dorsal/arxiv
View SchemaGraph-based simulation of quantum computation in the density matrix representation
| Authors | George F. Viamontes, Igor L. Markov, John P. Hayes |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403114 |
| URL | https://arxiv.org/abs/quant-ph/0403114 |
| DOI | 10.1117/12.542767 |
| Journal | Quantum Information & Computation, Vol. 5, No. 2, pp. 113-130 (2005). |
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 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.
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"abstract": "Quantum-mechanical phenomena are playing an increasing role in information\nprocessing, as transistor sizes approach the nanometer level, and quantum\ncircuits and data encoding methods appear in the securest forms of\ncommunication. Simulating such phenomena efficiently is exceedingly difficult\nbecause of the vast size of the quantum state space involved. A major\ncomplication is caused by errors (noise) due to unwanted interactions between\nthe quantum states and the environment. Consequently, simulating quantum\ncircuits and their associated errors using the density matrix representation is\npotentially significant in many applications, but is well beyond the\ncomputational abilities of most classical simulation techniques in both time\nand memory resources. The size of a density matrix grows exponentially with the\nnumber of qubits simulated, rendering array-based simulation techniques that\nexplicitly store the density matrix intractable. In this work, we propose a new\ntechnique aimed at efficiently simulating quantum circuits that are subject to\nerrors. In particular, we describe new graph-based algorithms implemented in\nthe simulator QuIDDPro/D. While previously reported graph-based simulators\noperate in terms of the state-vector representation, these new algorithms use\nthe density matrix representation. To gauge the improvements offered by\nQuIDDPro/D, we compare its simulation performance with an optimized array-based\nsimulator called QCSim. Empirical results, generated by both simulators on a\nset of quantum circuit benchmarks involving error correction, reversible logic,\ncommunication, and quantum search, show that the graph-based approach far\noutperforms the array-based approach.",
"arxiv_id": "quant-ph/0403114",
"authors": [
"George F. Viamontes",
"Igor L. Markov",
"John P. Hayes"
],
"categories": [
"quant-ph"
],
"doi": "10.1117/12.542767",
"journal_ref": "Quantum Information \u0026 Computation, Vol. 5, No. 2, pp. 113-130\n (2005).",
"title": "Graph-based simulation of quantum computation in the density matrix representation",
"url": "https://arxiv.org/abs/quant-ph/0403114"
},
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