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arXiv quant-ph/0005015quant-phcond-mat
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量子计算机内核中量子混沌的出现及其管理

Emergence of Quantum Chaos in Quantum Computer Core and How to Manage It

B. Georgeot, D. L. Shepelyansky

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revtex, 10 pages, 18 figures
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摘要：

我们研究了标准的通用量子计算机模型，该模型描述了一个现实的孤立的量子计算机，其中单个量子比特能量的波动和剩余的短程量子比特间耦合。结果表明，在涨落和耦合小于单量子比特能量间隔的极限下，谱具有能带结构，并得到了描述能带内本征态性质的重整化哈密顿量.研究集中在计算机的中心带（“核心”），具有最高的态密度。我们发现，超过一个临界的量子比特间的耦合强度，量子混沌集，导致量子遍历的计算机本征态。在这种情况下，理想的量子比特结构消失了，本征态变得复杂，计算机的可操作性很快就被破坏了。我们证实了量子混沌边界仅随量子比特数n线性减小，尽管多量子比特态之间的间隔随n呈指数下降。量子计算机中时间演化的研究表明，在量子混沌状态下，一个理想的（非相互作用）状态很快消失，并在一个短的混沌时间尺度后，许多状态呈指数级混合，确定了对系统参数的依赖性。在量子混沌边界之下，理想状态可以存活很长时间并用于计算。结果表明，一个广泛的参数区域确实存在的量子计算机的有效操作是可能的。

英文摘要：

We study the standard generic quantum computer model, which describes a realistic isolated quantum computer with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. It is shown that in the limit where the fluctuations and couplings are small compared to one-qubit energy spacing the spectrum has a band structure and a renormalized Hamiltonian is obtained which describes the eigenstate properties inside one band. The studies are concentrated on the central band of the computer (``core'') with the highest density of states. We show that above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In this regime the ideal qubit structure disappears, the eigenstates become complex and the operability of the computer is quickly destroyed. We confirm that the quantum chaos border decreases only linearly with the number of qubits n, although the spacing between multi-qubit states drops exponentially with n. The investigation of time-evolution in the quantum computer shows that in the quantum chaos regime, an ideal (noninteracting) state quickly disappears and exponentially many states become mixed after a short chaotic time scale for which the dependence on system parameters is determined. Below the quantum chaos border an ideal state can survive for long times and be used for computation. The results show that a broad parameter region does exist where the efficient operation of a quantum computer is possible.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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