这里量子效应变得相关,为了将切换时间内的错误降至最低,由于海森堡不确定性原理 Delta E Delta t >= ℏ\Delta E \Delta t \geq \hbar (如果能量小于 ℏ//Delta t\hbar / \Delta t ,量子涨落将大于输入信号),切换所需的能量必须更高。在核物质的情况下,所需的切换能量必须大于 3.75*10^(-20)J3.75 \cdot 10^{-20} \mathrm{~J} 每操作一次。请注意,这种能量不必耗散,只需防止量子噪声干扰计算即可。
量子力学对系统状态变化的速度也有限制。可以证明,具有平均能量 EE 高于基态的系统,决定了系统每单位时间内可以经过的最大正交状态数 2E//h2 E / h [53]。即使在完全无噪声的情况下,这种能量也是必要的。
一个类似的开关时间限制可以基于贝肯斯坦界限:如果一个开关将 n 个输入位转换为 n 个输出位,那么这个开关必须大于
R >= [(nℏc ln 2)/(2pi)](1)/(E)R \geq\left[\frac{n \hbar c \ln 2}{2 \pi}\right] \frac{1}{E}
E 是开关内的能量,仅为了包含信息。由于信息只能以光速传输,因此结果比特移动到下一个开关的距离 R 所需的时间(这是忽略开关时间后的循环时间的下限)是
t >= [(nℏln 2)/(2pi)](1)/(E)t \geq\left[\frac{n \hbar \ln 2}{2 \pi}\right] \frac{1}{E}
where Delta E\Delta E is the amount of energy expended, k_(B)k_{B} is the Boltzmann constant, TT is the absolute temperature. At room temperature this cost is 2.9*10^(-21)J2.9 \cdot 10^{-21} \mathrm{~J}, while at 3 K (the cosmic background temperature) it has decreased to 2.87*10^(-23)2.87 \cdot 10^{-23} J. Obviously, to be able to process information cheaply the system should be very cold, but that may require extensive cooling. Thus there will be extensive demands for energy in large information processing systems. Very dense and fast systems will dissipate huge amounts of energy; assuming a molecular computing system with 10^(12)bits//cm^(3)10^{12} \mathrm{bits} / \mathrm{cm}^{3} and a switching speed of 10^(15)Hz10^{15} \mathrm{~Hz} would lead to an energy dissipation of 2.8*10^(6)W//cm^(3)2.8 \cdot 10^{6} \mathrm{~W} / \mathrm{cm}^{3}, which would obviously vaporise the material. 能量消耗量为 Delta E\Delta E ,玻尔兹曼常数为 k_(B)k_{B} ,绝对温度为 TT 。在室温下,这种成本为 2.9*10^(-21)J2.9 \cdot 10^{-21} \mathrm{~J} ,而在 3 K(宇宙背景温度)时,它已降至 2.87*10^(-23)2.87 \cdot 10^{-23} 焦耳。显然,为了以低成本处理信息,系统应该非常冷,但这可能需要大量的冷却。因此,在大规模信息处理系统中将会有大量的能源需求。非常密集和快速的系统将消耗巨大的能量;假设一个具有 10^(12)bits//cm^(3)10^{12} \mathrm{bits} / \mathrm{cm}^{3} 和切换速度为 10^(15)Hz10^{15} \mathrm{~Hz} 的分子计算系统会导致 2.8*10^(6)W//cm^(3)2.8 \cdot 10^{6} \mathrm{~W} / \mathrm{cm}^{3} 的能量耗散,这显然会蒸发材料。
6.1 可逆计算
It may be possible to do computations without having to expend energy at all if no bits are erased, so called reversible computation. In a logically reversible process the input and output can be logically retrieved from each other. A physically reversible process is not just logically reversible, but it can be run 可能在不删除任何比特的情况下进行计算,从而无需消耗能量,这就是所谓的可逆计算。在逻辑上可逆的过程中,输入和输出可以从彼此中逻辑地检索出来。一个物理上可逆的过程不仅仅是逻辑上可逆的,它还可以运行
Logically reversible computers could be built from reversible circuits [32] or the reversible Turing machine [6]. Physical reversibility can be achieved using reversible logical circuits [54], mechanical logic [55] or by using quantum computation which by its nature is reversible (see section 8.1). 逻辑可逆计算机可以由可逆电路[32]或可逆图灵机[6]构建。物理可逆性可以通过使用可逆逻辑电路[54]、机械逻辑[55]或使用量子计算来实现,量子计算的本质是可逆的(参见第 8.1 节)。
It has been shown that any irreversible computation can be turned into a reversible computation with a slight increase in memory and time complexity [7]: if the time needed is TT and the memory demand SS, then the output can be calculated reversibly in time linear in TT and space of the order O(ST^(a))O\left(S T^{a}\right), where aa can be made arbitrarily small. It is also possible to communicate reversibly [35] between two reversible minds. 已被证明,任何不可逆计算都可以通过略微增加内存和时间复杂度转变为可逆计算[7]:如果所需时间是 TT ,内存需求是 SS ,那么输出可以在时间线性于 TT 和空间阶数为 O(ST^(a))O\left(S T^{a}\right) 的情况下可逆计算,其中 aa 可以任意小。在两个可逆心智之间进行可逆通信也是可能的[35]。
Unfortunately there are limits to the usefulness of reversible computation. Error correction is by necessity irreversible (several erroneous states are mapped to a single correct state), and hence needs irreversible operations. There is a tradeoff between dissipation and decreasing the risk of undetected bit errors; by using error-correcting codes the number of bits in the system is increased (and hence the net number of bit errors) but more can be corrected. 不幸的是,可逆计算的实用性存在限制。纠错本质上是不可逆的(多个错误状态映射到单个正确状态),因此需要不可逆操作。在耗散和降低未检测到比特错误的风险之间存在着权衡;通过使用纠错码,系统中的比特数增加(因此净比特错误数增加),但可以纠正的比特数更多。
