Programming Quantum Hardware via Levenberg Marquardt Machine Learning
Significant challenges remain with the development of macroscopic quantum
computing, hardware problems of noise, decoherence, and scaling, software
problems of error correction, and, most important, algorithm construction.
Finding truly quantum algorithms is quite difficult, and many quantum
algorithms, like Shor prime factoring or phase estimation, require extremely
long circuit depth for any practical application, necessitating error
correction. Machine learning can be used as a systematic method to
nonalgorithmically program quantum computers. Quantum machine learning enables
us to perform computations without breaking down an algorithm into its gate
building blocks, eliminating that difficult step and potentially reducing
unnecessary complexity. In addition, we have shown that our machine learning
approach is robust to both noise and to decoherence, which is ideal for running
on inherently noisy NISQ devices which are limited in the number of qubits
available for error correction. We demonstrated this using a fundamentally non
classical calculation, experimentally estimating the entanglement of an unknown
quantum state. Results from this have been successfully ported to the IBM
hardware and trained using a powerful hybrid reinforcement learning technique
which is a modified Levenberg Marquardt LM method. The LM method is ideally
suited to quantum machine learning as it only requires knowledge of the final
measured output of the quantum computation, not intermediate quantum states
which are generally not accessible. Since it processes all the learning data
simultaneously, it also requires significantly fewer hits on the quantum
hardware. Machine learning is demonstrated with results from simulations and
runs on the IBM Qiskit hardware interface.
James E. Steck Nathan L. Thompson Elizabeth C. Behrman