24 August 2004 Graph-based simulation of quantum computation in the density matrix representation
Author Affiliations +
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.
© (2004) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
George F. Viamontes, Igor L. Markov, John P. Hayes, "Graph-based simulation of quantum computation in the density matrix representation", Proc. SPIE 5436, Quantum Information and Computation II, (24 August 2004); doi: 10.1117/12.542767; https://doi.org/10.1117/12.542767


Quantum search simulation with Wolfram Mathematica
Proceedings of SPIE (September 28 2016)
GFSOP-based ternary quantum logic synthesis
Proceedings of SPIE (September 07 2010)
ZENO a new graphical tool for design and simulation...
Proceedings of SPIE (May 25 2005)
Finding small two-qubit circuits
Proceedings of SPIE (August 24 2004)

Back to Top