arXiv quant-ph/06080852006-08quant-ph

态蒸馏的量子普适性

Quantum universality by state distillation

Ben W. Reichardt

备注：: 24 pages, 4 figures; improved presentation, new stability result
发表信息：: Quantum Inf. Comput. 9:1030-1052, 2009

摘要：

量子普适性可以使用经典控制的稳定器操作和重复制备某些辅助状态来实现。哪一个附属国足以实现普遍性？这个“幻态蒸馏”问题与量子容错密切相关。在辅助上容许的噪声的下限有助于给出用于容错计算的容许噪声率阈值的下限。上界显示基于Gottesman-Knill定理的阈值上界参数的限制。我们扩展的范围内的单量子比特混合状态，已知的普适性，通过使用一个简单的奇偶校验操作。对于证明阈值下限的应用程序，往往需要一定的实际稳定性特征，我们也展示了一个稳定的蒸馏过程。没有蒸馏上限已知超出Gottesman-Knill定理给出的。人们可能会问，蒸馏上限是否可以简化为单量子位辅助态的上限。对于多量子位纯态和先前考虑的双量子位辅助态，答案是肯定的。然而，我们展示了两个量子位的混合状态，不是稳定状态的混合物，但对于每个后选择的稳定剂减少从两个量子位到一个输出稳定剂状态的混合物。蒸馏这种状态需要真正的多量子比特状态蒸馏方法。

英文摘要：

Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give universality, by using a simple parity-checking operation. For applications to proving threshold lower bounds, certain practical stability characteristics are often required, and we also show a stable distillation procedure. No distillation upper bounds are known beyond those given by the Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce to upper bounds for single-qubit ancilla states. For multi-qubit pure states and previously considered two-qubit ancilla states, the answer is yes. However, we exhibit two-qubit mixed states that are not mixtures of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. Distilling such states would require true multi-qubit state distillation methods.

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