Sbo-QAOA Achieves Fair Sampling of Degenerate States with Four Variational Parameters

Why It Matters

Fair sampling eliminates solution bias, crucial for logistics, finance, and drug discovery where diverse optimal outcomes improve robustness. SBO‑QAOA’s low‑parameter design also lowers quantum hardware requirements, accelerating near‑term deployment.

Key Takeaways

• SBO‑QAOA uses only four variational parameters.
• Targets Gibbs distribution at chosen temperature for fair sampling.
• Achieves near‑uniform degenerate ground‑state probabilities.
• Outperforms standard QAOA across circuit depths.
• Enables scalable quantum sampling for logistics, finance, drug discovery.

Pulse Analysis

Quantum optimisation algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have become a cornerstone for tackling combinatorial problems on emerging quantum hardware. However, standard QAOA often exhibits sampling bias when multiple optimal solutions exist, limiting its usefulness in real‑world scenarios where a diverse set of solutions is needed. Addressing this gap, the research community has turned to temperature‑targeted approaches that align the quantum cost function with a classical Gibbs distribution, thereby promoting equitable sampling across degenerate states.

The newly proposed SBO‑QAOA builds on this concept by introducing an SBO Hamiltonian that encodes the desired thermal state and by applying a linear‑schedule parameterization. This reduces the usual 2p variational parameters to just four: two slopes and two intercepts for the gamma and beta angles. Despite the drastic simplification, experimental results on an Ising‑model benchmark demonstrate a total variation distance that shrinks toward zero as circuit depth increases, and a ground‑state probability near 0.83—significantly better than conventional QAOA, which retains bias even at large depths.

Beyond the technical achievement, SBO‑QAOA opens pathways for practical quantum advantage in sectors that rely on fair solution sampling, such as supply‑chain optimisation, portfolio diversification, and molecular design. The primary hurdle remains scaling the temperature‑dependent Hamiltonian to larger qubit counts, prompting future work on efficient Pauli‑string expansions and low‑order approximations suitable for near‑term devices. As quantum processors mature, a low‑parameter, bias‑free algorithm like SBO‑QAOA could become a standard tool for enterprises seeking robust, quantum‑enhanced decision making.