Low-Depth Gradient Measurements Can Improve Convergence in Variational Hybrid Quantum-Classical Algorithms.

Area of Science:

• Quantum computing
• Optimization theory
• Machine learning

Background:

• Quantum variational algorithms are increasingly used for complex optimization problems.
• The efficiency of these algorithms can depend on how gradients are measured.
• Previous studies have debated the benefit of measuring analytic gradients versus objective functions alone.

Purpose of the Study:

• To determine if measuring analytic gradients offers a performance advantage in quantum variational algorithms.
• To provide theoretical guarantees for the convergence speed of gradient-based quantum optimization.
• To establish bounds on the computational cost associated with gradient-based variational optimization.

Main Methods:

• Developed a simple optimization problem within a natural black-box setting.
• Utilized a quantum variational algorithm employing a low-depth circuit to measure analytic gradients.
• Applied stochastic gradient descent for optimization.
• Derived theoretical upper bounds for optimization costs near local minima.

Main Results:

• Proved that the quantum variational algorithm measuring analytic gradients converges provably faster than algorithms relying solely on objective function measurements.
• Demonstrated the benefit of incorporating analytic gradient measurements in quantum optimization.
• Established new upper bounds on the cost of gradient-based variational optimization.

Conclusions:

• Measuring analytic gradients with low-depth circuits enhances the convergence speed of quantum variational algorithms.
• This finding confirms the practical advantage of gradient-based approaches in quantum optimization.
• The derived bounds offer insights into the efficiency of near-local minimum optimization strategies.