Another way to decrease the problem of bit errors is to make the potential wells of the registers deeper; this makes it less likely that thermal noise or outside interference (such as cosmic rays) will throw the register from one state to the other. If the register is similar to a harmonic oscillator, then the probability that thermal noise kicks it out of the current potential well of height EE is proportional to e^(-E//k_(B)T)e^{-E / k_{B} T}, and can be made arbitrarily small by increasing EE. Fortunately, the depth of the potential well does not matter for reversible computation, so during error-free operation no energy has to be dissipated even when EE is large, and correcting the error only requires k_(B)T ln 2k_{B} T \ln 2 Joules per bit. If there are nn bits in the system, then the total energy that has to be dissipated for error correction is proportional to 另一种减少比特错误的方法是使寄存器的势阱更深;这使得热噪声或外部干扰(如宇宙射线)将寄存器从一个状态抛到另一个状态的可能性降低。如果寄存器类似于一个谐波振荡器,那么热噪声将其踢出高度为 EE 的当前势阱的概率与 e^(-E//k_(B)T)e^{-E / k_{B} T} 成正比,可以通过增加 EE 使其任意小。幸运的是,势阱的深度对于可逆计算并不重要,因此在无错误操作期间,即使 EE 很大,也不需要耗散能量,纠正错误只需要 k_(B)T ln 2k_{B} T \ln 2 焦耳每比特。如果系统中存在 nn 比特,那么用于纠错的能量耗散总量与
E_("diss ")prop n ln 2k_(B)Te^(-E//k_(B)T)E_{\text {diss }} \propto n \ln 2 k_{B} T e^{-E / k_{B} T}
((dI//dt))/((dE//dt)) <= (1.05*10^(23))/(T)bit//sW\frac{(d I / d t)}{(d E / d t)} \leq \frac{1.05 \cdot 10^{23}}{T} \mathrm{bit} / \mathrm{sW}
如果我们将其代入斯蒂芬定律,我们得到
((dI//dt))/((dE//dt)) <= ((4pi sigma)/(k_(B)ln 2))T^(3)r^(2)\frac{(d I / d t)}{(d E / d t)} \leq\left(\frac{4 \pi \sigma}{k_{B} \ln 2}\right) T^{3} r^{2}
在人类的情况下,神经循环时间大约为 10^(-3)s10^{-3} \mathrm{~s} ,通信速度约为 100m//s100 \mathrm{~m} / \mathrm{s} ,长度尺度为 0.1 米,这给出了大约为 1 的 SS 值。对于标准微处理器, SS 大约为 10^(-2)-10^(-3)10^{-2}-10^{-3} ,这意味着微处理器目前不需要长时间等待来自芯片其他部分的信息(截至 1999 年,但问题显然正在增长)。[27]中的机械纳米计算机有 S=10^(-2)S=10^{-2} 。互联网的大小约为 10^(6)m10^{6} \mathrm{~m} ,通信速度接近光速,洲际延迟约为数百毫秒; SS 大约为 3,略高于人类大脑。
S 的主观效果取决于应用。对于数据检索和通信,它仅仅造成主观上的延迟,这种延迟可能或可能不被接受(发送电子邮件的延迟一分钟通常是可接受的;发送一帧视频的延迟一分钟是不可接受的)。对于非常快的心智,主观距离会增加;对于以光速利用纳秒时间尺度的实体,厘米距离是显著的,对于飞秒实体是微米,对于核实体是飞米。比这更大的结构将相对于其中的过程被认为是“大”。
对于信息形态,延迟限制了其组成部分的物理分布:如果它们相距太远,生物将不得不减慢其主观时间的速率以保持同步。即使处理速度无限快,光速也会限制信息形态的速度,如果它们希望以一定速率与外界环境互动;由于人类大脑在数百毫秒的时间尺度上作为一个整体运作,一个以“正常”速度运行的类似人类的形态最多能延伸 30,000 公里,然后延迟开始限制其速度。
How can humans react quickly when their brains as a whole are so slow? The answer lies in modularization: low-level systems do most of the basic processing quickly and often manage most of perception and behavior on their own; slower higher level systems consisting of many low-level systems step in to regulate lower levels when needed. The most interesting aspect of this is that the conscious mind consistently seems to misattribute behavior and perception to itself, even when they are done by lower levels and occur several hundred milliseconds before they become conscious [47, 46]. In the same way the conscious mind experiences itself as unitary, despite all internal delays or even removal of central interconnections as the corpus callossum. 人类如何快速反应,尽管他们的整体大脑如此缓慢?答案在于模块化:低级系统快速处理大部分基本任务,并且经常独立管理感知和行为;当需要时,由许多低级系统组成的较慢的高级系统介入以调节低级系统。最有趣的是,意识似乎始终将行为和感知归因于自己,即使它们是由低级系统完成的,并且发生在成为意识之前几百毫秒 [47, 46]。同样,尽管存在所有内部延迟或甚至移除中央连接(如胼胝体),意识仍然将自己体验为统一的。
This suggests that a mind may exist on a wide range of timescales. One may conjecture that similar hierarchical modularizations with even more levels are possible, which would enable much larger minds with longer internal delays without loosing their high-level unity. By necessity, the highest levels would be much slower than lower levels, but this would not significantly impair their performance since most of it would take place at the quicker lower levels, and the higher levels would experience it as if they were doing things in realtime despite their slowness. 这表明心智可能存在于广泛的时标上。人们可能会推测,具有更多层次的类似分层模块化是可能的,这将使心智更大,内部延迟更长,而不会失去其高级统一性。由于必要性,最高级别将比低级别慢得多,但这不会显著损害其性能,因为大部分活动将在较快的低级别进行,而高级别会将其体验为实时操作,尽管它们较慢。
Unfortunately, the amount of information that can be sent over an information channel is limited. According to the Nyquist theorem, the highest signal rate that can be carried over a channel with bandwidth WHzW \mathrm{~Hz} is C=2WC=2 W bits/second. By using multilevel signaling C=2Wlog_(2)MC=2 W \log _{2} M, where MM is the number of discrete signal levels, but the more levels in the signal, the more noise-sensitive it becomes. Furthermore, forcing a physical quantity into one of 2^(k)2^{k} possible ranges seems to be 2^(k)2^{k} as hard as forcing it into one of two ranges, rather than just kk times as hard [8]. In the following we will assume binary signals through the channel. 不幸的是,通过信息通道可以发送的信息量是有限的。根据奈奎斯特定理,带宽为 WHzW \mathrm{~Hz} 的通道可以携带的最高信号速率为 C=2WC=2 W 比特/秒。通过使用多电平信号 C=2Wlog_(2)MC=2 W \log _{2} M ,其中 MM 是离散信号电平的数量,但信号中的电平越多,它就越容易受到噪声的影响。此外,将一个物理量强制放入 2^(k)2^{k} 个可能范围之一似乎与将其放入两个范围之一一样困难,而不是仅仅 kk 倍困难[8]。在以下内容中,我们将假设通过通道传输二进制信号。
