New Approaches for Optimization in Quantum Computing: Two-step QAOA and HOBO
As part of research ideas for leveraging quantum computing in optimization, we introduce Two-step QAOA and HOBO (Higher-Order Binary Optimization). Both approaches enable effective utilization of constraint conditions, making them potentially useful for overcoming challenges in optimization formulation.
Two-step QAOA: Efficient Handling of k-hot Constraints
Two-step QAOA allows the removal of k-hot constraints (where k out of n qubits must be set to 1, and the rest to 0) from the Hamiltonian. Traditionally, maintaining this constraint required preparing a specialized initial state, which was often cumbersome. However, Two-step QAOA simplifies this process by separating the formulation into two stages.
This method consists of:
- First performing optimization with k-hot constraints, using the solution as
- The initial state for the next optimization
By leveraging this approach, quantum circuits are used more efficiently without unnecessary resource consumption, significantly expanding the possibilities for solving combinatorial optimization problems with quantum circuits.
HOBO: A More Powerful Formulation Eliminating Constraints
HOBO (Higher-Order Binary Optimization) is a robust optimization method that can potentially eliminate the need for even Two-step QAOA. In traditional QUBO (Quadratic Unconstrained Binary Optimization) formulations, handling k-hot constraints required assigning n qubits to ensure k are set to 1 and the rest to 0, leading to substantial qubit waste.
However, HOBO enables the use of higher-order formulations, removing the necessity for k-hot constraints by utilizing:
- Integer encoding (1,2,3,4,…,k) to directly specify constraints
- Reduction in the number of required qubits
- Improved computational accuracy
With HOBO, optimization can be performed more efficiently and with greater precision than with traditional methods.
Conclusion
Two-step QAOA and HOBO present promising advancements in quantum computing for optimization:
- Two-step QAOA simplifies k-hot constraint handling, reducing quantum circuit overhead.
- HOBO eliminates k-hot constraints altogether, utilizing integer encoding for more efficient computation.
By adopting these approaches, new solutions for previously difficult optimization problems become possible.