Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count of current quantum computers is a major obstacle to competing against classical methods. Here, we develop a qubit-efficient algorithm that overcomes this limitation by mapping a candidate bit-string solution to an entangled wave function of fewer qubits. We propose a variational quantum circuit generalizing the quantum approximate optimization ansatz. Extremizing the ansatz for Sherrington-Kirkpatrick spin-glass problems, we show valuable properties such as the concentration of ansatz parameters and derive performance guarantees. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices.

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• Adiabatic quantum optimization
• Optimization problems
• Quantum algorithms
• Quantum circuits
• Quantum information with solid state qubits
• Spin glasses
• Superconducting qubits
• Variational approach