Using higher and higher frequencies of the electromagnetic spectrum extremely high signal rates can be sent in a directional manner, for example using lasers. Unfortunately there are some problems involved with extremely high frequencies due to pair production: in the presence of another particle or a field, the gammaray photon may split up into pairs of electrons and positrons. This occurs at a frequency of 使用更高频率的电磁频谱,可以以定向方式发送极高信号速率,例如使用激光。不幸的是,由于对产生,极高频率存在一些问题:在另一个粒子或场的存在下,伽马射线光子可能会分裂成电子和正电子对。这发生在频率为
nu=(2m_(e)c^(2))/(h)\nu=\frac{2 m_{e} c^{2}}{h}
at a bandwidth of 2nu~~4.9*10^(20)2 \nu \approx 4.9 \cdot 10^{20} bit/s. Although this does not necessarily imply a limit on the bandwidth, it implies a growing source of noise. And since the energies of individual quanta become higher, the number of quanta per Watt signal-strength decreases, leading to increasing noise (see below). 在 0#比特/秒的带宽下。尽管这并不一定意味着带宽的限制,但它暗示了一个噪声不断增长的原因。由于单个量子能量变得更高,每瓦信号强度的量子数量减少,导致噪声增加(见下文)。
Also, there is an upper limit to the rate of information that can be sent using electromagnetic radiation for a given average energy [17, 42]: 此外,对于给定的平均能量[17, 42],使用电磁辐射发送信息的速率有一个上限:
where A_(t)A_{t} and A_(r)A_{r} are the areas of the the transmitter and receiver respectively, dd their distance and EE the power of the transmitter. For a transmitter and receiver one square meter each one meter apart and with a 1J//s1 \mathrm{~J} / \mathrm{s} energy budget the information rate is 1.61*10^(21)1.61 \cdot 10^{21} bits per second. The rate scales as E^(3//4)E^{3 / 4}. The optimal spectrum turns out to correspond to blackbody radiation, but if the receiver can only detect the energy and timing of arriving photons the spectrum instead corresponds to the spectrum of black bodies in a one-dimensional world and the information rate becomes A_(t)A_{t} 和 A_(r)A_{r} 分别是发射机和接收机的区域, dd 是它们之间的距离, EE 是发射机的功率。对于每个面积为一平方米、相距一米的发射机和接收机,以及 1J//s1 \mathrm{~J} / \mathrm{s} 能量预算,信息速率为 1.61*10^(21)1.61 \cdot 10^{21} 每秒比特。速率按 E^(3//4)E^{3 / 4} 规模。最佳频谱最终对应于黑体辐射,但如果接收机只能检测到达光子的能量和时序,则频谱对应于一维世界中的黑体频谱,信息速率变为
which is independent of transmitter and receiver area and distance. For an 1 J//s\mathrm{J} / \mathrm{s} energy budget the maximum information rate becomes 2.03*10^(17)2.03 \cdot 10^{17}. 该值与发射机和接收机区域和距离无关。对于 1 J//s\mathrm{J} / \mathrm{s} 能量预算,最大信息速率变为 2.03*10^(17)2.03 \cdot 10^{17} 。
One obvious way to circumvent this problem is to send information encoded in small pieces of matter at high speed. The energy requirements are much larger when lightspeed is approached, so the energy efficiency 一种明显的绕过这个问题的方法是以高速发送编码在微小物质碎片中的信息。当接近光速时,所需的能量要大得多,因此能量效率
eta=(C)/(P)=(km)/((gamma-1)mc^(2))=(k)/(c^(2))(sqrt(1-v^(2)//c^(2)))/(1-sqrt(1-v^(2)//c^(2)))\eta=\frac{C}{P}=\frac{k m}{(\gamma-1) m c^{2}}=\frac{k}{c^{2}} \frac{\sqrt{1-v^{2} / c^{2}}}{1-\sqrt{1-v^{2} / c^{2}}}
(where PP is the energy used to accelerate the matter, kk is the number of bits per kilogram and vv is the final speed) decreases towards zero. On the other hand, the efficiency for very low speeds is high, but is balanced by the longer delays. (其中 PP 是加速物质所需的能量, kk 是每千克的比特数, vv 是最终速度)趋向于零。另一方面,非常低速度的效率很高,但被更长的延迟所平衡。
As always, Bekenstein’s bound introduces a constraint on information flow. The message channel can be viewed as a chain of regions of size RR containing energy EE, in which information flows from one to the next in time R//cR / c (assuming light-speed transmission). This gives a bandwidth limitation of 如常,贝肯斯坦界限为信息流引入了约束。消息通道可以被视为一系列大小为 RR 的区域,其中包含能量 EE ,信息在时间 R//cR / c (假设光速传输)中从一个区域流向下一个区域。这给出了带宽限制为
C <= ((2pi c)/(ℏln 2))(RE)/((R//c))=((2pi)/(ℏln 2))EC \leq\left(\frac{2 \pi c}{\hbar \ln 2}\right) \frac{R E}{(R / c)}=\left(\frac{2 \pi}{\hbar \ln 2}\right) E
