Parametric Synthesis of Quantum Circuits for Training Perceptron Neural Networks

Abstract

This work contains the analysis of results received after running synthesized quantum circuits for training perceptron neural networks. The training is performed by creating a Grover’s algorithm with a custom oracle function. The concept of synthesizing quantum circuits was showcased in the process of generating training circuits for three perceptron topologies, which were designed to test the accuracy of the synthesis process. The test circuits serve to prove that the proposed synthesis approach could be scaled to utilize more complex quantum computing systems and to solve more practical tasks. IBM’s 100-qubit cloud quantum simulator was used as the debugging environment. Quantum circuits for described algorithms are generated by the "Naginata" quantum synthesizer, its source code is published and further documented on GitHub along with the code for the provided example algorithms. The article describes the processes behind the algorithm for synthesizing quantum circuits that perform the training process of single-layer perceptrons by finding their weights by filtering all possible input values through a predefined accuracy criterion. Since quantum computing is still in its early development phase, quantum circuits are created mainly by manual placement of logic elements. Implementing quantum algorithms, especially more use-case specific ones, directly on the quantum circuit level could lead to the circuit easily becoming too complex for human comprehension. Quantum Circuit Synthesizer "Naginata" was created to simplify the development and debugging process of quantum algorithms, by adding better clarity to their development process. In our case, better clarity for the development process is achieved by composing functions for commonly used operations performed in the implemented quantum algorithm. The programmer could now implement the quantum algorithm as a set of functions, instead of manually creating a circuit from single logic elements. After this, the synthesizer would handle the task of creating the data for placing logic elements on the circuit. This enables an opportunity of implementing quantum algorithms with higher-level commands. In the scope of this work, parametrically generated generic blocks for frequently used operations such as: the adder, multiplier and digital comparator were created and utilized to form the training circuits. The test results, proved that with the help of the proposed quantum synthesizer, these compositions could be used efficiently as building blocks for implementing quantum algorithms. And by visually comparing sizes of both code and circuit representations of the synthesized circuits, to the code examples used to synthesize these circuits, it is determined that the proposed approach for implementing quantum circuits greatly simplifies the processes of development and debugging a quantum algorithm.