量子计算与经典信息：运算符负性揭示混沌系统 scrambling 现象

Open

Access

46 浏览量更新于2024-07-16 收藏 1.22MB PDF 举报

身份认证购VIP最低享 7 折!

30元优惠券

"这篇研究论文深入探讨了量子与经典信息之间的差异，特别是在运算符负性作为加扰探针的角色方面。作者通过分析自由费米子、致密玻色子、全息共形场理论（CFT）以及随机Unitary电路和可积与混沌自旋链的数值模拟，揭示了信息处理的复杂动态。文章指出，全息CFT的行为与非全息CFT有显著区别，显示出最大加扰的特征。同时，随机Unit电路表现出与全息通道类似的行为。文章中提到的“线张力图”和“可粒子图”是用于理解和捕捉不同系统中纠缠动力学的有效工具。线张力图在混沌系统中特别有用，而可粒子图则适用于可积系统。作者还提出了一个“线张力”概念，用于描述时空缩放极限内混沌系统中对数负性的动态。通过对负性和互信息的比较，研究者发现了量子信息和经典信息动力学的独特性质，这可能影响到经典计算机上对量子系统的仿真能力。在研究中，作者观察到的“虚假纠缠”现象为经典计算机模拟量子系统的能力带来了新的挑战。此外，他们使用测地维滕图来阐述共形场论中部分转置密度矩阵操作与Anti-de Sitter空间中纠缠楔形截面的关系，进一步深化了对量子纠缠的理解。这篇论文发表于JHEP01(2020)031，并由Springer为SISSA出版。研究工作始于2019年7月，经过修改和接受，最终于2020年1月发布。" 该研究的核心知识点包括： 1. 运算符负性：作为量子系统加扰程度的度量，它能揭示系统的信息处理能力。 2. 全息共形场理论（CFT）：其行为与非全息CFT显著不同，具有最大加扰的特性。 3. 随机Unitary电路：表现出与全息通道相似的行为，这在量子计算和信息处理中有重要应用。 4. 线张力图和可粒子图：是研究混沌系统和可积系统纠缠动力学的有效工具。 5. 虚假纠缠：对经典计算机模拟量子系统的可仿真性有潜在影响。 6. 测地维滕图：用于解释共形场论中的量子纠缠现象，关联了部分转置密度矩阵与Anti-de Sitter空间的结构。

资源详情

资源推荐

JHEP01(2020)031

5 10 15 20 25

20 40 60 80 100

-40

-30

-20

-10

20 40 60 80 100

-40

-30

-20

-10

5 10 15 20 25

20 40 60 80 100

-5

-4

-3

-2

-1

Figure 1. Numerical simulation of Cliﬀord circuits. (top left) BOMI for asymmetric overlap with

the left endpoints of the input and output intervals ﬂush. The input interval is of length 10 and

the output varies in length as 10 (blue), 15 (magenta), 20 (yellow), 25 (purple). The dotted gray

lines are the times that the line-tension picture predicts the kink to occur at. (top right) TOMI for

A of length 10 (magenta), 15 (yellow), 20 (purple). We average over 100 disorder realizations. The

inset shows a single disorder realization. The mutual information is in units of log 2. These plots

should be compared to the holographic results for the same conﬁgurations that are shown in the

bottom row. For the BOMI and TOMI, we use β = 2 and β = 4 respectively. The structure of the

Cliﬀord circuit is brick-layered with CNOT gates and Hadamard and phase gates applied randomly

on each site with probability 0.5 on every layer. The Hadamard and phase gates are essential for

integrability breaking as we observe recurrence times of order L when only using CNOT gates (see

ﬁgure 17).

be a phase transition at a critical time when the disconnected regime becomes dominant.

At this point, the operator mutual information is manifestly zero. We demonstrate how

the membrane predicts the kink in the BOMI in ﬁgure 2. The kink occurs because infor-

mation can only leak out of the left side of the interval initially, but after a time equal to

the distance between the two right endpoints, the information can leak out of both sides.

This causes the operator mutual information to decrease at twice the speed i.e. the slope

doubles. Precisely the same phenomenon was found for large c conformal ﬁeld theories in

ref. [33] where the same slope and causality arguments apply.

