Method and system for quantum machine learning

A quantum computing system comprising:

• a data input and transformation module configured to receive time-dependent input data of a dynamical system and transform a first element of the input data into a set of transformed data, wherein the first element corresponds to an initial time;
• a quantum data encoding module configured to encode the transformed data into a quantum circuit by performing a first set of quantum operations, wherein the quantum circuit comprises multiple layers, including data encoding layers, feedback layers, and a reservoir circuit layer;
• a quantum measurement model configured to generate a previous measurement vector;
• a quantum feedback module configured to integrate a measurement feedback from the previous measurement vector into the quantum circuit by executing a second set of quantum operations;
• a random transformation module configured to output a quantum state configuration that is measured by the quantum measurement module to generate an updated measurement vector;
• and
• a reservoir state creation module configured to produce a reservoir state from the updated measurement vector, a previous reservoir state, and the input data, wherein the system utilizes fixed transformation matrices which remain invariant across training and prediction phases of the system's operation.