Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping

We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. In a standard setting, such noise can be detrimental to the quantum optimization performance. Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions. The transformation effectively changes the attractor into a higher-quality solution of the Hamiltonian based on the results of the previous step. The end result is that noise aids variational optimization, as opposed to hindering it. We present an improved Quantum Approximate Optimization Algorithm (QAOA) runs in experiments on Rigetti's quantum device. We report approximation ratios <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.9</mml:mn> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.96</mml:mn> </mml:math> for random, fully connected graphs on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>82</mml:mn> </mml:math> qubits, using only depth <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> QAOA with NDAR. This compares to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.34</mml:mn> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0.51</mml:mn> </mml:math> for standard <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> QAOA with the same number of function calls.