of depth d=4) For each realization: There is a list of length d+1. Each element corresponds to the value of the quantity computed using a QAOA circuit with an increasing number of layers: p=0,1,…,d Importantly: For each value of p, the quantities is evaluated using the optimized QAOA parameters obtained for that specific circuit depth. Thus, the lists track the progressive performance of circuits with increasing layers up to the maximum depth. 3. qutrits/ folder: The qutrits/ directory follows the same organizational structure described for the qubit simulations (Section 2), including: Subfolders corresponding to different system sizes, Depth-resolved folders containing optimization data for 50 disorder realizations, An exact/ subfolder with exact diagonalization results, Magic quantifier files (including both SRE and MANA). In particular, the file SK-[3, 3, 3, 3]_in_DEPTH.json contains the aggregated performance metrics for the qutrit simulations across all disorder realizations and circuit depths. Its internal structure is identical to the qubit case described in Section 2.5, with top-level entries: "normalized energy" (energy ratio with respect to the exact ground-state energy), "fidelity", "sre" and "Mana" For each fixed depth, the file stores the depth-resolved lists (across 50 realizations) of these quantities for increasing numbers of QAOA layers p=0,…,d computed using the optimized parameters at that depth. This ensures full reproducibility of all depth-dependent results reported for the qutrit systems in the article.