or around 9*10^(34)9 \cdot 10^{34} bit/(s J). 或约等于 9*10^(34)9 \cdot 10^{34} 位/(秒 J)。
Regardless of the amount of energy used in transmitting information, an additional limit is the Planck bandwidth 无论在传输信息时使用多少能量,还有一个额外的限制是普朗克带宽
W=2sqrt(c^(5)//hG)=2*10^(43)bit//sW=2 \sqrt{c^{5} / h G}=2 \cdot 10^{43} \mathrm{bit} / \mathrm{s}
At this bandwidth, quantum gravity becomes important and the wavelength of individual quanta becomes less than their Schwartzchild-radius. 在这个频宽下,量子引力变得重要,单个量子波长小于其史瓦西半径。
It should be noted that the above limits apply to single channels; by using several noninteracting channels the information transmission can be increased further. 应注意,上述限制适用于单个通道;通过使用多个非交互通道,可以进一步提高信息传输。
7.3 Noise 7.3 噪音
In reality, the channel capacity is somewhat lower due to noise. Shannon demonstrated that the maximal channel capacity (also called the error-free capacity) in the presence of noise is 实际上,由于噪声,信道容量略低。香农证明了在有噪声存在的情况下,最大信道容量(也称为无误差容量)是
where SS is the signal power and NN the noise power. Shannon also proved that if the information rate is lower than the error-free capacity, then it is possible to use a suitable coding to completely avoid errors. If energy dissipation is no problem, then noise can be ignored. Otherwise, the bandwidth will at least grow as the logarithm of the power used. SS 是信号功率, NN 是噪声功率。香农还证明了,如果信息速率低于无误差容量,则可以使用合适的编码完全避免错误。如果能量耗散没有问题,则可以忽略噪声。否则,带宽至少会随着所用功率的对数增长。
Noise leads to the problem that energy has to be expended in sending the information. In a noiseless channel information can be sent without dissipation [43], but the minimum energy per unit of information required to transmit information over a channel with effective noise temperature TT satisfies the inequality 噪声导致的问题是需要消耗能量来发送信息。在无噪声信道中,信息可以无损耗地发送[43],但要在具有有效噪声温度 TT 的信道上传输信息,每单位信息所需的最小能量满足不等式
(E)/(I) >= kT\frac{E}{I} \geq k T
as shown by [45]. The dissipation will be E(T)JE(T) \mathrm{J}, where E(T)E(T) is the minimum possible energy for the system with a given entropy; not all energy used in the information channel will be lost. 如[45]所示,耗散将为 E(T)JE(T) \mathrm{J} ,其中 E(T)E(T) 是给定熵的系统可能的最小能量;信息通道中使用的所有能量不会全部损失。
For extremely dense and high-bandwith systems energy dissipation from communication will likely play an important role, a role that cannot easily be circumvented with reversible computing. The exact amount of communications used is however very architecture dependent, ranging from nearly none in passive repositories of information to R^(6)R^{6} in 3D-structures where every node communicates with every other node. 对于极其密集和高带宽的系统,通信中的能量损耗可能会发挥重要作用,这种作用无法通过可逆计算轻易规避。然而,所使用的通信的确切数量却非常依赖于架构,从信息被动存储库中的几乎为零到在 3D 结构中每个节点都与每个其他节点通信的 R^(6)R^{6} 不等。
8 Exotica 8 异域风情
Any sufficiently advanced technology is indistinguishable from magic. - Arthur C Clarke 任何足够先进的技术都与魔法无法区分。 - 亚瑟·C·克拉克
So far we have looked mainly at what may be possible according to classical physics. If we turn towards purely quantum phenomena or more speculative areas, new possibilities emerge for information processing systems. 到目前为止,我们主要关注了根据经典物理学可能发生的情况。如果我们转向纯粹量子现象或更具有推测性的领域,信息处理系统将出现新的可能性。
8.1 Quantum computers 8.1 量子计算机
We have mainly assumed that information processing is done using classical Turing machines. If quantum computation is taken into account, the potential power grows significantly. 我们主要假设信息处理是通过经典图灵机完成的。如果考虑量子计算,潜在的能力将显著增长。
Formally, programs are executed on quantum computers by the unitary evolution of an input that is given by a state of the system. This form of computation uses the counterintuitive properties of quantum mechanics, like placing bits in superpositions of 0 and 1 , using quantum uncertainty to generate random numbers and creating states that exhibit purely quantum-mechanical correlations [31]. A famous result by [69] showed how factoring can be achieved in polynomial time on a quantum computer, database searches can be done in O(sqrtn)O(\sqrt{n}) time [33] and many-body quantum mechanical simulations can be run with an exponential increase in speed [11]. 形式上,程序通过输入状态的单位演化在量子计算机上执行。这种计算方式利用了量子力学的反直觉特性,如将比特放置在 0 和 1 的叠加态中,使用量子不确定性生成随机数,以及创建表现出纯粹量子力学相关性的状态[31]。[69]的一个著名结果展示了如何在量子计算机上以多项式时间完成因式分解,数据库搜索可以在 O(sqrtn)O(\sqrt{n}) 时间内完成[33],以及许多体量子力学模拟可以以指数速度增加[11]。
