ar X iv : q ua nt - p h / 03 09 06 0 v 1 6 S ep 2 00 3 Improving Gate - Level Simulation of Quantum Circuits ∗

Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a novel data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, many of these matrices and vectors can be represented in a form that grows polynomially with an increase in the number of qubits. Using QuIDDs, we implemented a general-purpose quantum computing simulator in C++ called QuIDDPro and tested it on Grover’s algorithm. Our QuIDD technique asymptotically outperforms other known simulation techniques. ∗Earlier results of this work were reported at ASPDAC ’03 [18]. New material includes significantly better experimental results and a description of a large class of matrices and vectors which can be manipulated in polynomial time and memory using QuIDDPro.