Efficient Variational Quantum Algorithms Solve Generalized Assignment Problem with Reduced Circuit Width

The Generalized Assignment Problem, a notoriously difficult challenge in optimisation, receives a novel approach from Carlo Mastroianni and Andrea Vinci of the National Research Council of Italy, alongside Francesco Plastina and Jacopo Settino from the University of Calabria. Their work introduces a new algorithm, VQGAP, which tackles this complex problem using the principles of Variational Quantum Algorithms. Recognising the limitations of current quantum hardware, the team focuses on minimising the resources required for computation, specifically reducing the number of qubits and the complexity of the quantum circuits needed to find solutions. Initial results demonstrate that VQGAP performs comparably to standard Variational Eigensolver methods, while offering a significant advantage in terms of computational efficiency, paving the way for tackling larger and more complex optimisation problems with near-term quantum devices.

This innovative approach decouples the quantum circuit from the process of measuring the solution, aiming to reduce the number of qubits required and make the problem solvable on today’s limited quantum computers. A further refinement, VQGAPe, achieves even greater efficiency by scaling the qubit requirement logarithmically with the number of agents, a significant improvement over the linear scaling of standard VQE. The team demonstrates promising results, suggesting VQGAPe can achieve comparable performance to VQE while utilizing fewer quantum resources. This decoupling strategy allows scientists to explore a wider range of potential solutions with a reduced quantum circuit size, mitigating the impact of noise and errors inherent in current quantum hardware. This work addresses the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices by reducing the width of the quantum circuits needed to find solutions. Researchers decoupled the qubits within the quantum circuit from the binary variables defining the GAP, enabling a transformation of solutions generated in the quantum realm into feasible solutions within the problem’s variable space. Scientists then designed encoding and decoding functions that bridge the gap between the quantum and classical domains, translating solutions generated by the quantum ansatz into valid assignments for the GAP. Researchers decoupled the qubits within the quantum circuit from the binary variables defining the assignment problem, utilizing encoding and decoding functions to translate solutions between the quantum and classical domains. This innovative approach maintains performance comparable to VQE while significantly streamlining quantum resource requirements, a crucial step for implementation on current, limited-scale quantum hardware. The team demonstrated that VQGAP effectively reduces both the number of qubits needed and the depth of the quantum circuit, essential for mitigating the effects of noise in near-term quantum computers. The core innovation lies in decoupling the quantum circuits from the problem’s variables through encoding and decoding functions, effectively reducing the number of qubits needed to find solutions. Preliminary results demonstrate that VQGAP achieves performance comparable to standard VQE methods while optimizing quantum resource usage.

Notably, the number of qubits required scales logarithmically with the number of agents in the problem, a significant improvement over the linear scaling of conventional methods. This reduction in qubit requirements could enable the solution of larger, more complex problems.