It is important to realize that quantum computers are qualitatively more powerful than classical computers, not just quantitatively better. They are at least equivalent to probabilistic Turing machines, and possibly more powerful [71], although they cannot solve general NP-complete problems [8]. It is known that there exist universal quantum computers that can emulate all other quantum computers just as universal Turing machines can emulate all other Turing machines [24]. 量子计算机在本质上比经典计算机更强大,而不仅仅是数量上的优势。它们至少与概率图灵机相当,甚至可能更强大[71],尽管它们不能解决一般的 NP 完全问题[8]。已知存在可以模拟所有其他量子计算机的通用量子计算机,就像通用图灵机可以模拟所有其他图灵机一样[24]。
Quantum computation is reversible except for the irreversible observation step when the state of the computer is measured macroscopically. This is due to the fact that the quantum computer operators are all unitary (and hence logically reversible). At first this suggests that quantum computers will be unusable in reality, since they would lack error correction, but this is surprisingly not true. By splitting the signal across several channels with partial error correction and then merging them, error-correction can be achieved [70]. It is also possible to make the system fault tolerant so that errors during error correction can be avoided [25]. A theorem similar to the Shannon theorem holds for quantum channels [49], although quantum information introduces some new complexities [3]. 量子计算是可逆的,除了在计算机状态被宏观测量时的不可逆观察步骤。这是因为量子计算机算符都是幺正的(因此逻辑上是可逆的)。起初这表明量子计算机在现实中将无法使用,因为它们将缺乏纠错能力,但出人意料的是这并不正确。通过将信号分割到几个通道中,进行部分纠错,然后合并它们,可以实现纠错[70]。还可以使系统容错,从而避免纠错过程中的错误[25]。对于量子信道,存在一个类似于香农定理的定理[49],尽管量子信息引入了一些新的复杂性[3]。
Quantum computation also relates to the field of quantum cryptography, the use of quantum mechanical effects to transmit information in a way that cannot be eavesdropped, even against an adversary with unlimited computing power. The basic idea is to exploit the existence of pairs of conjugate properties, where one cannot be measured without disturbing the other; the eavesdropper cannot avoid disturbing the communication. Quantum-secured communication has already been demonstrated [18,14][18,14] and will likely be an important part in secure communication in a world with extremely powerful computation. It might be possible that quantum devices and quantum computers could eavesdrop this kind of channel, but it is highly uncertain. While quantum key-distribution is secure, “post-cold-war” applications such as two-party secure computation (where both parts want to know the answer but not reveal their data) have been shown to be breakable [19]. 量子计算也与量子密码学领域相关,即利用量子力学效应以无法被窃听的方式传输信息,即使是对抗拥有无限计算能力的对手。基本思想是利用共轭属性对的存在,其中一个属性无法被测量而不干扰另一个;窃听者无法避免干扰通信。量子安全通信已经被证明 [18,14][18,14] ,并可能在计算极其强大的世界中成为安全通信的重要组成部分。可能存在量子设备和量子计算机可以窃听此类通道的情况,但这是高度不确定的。虽然量子密钥分发是安全的,“冷战”后的应用,如双方安全计算(其中双方都想知道答案但不想透露他们的数据)已被证明是可破解的[19]。
Quantum computers are the natural choice of computing systems on the nanoscale (and even moreso on the femtoscale). A physical implementation requires coherent, controlled evolution of the wavefunction at least until the computa- 量子计算机是纳米尺度(甚至在飞米尺度上更是如此)上计算系统的自然选择。物理实现需要至少在计算过程中波函数的连贯、受控演化。
tion is completed. Various possibilities for implementing quantum gates have been proposed, such as influencing the excitation states of atoms using external electromagnetic fields or laser pulses, interacting quantum dots [44, 31] or heteropolymers [50]. Prototypes of quantum gates based on nuclear magnetic resonance in bulk liquids have actually been made to work [20], with up to seven qbits [40]. 量子门实现的各种可能性已被提出,例如使用外部电磁场或激光脉冲影响原子的激发态,相互作用量子点[44, 31]或异聚物[50]。基于大量液体中核磁共振的量子门原型实际上已经实现,最多可达七个量子位[40]。
It is hard to tell what importance quantum computation will have in very large computational systems except for the obvious speed, density, security and complexity power advantages. For example, is there a difference in power between minds using quantum information and minds using classical information? The exponential speedups and possibility of simulating physical systems efficiently appears to be a great advantage, but are they generally useful for advanced information processing? 很难说量子计算在非常大的计算系统中将具有何种重要性,除了明显的速度、密度、安全性和复杂性优势。例如,使用量子信息和使用经典信息的大脑之间有能量差异吗?指数级加速和高效模拟物理系统的可能性似乎是一个巨大的优势,但它们对高级信息处理通常有用吗?
