A Quantum Circuit Simulator Based on Decision Diagrams

The advantages of quantum computing as compared to classical computing are currently being researched; therefore, the ability to correctly simulate quantum circuits is becoming increasingly more important. A Quantum Multiple-valued Decision Diagram, or QMDD, is a structure which allows for an efficient implementation of a quantum circuit simulator. This structure can be used to create a quantum circuit simulator that is both computationally efficient as well as economic with memory usage. In this thesis, a background of quantum computing and analyzing quantum gates and circuits is given. The concept of a QMDD is presented, and the relationship between a QMDD and a quantum circuit simulator is discussed. In addition to these topics, the basic theory behind creating a quantum circuit simulator is discussed. This thesis proposes two different approaches for creating a quantum circuit simulator and analyzes the results generated from both approaches. The first approach utilizes explicit matrix-vector multiplication using QMDD representations of the quantum circuit as well as the input vector. The second approach utilizes implicit matrix-vector multiplication where a QMDD structure representing the quantum circuit undergoes a guided traversal based on the input vector. Both of these approaches are v compared to explicit multiplication using matrices and vectors instead of the QMDD structure. Finally, results are discussed, and the effectiveness of the two circuit simulation methods is analyzed and compared with an existing quantum circuit simulator.