The holographic results have the same origin as in the random unitary circuit model,

only it is more complicated to analyze due to the increased complexity of hyperbolic space

over the simple “metric” deﬁned by the line-tension for random unitary circuits (2.2).

– 8 –

JHEP01(2020)031

Figure 2. The cartoon shows the time evolution of the minimal membrane for operator mutual

information (dotted lines) and operator logarithmic negativity (dashed lines) between input (blue)

and output (red) ﬁnite intervals. In the connected regime, the membrane connecting the left

ends of the intervals grows linearly, displaying the leaking of quantum information. The length

of the minimal cross-section decreases linearly, showing the same leaking. The length of the right

membrane remains constant for the ﬁrst three time steps as the slope remains above 1; after,

the length grows linearly. Similarly, the length of the minimal cross-section decreases at twice

the speed after the slope decreases below 1. This demonstrates causality in that the quantum

information cannot leak out the right side until the endpoints are time-like separated. At late

times, the membrane reaches the disconnected regime where the BOMI and BOLN are manifestly

trivial (bottom right).

Heuristically, this may be seen by viewing the time slices of the growth of the wormhole as

the MERA tensor network presented in ref. [70]. There, the MERA wormhole geometry is

equivalent to the geometry of a brick-layered random unitary circuit at scales larger than

β which is a UV cutoﬀ in the BOMI. Therefore, the agreement should come as no surprise.

We again stress that we have traded the time direction for the radial direction.

We can take this analogy between random unitary circuits and holographic CFTs

further by comparing the rates at which the information leaks. For holographic CFTs,

the BOMI decreases by

cπ

3β

each time step, while in random unitary circuits, the BOMI

decreases by log q. We can equate these and heuristically identify the local Hilbert space

dimension in holographic CFTs

q ∼ e

cπ

3β

, (2.3)

which precisely corresponds to the entropy density in the Cardy regime [72]

Cardy

cπ

3β

. (2.4)

2.2 Line-tension for logarithmic negativity

Drawing motivation from the discussion above and ref. [9] as reviewed in section 1.2 and

appendix A, we consider a membrane picture for the logarithmic negativity in random

One may also seek a connection to computational complexity. In the random unitary circuit, the

complexity may be well deﬁned; it grows linearly with time and is proportional to the volume of the circuit,

consistent with the “Complexity = Volume” conjecture where this picture was originally discussed [71].

– 9 –

剩余47页未读，继续阅读

weixin_38704857

粉丝: 10
资源: 895

量子计算与经典信息：运算符负性揭示混沌系统 scrambling 现象

量子计算和量子信息.zip

量子通信经典教材：Protecting Information~ From Classical Error Correction to Quantum Cryptography - Susan Loepp (2006)

{'量子信息': 255, '量子科技': 256, '金融安全': 257, '长城': 258}是列表吗

解释下列术语。 信息的熵： 固件： 解释： 透明性： 颗粒度： 空间局部性： 存储体系： 超标量流水线： RISC： 量子纠缠效应： 量子比特： 量子计算机： 向量处理机： 数值并行算法： 并行处理： 机群： 网格计算： 进程：

如何将'量子信息': 255, '量子科技': 256, '金融安全': 257, '长城': 258}写入CSV文件中

量子计算与量子信息赵千川pdf

量子通信的应用实例有哪些

量子计算与量子信息原理 pdf

智算研究的重点是什么

未来6G量子通信的认识

学量子计算机，需要具体学习哪些课程

遗传算法结合量子交叉

基于量子通信技术的网络安全加密算法案例

量子计算与量子信息(英文).pdf

深度学习怎么应用到量子精密测量、量子物态、量子计算、量子工程应用上

pyqpanda绘制量子线路图

怎么制作一台量子计算机

量子通信中离散变量的量子互信息

请给我简要解释量子通信的原理和应用

最新资源

解释下列术语。信息的熵：固件：解释：透明性：颗粒度：空间局部性：存储体系：超标量流水线： RISC：量子纠缠效应：量子比特：量子计算机：向量处理机：数值并行算法：并行处理：机群：网格计算：进程：