8.2 Black Holes 8.2 黑洞
If black holes do not destroy information (this is currently controversial), then information trapped inside will be released through Hawking radiation, and if they evaporate unitarily they can in principle be used as processing elements as suggested in [51]. 如果黑洞不会毁灭信息(这目前存在争议),那么被困在其中的信息将通过霍金辐射释放出来,如果它们以单元形式蒸发,原则上可以像[51]中建议的那样用作处理元素。
一个压缩到史瓦西半径的计算机系统将具有信息含量为
I=(4pi Gm^(2))/(ℏc ln 2)I=\frac{4 \pi G m^{2}}{\hbar c \ln 2}
考虑到第 4 节中量子力学对状态切换的限制,翻转一个比特所需的时间
t_(flip)=2piℏI//E=4pi^(2)R//c ln 2t_{f l i p}=2 \pi \hbar I / E=4 \pi^{2} R / c \ln 2
这等于从洞的一边传到另一边所需的时间。
该孔的总使用寿命将是
t_("life ")=(G^(2)M^(3))/(3Cℏc^(4))t_{\text {life }}=\frac{G^{2} M^{3}}{3 C \hbar c^{4}}
CC 是一个常数,取决于空穴中质量小于 k_(B)Tk_{B} T 的粒子种类数量。对于 O(10^(1)-10^(2))O\left(10^{1}-10^{2}\right) 种类, CC 大约是 10^(-3)-10^{-3}-10^(-2)10^{-2} 的数量级。对于一个一公斤的黑洞,其寿命大约为 10^(-19)s10^{-19} \mathrm{~s} ,在这段时间内可以在 10^(16)10^{16} 位上执行 10^(31)10^{31} 操作。在一秒钟内,这将产生 10^(50)10^{50} 操作,这是质量为一公斤的物质量子力学最大信息处理速率。
在 Tipler 场景中,信息存储在越来越有能量的粒子中,以防止其在热噪声中丢失。这意味着如果粒子状态的密度太低,信息不能无限增长,如果太高,剪切能将被高能量粒子的自发产生所阻尼。这意味着当 N 为粒子状态的数量时, dN//dEd N / d E 发散,但渐近地被 E^(2)E^{2} 所界定。这是该场景的一个可测试的预测。
节点之间的连接被假定为“小世界”网络结构[75],这允许稀疏的连接,其中任意两个选定的节点将通过一系列短的中介链接连接。每个处理节点(其中共有 NN 个)将与其他节点有多个链接 k≫log(N)k \gg \log (N) ,大多数连接到相邻节点,但少数( p~~0.01p \approx 0.01 )连接到远程节点。总链接数为 kN//2k N / 2 ,但只有 pkN//2p k N / 2 是长距离的,并占据显著的空间。假设通信链接具有恒定的横截面积 aa 和长度 prop r\propto r 以及节点数 propr^(3)\propto r^{3} ,系统中通信的总体积为 V_(comm)prop pkr^(4)V_{c o m m} \propto p k r^{4} 。这意味着即使对于非常低的 kk ,系统也将由通信链接的体积主导。
总 S 将按节点顺序为 4*10^(10)4 \cdot 10^{10} ,表明远程信息的延迟与它们的速度相比非常大。对于整个
系统特征时间尺度为 r//c=0.03sr / c=0.03 \mathrm{~s} 。
如果整个结构保持 4 开尔文温度,那么它可以向周围 3 开尔文宇宙辐射 10^(10)W10^{10} \mathrm{~W} 。这种能量对应于每秒 2.6*10^(32)2.6 \cdot 10^{32} 比特擦除。在此温度下,由于方程 12 引起的热误差接近于零,只要能量壁垒大于 10^(-21)J10^{-21} J 。这表明,主要的错误来源将是非热误差,如宇宙射线;原则上可以通过屏蔽将它们保持非常低(除了中微子;然而,由于它们非常低的相互作用,它们似乎不会对耗散产生显著贡献)。
A major contribution to energy dissipation will likely be communication. Equation 32 shows that a sizeable amount of energy needs to circulate in the system just to enable communication. Dissipation will likely be a few orders of magnitude less, but even changes in bandwidth usage would require buffering of communications energy. The effective noise temperature in the communications links is likely ≪4K\ll 4 \mathrm{~K}, but since there are 2.5*10^(39)2.5 \cdot 10^{39} links the maximal temperaturebandwidth product (with 10^(10)W10^{10} \mathrm{~W} budget) becomes 2.9*10^(-7)K2.9 \cdot 10^{-7} \mathrm{~K} bits/second. If the bandwidth per channel is a modest 10^(6)bits//s10^{6} \mathrm{bits} / \mathrm{s}, the noise temperature has to be less than 10^(-13)K10^{-13} \mathrm{~K}. At a given dissipation power, there is a trade-off between bit erasure and communication dissipation. 能源耗散的主要贡献可能是通信。方程 32 表明,为了仅仅实现通信,系统中需要循环大量的能量。耗散可能低几个数量级,但即使是带宽使用的改变也要求缓冲通信能量。通信链路中的有效噪声温度可能是 ≪4K\ll 4 \mathrm{~K} ,但由于有 2.5*10^(39)2.5 \cdot 10^{39} 个链路,最大温度带宽乘积(在 10^(10)W10^{10} \mathrm{~W} 预算下)变为 2.9*10^(-7)K2.9 \cdot 10^{-7} \mathrm{~K} 比特/秒。如果每信道的带宽是适度的 10^(6)bits//s10^{6} \mathrm{bits} / \mathrm{s} ,则噪声温度必须低于 10^(-13)K10^{-13} \mathrm{~K} 。在给定的耗散功率下,比特擦除和通信耗散之间存在权衡。
Uranos gradually emerged when the matter of a solar system was converted by intelligent life into a Dyson sphere surrounding its sun-like star at a distance of 1 AU . It consists of numerous independently orbiting structures, ranging from large (hundreds of kilometers) solar collectors to microscale devices moving between the structures for repair and adjustment. 天王星逐渐形成,当太阳系物质被智能生命转化为围绕其类似太阳的恒星,距离为 1 天文单位的戴森球时。它由众多独立轨道的结构组成,从大型(数百公里)太阳能收集器到在结构之间移动进行维修和调整的微尺度设备。
The efficiency of converting solar energy to work is around 30%30 \%, giving 3*10^(25)3 \cdot 10^{25} Watt of available energy. The working temperature for an unshielded object in an 1 AU orbit is 395 K . The number of bit-erasures that can be achieved under these conditions is 7.9*10^(45)7.9 \cdot 10^{45} bits/second. 太阳能转化为功的效率约为 30%30 \% ,提供 3*10^(25)3 \cdot 10^{25} 瓦特的可用能量。在 1 AU 轨道上未屏蔽物体的工作温度为 395 K。在这些条件下可以达到的比特擦除数量为 7.9*10^(45)7.9 \cdot 10^{45} 比特/秒。
