dorsal/arxiv
View SchemaA Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations
| Authors | Y. C. Cheng, R. J. Silbey |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312053 |
| URL | https://arxiv.org/abs/quant-ph/0312053 |
| DOI | 10.1103/PhysRevA.69.052325 |
| Journal | Phys. Rev. A 69, 052325 (2004) |
Abstract
We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and delta function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct inter-qubit coupling and fluctuations on the control fields are also studied. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.
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"abstract": "We propose a model based on a generalized effective Hamiltonian for studying\nthe effect of noise in quantum computations. The system-environment\ninteractions are taken into account by including stochastic fluctuating terms\nin the system Hamiltonian. Treating these fluctuations as Gaussian Markov\nprocesses with zero mean and delta function correlation times, we derive an\nexact equation of motion describing the dissipative dynamics for a system of n\nqubits. We then apply this model to study the effect of noise on the quantum\nteleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum\nCNOT gate, we study the effect of noise on a set of one- and two-qubit quantum\ngates, and show that the results can be assembled together to investigate the\nquality of a quantum CNOT gate operation. We compute the averaged gate fidelity\nand gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and\nflip-flop errors during the CNOT gate operation. The effects of direct\ninter-qubit coupling and fluctuations on the control fields are also studied.\nWe discuss the limitations and possible extensions of this model. In sum, we\ndemonstrate a simple model that enables us to investigate the effect of noise\nin arbitrary quantum circuits under realistic device conditions.",
"arxiv_id": "quant-ph/0312053",
"authors": [
"Y. C. Cheng",
"R. J. Silbey"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.052325",
"journal_ref": "Phys. Rev. A 69, 052325 (2004)",
"title": "A Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations",
"url": "https://arxiv.org/abs/quant-ph/0312053"
},
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