Graph-based simulation of quantum computation in the density matrix representation

作     者：Viamontes, GF Markov, IL Hayes, JP 

作者机构：Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA 

出 版 物：《QUANTUM INFORMATION & COMPUTATION》 (Quantum Inf. Comput.)

年 卷 期：2005年第5卷第2期

页      面：113-130页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：quantum circuits quantum algorithms simulation density matrices quantum errors graph data structures decision diagrams QuIDDs 

摘      要：Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication. Simulating such phenomena efficiently is exceedingly difficult because of the vast size of the quantum state space involved. A major complication is caused by errors (noise) due to unwanted interactions between the quantum states and the environment. Consequently, simulating quantum circuits and their associated errors using the density matrix representation is potentially significant in many applications, but is well beyond the computational abilities of most classical simulation techniques in both time and memory resources. The size of a density matrix grows exponentially with the number of qubits simulated, rendering array-based simulation techniques that explicitly store the density matrix intractable. In this work, we propose a new technique aimed at efficiently simulating quantum circuits that are subject to errors. In particular, we describe new graph-based algorithms implemented in the simulator QuIDDPro/D. While previously reported graph-based simulators operate in terms of the state-vector representation, these new algorithms use the density matrix representation. To gauge the improvements offered by QuIDDPro/D, we compare its simulation performance with an optimized array-based simulator called QCSim. Empirical results, generated by both simulators on a set of quantum circuit benchmarks involving error correction, reversible logic, communication, and quantum search, show that the graph-based approach far outperforms the array-based approach for these circuits.