The total amount of matter available in the solar system (disregarding hydrogen and helium) beside the sun is ~~1.7*10^(26)kg\approx 1.7 \cdot 10^{26} \mathrm{~kg} [66]. If the energy collecting system is assumed to hold a fairly minor fraction ( 1%1 \% ) of the total mass, and assuming molecular densities, then Uranos can contain up to 10^(52)10^{52} bits. Assuming processing nodes of the same type as Zeus, we get 10^(39)10^{39} nodes and 10^(51)10^{51} operations per second. 太阳系中(不考虑氢和氦)除太阳外可用的物质总量为 ~~1.7*10^(26)kg\approx 1.7 \cdot 10^{26} \mathrm{~kg} [66]。如果假设能量收集系统只占据总质量的一小部分( 1%1 \% ),并且假设分子密度,那么天王星可以容纳多达 10^(52)10^{52} 位。假设处理节点与宙斯相同类型,我们得到 10^(39)10^{39} 个节点和每秒 10^(51)10^{51} 次操作。
The internal delays between distant nodes are on average 660 seconds. Assuming the same picosecond switching as in Zeus gives S~~6.7*10^(14)S \approx 6.7 \cdot 10^{14}, suggesting even less synchronization than Zeus. 节点之间的内部延迟平均为 660 秒。假设与宙斯相同的皮秒级切换,给出 S~~6.7*10^(14)S \approx 6.7 \cdot 10^{14} ,表明比宙斯更少的同步。
Where Uranos really outperforms Zeus is information production/destruction; the high energy throughput makes it possible to dissipate 10^(22)10^{22} times as many bits as Zeus. It might make sense to keep Zeus-like structures in orbit outside 天王星真正超越宙斯的地方是信息生产/破坏;高能量吞吐量使得它能够消散比宙斯多 10^(22)10^{22} 倍的比特。保留类似宙斯的构造在外轨道上可能是有意义的
Uranos to act as information repositories and the Dyson shell itself for processing. 天王星将作为信息库和戴森球本身用于处理。
The main limitation of Uranos is the availability of matter, and the amount of energy that can be extracted from the sun. 天王星的主要限制是物质的可用性,以及从太阳中提取的能量量。
Chronos was originally created by the carefully orchestrated collapse of a globular cluster. By manipulating the orbits of the stars and organizing close encounters half of the stars were ejected from the cluster and the other half dropped into the core. During this process star lifting was used [23] to redistribute mass in order to produce a maximal amount of iron. The iron was merged with a central neutron star kept stable by strong mass flows. Iron was used to avoid inducing fusion reactions, and later moved inside where neutron drip and eventual conversion to quark matter occured. Energy for the merging process and cooling was supplied by the matter-energy conversion in a series of micro-black holes surrounded by Dyson spheres. The result is an extremely massive body delicately balanced between gravity and rotation, surrounded by a huge system of support systems. 时序最初是由一个球状星团的精心策划的坍塌而创造的。通过操纵恒星的轨道和组织近距离相遇,一半的恒星被从星团中弹出,另一半则落入核心。在这个过程中,使用了星提升技术[23]来重新分配质量,以产生最大量的铁。铁与一个由强质量流维持稳定的中心中子星合并。铁被用来避免引发聚变反应,后来被移动到内部,在那里发生了中子滴落和最终转化为夸克物质。合并过程和冷却所需的能量由一系列围绕戴森球体的微黑洞中的物质-能量转换提供。结果是,一个极其庞大的物体在重力和旋转之间微妙地保持平衡,周围环绕着一个庞大的支持系统。
Note that without stabilizing the system using large amounts of angular momentum, just combining all available mass into a single system does not maximize information processing; in order to avoid gravitational collapse the density has to decrease as more matter is added, and beyond a certain point the desirable nuclear densities are no longer available. On the other hand, if communications delays are acceptable, spreading out the mass into a number of neutronium spheres orbiting each other would enable better energy dissipation and hence a higher bit erasure rate. 请注意,如果不使用大量角动量稳定系统,仅仅将所有可用质量组合成一个系统并不能最大化信息处理;为了防止引力坍缩,随着更多物质的增加,密度必须降低,并且超过某个点,理想的核密度就不再可用。另一方面,如果可以接受通信延迟,将质量分散成多个相互环绕的中子星球,将能够实现更好的能量耗散,从而提高比特擦除率。
Assuming an original mass of 10^(36)kg10^{36} \mathrm{~kg}, half of it ends up in the core. Seeking a density of 10^(20)kg//m^(3)10^{20} \mathrm{~kg} / \mathrm{m}^{3} produces a 100 kilometer sphere of quark matter. This corresponds to a maximum 5*10^(61)5 \cdot 10^{61} bits of potential storage capacity, although in practice only part of it is available due to the need of using a significant amount of the mass for support, communications and processing. 假设原始质量为 10^(36)kg10^{36} \mathrm{~kg} ,其中一半最终进入核心。寻求密度为 10^(20)kg//m^(3)10^{20} \mathrm{~kg} / \mathrm{m}^{3} 会产生一个 100 公里半径的夸克物质球体。这对应于最大 5*10^(61)5 \cdot 10^{61} 位潜在存储容量,尽管在实际应用中,由于需要使用大量质量来支持、通信和处理,因此只有其中一部分可用。
