New Class of Quantum Error-Correcting Codes for a Bosonic Mode
New Class of Quantum Error-Correcting Codes for a Bosonic Mode
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DOI：
10.1103/physrevx.6.031006
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发表时间：
2016-07-14
影响因子：
12.5
通讯作者：
Girvin, S. M.
中科院分区：
文献类型：
--
作者：
Michael, Marios H.;Silveri, Matti;Girvin, S. M.
我们构造了一类新的玻色子模式的量子纠错码，这类码在量子存储、通信和可扩展计算中有着重要的应用。这些“二项式量子码”是由用二项式系数加权的Fock态的有限叠加形成的。二项式码可以精确地纠正玻色子产生和湮灭算子中特定次数的多项式误差，包括振幅阻尼和位移噪声以及玻色子添加和退相误差。对于现实的连续时间耗散演化，代码可以在错误检测测量之间的时间步长中执行任意给定阶的近似量子错误校正。我们提出了一个显式的近似量子错误恢复操作的基础上投影测量和幺正操作。通过测量广义数奇偶校验，设计了用于检测玻色子损失和增益误差的二项式码。我们讨论了优化的二项式码，并表明，通过放松奇偶校验结构，甚至可以实现更低的不可恢复的错误率的代码。二项式码与现有的双模式玻色子码相关，但是提供了仅需要单个玻色子模式来校正振幅阻尼以及校正其他误差的能力的优点。我们的代码在精神上类似于“猫码”的基础上叠加的相干态，但提供了几个优点，如较小的平均玻色子数，准确而不是近似的正交规范的码字，和明确的幺正操作的能量重新泵到玻色子模式。二项式量子码可以用当前的超导电路技术实现，并且它们应该在其他量子技术中证明是有用的，包括玻色子量子存储器，光子量子通信和光学到微波的上转换和下转换。
We construct a new class of quantum error-correcting codes for a bosonic mode, which are advantageous for applications in quantum memories, communication, and scalable computation. These "binomial quantum codes" are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the time step between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes, but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to "cat codes" based on superpositions of the coherent states but offer several advantages such as smaller mean boson number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology, and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up-and down-conversion.