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



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Graph based simulation of quantum computation in the density matrix representation George F Viamontes Igor L Markov John P Hayes University of Michigan Advanced Computer Architecture Laboratory 1301 Beal Ave Ann Arbor MI USA 48109 2122 ABSTRACT 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 arraybased 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 Keywords Quantum circuits quantum algorithms simulation density matrices



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