Decodable hybrid dynamics of open quantum systems with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> symmetry
Decodable hybrid dynamics of open quantum systems with
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
symmetry
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开放量子系统的可解码混合动力学 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck"
DOI：
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发表时间：
2021
影响因子：
3.7
通讯作者：
Matthew A. Fisher
中科院分区：
文献类型：
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作者：
Yaodong Li;Matthew A. Fisher
我们探索了一类具有局部退相干（“噪声”）和局部投影测量的“开放”量子电路模型，每个模型都尊重全局Z_2对称性。该模型支持一个Z_2对称性自发破缺的自旋玻璃相（在平衡一维系统中不可能），一个以发散磁化率为特征的顺磁相，以及一个中间“平凡”相。这三个相对于z_2对称的局部酉门都是稳定的，并且相之间的动态相变属于渗透普适性类。开路动力学可以通过明确引入具有自身“乱置”动力学的槽来净化，如[Bao， Choi, Altman, arXiv:2102.09164]，这不会改变任何宇宙物理。在自旋玻璃相中，电路动力学可以被解释为量子重复编码，编码的每个稳定器以有限速率随机测量，退相干作为有效的位翻转误差。受自旋玻璃相几何形状的启发，我们设计了一种新的解码算法，用于在编码空间中恢复任意初始量子比特状态，假设测量结果的历史知识，以及在最终状态上执行局部泡利测量和门的能力。对于L^d量子位运行时间为T的电路，执行解码器所需的时间为O(L^d T)（维数为d）。有了这个解码器，我们发现初始编码量子位状态的信息可以在一维电路的L中保留（然后恢复）对数时间，并且在有限误差阈值以下的2d中至少在L中保持线性时间。对于重复码和环形码，我们将我们的解码算法与早先将错误模型映射到随机键伊辛模型的算法进行了比较和对比。
We explore a class of"open"quantum circuit models with local decoherence ("noise") and local projective measurements, each respecting a global Z_2 symmetry. The model supports a spin glass phase where the Z_2 symmetry is spontaneously broken (not possible in an equilibrium 1d system), a paramagnetic phase characterized by a divergent susceptibility, and an intermediate"trivial"phase. All three phases are also stable to Z_2-symmetric local unitary gates, and the dynamical phase transitions between the phases are in the percolation universality class. The open circuit dynamics can be purified by explicitly introducing a bath with its own"scrambling"dynamics, as in [Bao, Choi, Altman, arXiv:2102.09164], which does not change any of the universal physics. Within the spin glass phase the circuit dynamics can be interpreted as a quantum repetition code, with each stabilizer of the code measured stochastically at a finite rate, and the decoherences as effective bit-flip errors. Motivated by the geometry of the spin glass phase, we devise a novel decoding algorithm for recovering an arbitrary initial qubit state in the code space, assuming knowledge of the history of the measurement outcomes, and the ability of performing local Pauli measurements and gates on the final state. For a circuit with L^d qubits running for time T, the time needed to execute the decoder scales as O(L^d T) (with dimensionality d). With this decoder in hand, we find that the information of the initial encoded qubit state can be retained (and then recovered) for a time logarithmic in L for a 1d circuit, and for a time at least linear in L in 2d below a finite error threshold. For both the repetition and toric codes, we compare and contrast our decoding algorithm with earlier algorithms that map the error model to the random bond Ising model.
影响因子：
19.6
作者：
Lavasani, Ali;Alavirad, Yahya;Barkeshli, Maissam
通讯作者：
Barkeshli, Maissam
动态量子存储器如何遗忘
影响因子：
6.4
作者：
Fidkowski, Lukasz;Haah, Jeongwan;Hastings, Matthew B.
通讯作者：
Hastings, Matthew B.