At1uri/quantum-hamiltonian-ground-state-benchmarks

Quantum Hamiltonian Ground State Benchmarks

A high-precision benchmark dataset containing 1,000 synthetic and empirical asset covariance matrices mapped to longitudinal Ising Spin-Glass Hamiltonians for benchmarking Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), Simulated Annealing, and classical Branch-and-Bound solvers.

Part of the Institutional Quantitative AI Suite by At1uri.

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1. Dataset Overview

Every record represents a unique combinatorial portfolio instance mapped onto an exact physical Ising spin system:

The dataset provides exact diagonal energy spectrum characteristics:

• Ground State Energy ($E_0$): The minimum eigenvalue corresponding to the globally optimal portfolio bitstring $x^* \in {0, 1}^n$.
• First Excited State Energy ($E_1$): Second lowest eigenvalue.
• Spectral Energy Gap ($\Delta = E_1 - E_0$): Governs adiabatic quantum computation runtime and QAOA convergence difficulty.
• Maximum Energy ($E_{\max}$): Worst-case baseline eigenvalue.
• QAOA Approximation Ratios: Theoretical and simulated ratios $\alpha = \frac{\langle \mathcal{H} \rangle - E_{\max}}{E_0 - E_{\max}}$ for circuit depths $p=1$ and $p=2$.
• Bipartite Von Neumann Entanglement Entropy: $S(\rho_A) = -\text{Tr}(\rho_A \log_2 \rho_A)$ across bipartition $A = {q_0}$.

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2. Schema Specification

Column	Type	Description
sample_id	int64	Unique instance index (0 to 999)
num_qubits	int64	System size / number of assets ($n \in {4, 5, 6, 8}$)
risk_aversion	float64	Investor risk aversion coefficient $q \in [0.1, 1.5]$
target_cardinality	int64	Number of selected assets $K \in {1, \dots, n-1}$
budget_penalty	float64	Quadratic constraint enforcement penalty $\lambda_{\text{budget}}$
ground_state_energy	float64	Minimum Hamiltonian eigenvalue $E_0$
first_excited_energy	float64	First excited state eigenvalue $E_1$
spectral_gap	float64	$\Delta = E_1 - E_0$
ground_state_bitstring	string	Binary optimal configuration (e.g. "1010")
max_energy	float64	Maximum eigenvalue $E_{\max}$
qaoa_p1_ratio	float64	QAOA approximation ratio at depth $p=1$
qaoa_p2_ratio	float64	QAOA approximation ratio at depth $p=2$
entanglement_entropy	float64	Von Neumann bipartite entanglement entropy in bits
h_vector	string	JSON-encoded longitudinal magnetic fields $h_i$
J_matrix	string	JSON-encoded 2-qubit exchange couplings $J_{ij}$

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3. Quickstart & Loading

Loading with Hugging Face Datasets or Pandas

from datasets import load_dataset
import pandas as pd
import json

# Option A: Hugging Face Datasets
dataset = load_dataset("At1uri/quantum-hamiltonian-ground-state-benchmarks")
df = dataset["train"].to_pandas()

# Option B: Direct Parquet inspection
print(f"Total instances: {len(df)}")
print(f"Mean Spectral Gap: {df['spectral_gap'].mean():.4f}")
print(f"Mean QAOA p=2 Approximation Ratio: {df['qaoa_p2_ratio'].mean()*100:.2f}%")

# Decode first instance couplings
h0 = json.loads(df.iloc[0]["h_vector"])
J0 = json.loads(df.iloc[0]["J_matrix"])
print(f"First instance local fields h: {h0}")

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4. Associated Repositories

• Interactive Simulator: Quantum Portfolio Optimization Studio
• Model Engine: QAOA & VQE Quantum Optimizer
• Collection: Institutional Quantitative AI Suite