论文标题
在验证量量子代码中的数量和相移弹性方面的权衡
Trade-offs on number and phase shift resilience in bosonic quantum codes
论文作者
论文摘要
量子代码通常依靠大量的自由度来达到较低的错误率。但是，每个额外的自由度都会引入一套新的错误机制。因此，最大程度地减少了量子代码使用的自由度是有帮助的。一种量子误差校正解决方案是将量子信息编码为一个或多个骨气模式。我们重新审视旋转不变的骨气代码，这些代码在fock的州受支持，这些州与整数$ g $相距，而差距$ g $赋予了这些代码的弹性。直观地，由于相位运算符和数字换档运算符不会通勤，因此人们期望在弹性到数字和旋转错误之间进行权衡。在这里，我们获得了与高斯dephasing错误校正$ g $键入的单模单模式代码的近似量子误差的不存在的结果。我们表明，通过使用任意多种模式，$ g $启用的多模式代码可以为任何有限的高斯dephasing和振幅阻尼误差提供良好的近似量子误差校正代码。
Quantum codes typically rely on large numbers of degrees of freedom to achieve low error rates. However each additional degree of freedom introduces a new set of error mechanisms. Hence minimizing the degrees of freedom that a quantum code utilizes is helpful. One quantum error correction solution is to encode quantum information into one or more bosonic modes. We revisit rotation-invariant bosonic codes, which are supported on Fock states that are gapped by an integer $g$ apart, and the gap $g$ imparts number shift resilience to these codes. Intuitively, since phase operators and number shift operators do not commute, one expects a trade-off between resilience to number-shift and rotation errors. Here, we obtain results pertaining to the non-existence of approximate quantum error correcting $g$-gapped single-mode bosonic codes with respect to Gaussian dephasing errors. We show that by using arbitrarily many modes, $g$-gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of Gaussian dephasing and amplitude damping errors.