Given the timescale of nuclear reactions, Chronos would be able to perform on the order of 10^(85)10^{85} operations per second. The SS value becomes 3*10^(20)3 \cdot 10^{20}, making it even more dispersed than Zeus and Uranos despite its smaller size. Subunits with S=1S=1 would be just 3*10^(-16)3 \cdot 10^{-16} meters across. These subunits roughly correspond to one or a few bits of storage each, so rather than processor clusters as in Zeus and Uranos they would likely be individual processors in Chronos. 考虑到核反应的时间尺度,Chronos 每秒能够执行大约 10^(85)10^{85} 次操作。 SS 的值变为 3*10^(20)3 \cdot 10^{20} ,尽管其尺寸更小,但使其比宙斯和乌拉诺斯更加分散。具有 S=1S=1 的亚单位直径仅为 3*10^(-16)3 \cdot 10^{-16} 米。这些亚单位大致对应每个或几个存储位,因此,与宙斯和乌拉诺斯中的处理器集群不同,Chronos 中可能更像是单个处理器。
Since nuclear bonds are stable up to around 10^(9)K10^{9} \mathrm{~K}, Chronos can operate in the high temperature region. If it dissipates energy through blackbody radiation, it could have a power on the order of 10^(39)W10^{39} \mathrm{~W}, similar to a quasar. This would correspond to 7*10^(53)7 \cdot 10^{53} bit erasures per second. However, other sources of dissipation would be communication and maintenance of the momentum flows keeping the system stable; since these flows would be highly relativistic dissipation losses would likely themselves have a noticeable mass-equivalent. 由于核键在约 10^(9)K10^{9} \mathrm{~K} 时稳定,Chronos 可以在高温区域运行。如果它通过黑体辐射散发热量,其功率可能达到 10^(39)W10^{39} \mathrm{~W} ,类似于类星体。这将对应每秒 7*10^(53)7 \cdot 10^{53} 位擦除。然而,其他耗散源将是保持系统稳定的动量流的通信和维护;由于这些流将是高度相对论性的耗散损失,它们自身可能具有明显的质量等效。
The major limitations of Chronos is the initial amount of mass in the globular cluster and the strength of nuclear bonds. Chronos outperforms Zeus and Ura- Chronos 的主要限制是球状星团中的初始质量以及核键的强度。Chronos 的表现优于宙斯和乌拉。
nos, but the performance might not be worth the cost. The energy demands are extreme, corresponding to a swarm of 10^(9)1kg10^{9} 1 \mathrm{~kg} black holes converting matter to energy; the remaining mass of the globular cluster would be exhausted after a million years. A smaller sphere of nuclear matter able to support itself would have a better efficiency in converting power into computation. 然而,性能可能不值得成本。能量需求极端,相当于一群 10^(9)1kg10^{9} 1 \mathrm{~kg} 黑洞将物质转化为能量;球状星团剩余的质量将在一百万年后耗尽。一个能够自维持的较小核物质球体在将能量转化为计算方面将具有更高的效率。
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^(1){ }^{1} Evolution of intelligent beings directed by them instead of natural selection. 智能生物的进化,由它们指导而非自然选择。 ^(2){ }^{2} The term originally coined by Charles Platt in The Silicon Man 1991 ^(2){ }^{2} 该术语最初由查尔斯·普拉特在 1991 年的《硅人》中提出
^(3){ }^{3} It has been argued in [51] that parallelization is relevant mainly when energy is relatively evenly distributed in the computer, and for compact computers serial processing becomes more efficient since high-energy quantum operations can be used. However, practical limits to energy density, operation speed and energy dissipation limit this approach, as discussed in section 3,4 and 7 . [51]中有人认为,当计算机中的能量相对均匀分布时,并行化才具有重要意义,而对于紧凑型计算机,由于可以使用高能量子操作,串行处理变得更加高效。然而,能量密度、操作速度和能量耗散的实际限制,如第 3、4 和 7 节所述,限制了这种方法。 ^(4){ }^{4} The term likely originated by Perry Metzger. 该术语可能起源于 Perry Metzger。
^(5){ }^{5} This argument was originally pointed out to me by a poster on the extropians mailing list in 1995 ^(5){ }^{5} 这个论点最初是由 1995 年在 extropians 邮件列表上的一个发件人指给我的
^(6){ }^{6} This idea of submerged “Dyson shells” is due to Nick Szabo. ^(6){ }^{6} 这个关于水下“戴森壳”的想法是尼克·萨博提出的。
^(7){ }^{7} the computer would simply report if it received a signal from the future or not, and then start running the program. If the program halts, the computer will send a signal back in time to itself. 计算机将简单地报告是否收到了来自未来的信号,然后开始运行程序。如果程序停止,计算机将向自己发送一个回溯信号。
^(8){ }^{8} by receiving the answer and then doing the calculation at some future time 通过接收答案然后在未来的某个时间进行计算