Entanglement Builds Space-Time. Now “Magic” Gives It Gravity.
I n 1973, John Archibald Wheeler described the relationship between space and matter in two sentences: “Space acts on matter, telling it how to move.
1973年，约翰·阿奇博尔德·惠勒用两句话描述了空间与物质的关系：“空间作用于物质，告诉它如何运动。
In turn, matter reacts back on space, telling it how to curve.” Wheeler’s words serve as a pithy encapsulation of general relativity, Albert Einstein’s theory of gravity.
反过来，物质会对空间做出反应，告诉它如何弯曲。”惠勒的话是对广义相对论（阿尔伯特·爱因斯坦的引力理论）的精辟概括。
Wheeler’s sentences also lay out a challenge that theorists face today: When they build a model of the universe — at least one that works at the quantum level — it’s been difficult to get space and matter to interact in the way that they must.
惠勒的句子还提出了理论学家今天面临的一个挑战：当他们建立一个宇宙模型时——至少是一个在量子水平上有效的模型——很难让空间和物质以它们必须的方式相互作用。
Einstein cast gravity not as a force but as the geometric bending of space and time.
爱因斯坦认为引力不是一种力，而是空间和时间的几何弯曲。
In a popular analogy, the fabric of space-time is like the flat expanse of a mattress, and a massive object like a star is like a bowling ball sitting on top.
用一个流行的比喻来说，时空的结构就像一张平坦的床垫，而像星星这样的巨大物体就像坐在上面的保龄球。
The weight of the bowling ball compresses the mattress, forming a dimple — matter tells space-time how to curve.
保龄球的重量压缩床垫，形成一个凹坑——物质告诉时空如何弯曲。
In this analogy, a planet is like a smaller ball.
在这个类比中，行星就像一个较小的球。
If it rolls close enough to the bowling ball, its path will be altered by the dimple in the mattress — space-time tells matter how to move.
如果它滚得离保龄球足够近，它的路径就会被床垫上的凹痕改变——时空告诉物质如何移动。
But general relativity has a fatal flaw.
但广义相对论有一个致命的缺陷。
When a star dies and collapses, its mass is concentrated into an unimaginably dense point.
当一颗恒星死亡并坍缩时，它的质量会集中到一个难以想象的密集点。
The dimple in the mattress stretches into a deep depression, one that essentially rips all the way through.
床垫上的凹痕延伸成一个深深的凹陷，基本上是一路撕裂的。
Physicists call this arrangement a black hole.
物理学家将这种排列称为黑洞。
If a ball reaches such a rip, it’s no longer guided by the fabric, and the analogy breaks down; scientists need a new theory to understand this and other, similarly extreme situations.
如果球到达这样的裂口，它就不再受织物的引导，这个类比就站不住脚了；科学家需要一种新的理论来理解这种情况以及其他类似的极端情况。
In the late 1990s, physicists had a stroke of luck.
20 世纪 90 年代末，物理学家遇到了好运。
They learned that if they imagined space-time as a collection of purely quantum particles, they could in principle describe a black hole — rip and all — in an entirely new way.
他们了解到，如果他们将时空想象为纯量子粒子的集合，原则上他们就可以以一种全新的方式描述黑洞——裂痕等等。
Theorists have spent the last few decades trying to understand exactly how a space-time constructed from such quantum particles could work.
过去几十年来，理论学家一直试图准确理解由这种量子粒子构建的时空是如何运作的。
And they’ve made progress: They’ve found that entanglement between particles gives space-time its structure, building an environment where matter can move — and satisfying the conditions of Wheeler’s first statement.
他们已经取得了进展：他们发现粒子之间的纠缠赋予了时空结构，构建了一个物质可以移动的环境——并满足了惠勒第一个陈述的条件。
But the origin of Wheeler’s second statement remained mysterious; in their models, matter didn’t tell space how to curve.
但惠勒第二句话的起源仍然是个谜。在他们的模型中，物质并没有告诉空间如何弯曲。
The bowling ball sat atop the mattress without making a dent.
保龄球坐在床垫上，没有留下任何凹痕。
Until now.
到目前为止。
Physicists including Charles Cao at Virginia Tech have recently determined how quantum particles could give space-time its bendiness.
包括弗吉尼亚理工大学查尔斯·曹在内的物理学家最近确定了量子粒子如何赋予时空弯曲性。
In a handful of recent works, multiple teams have identified a feature of quantum mechanics that Cao calls “the fabric softener of space.” It’s a measure of quantumness called “magic.”
在最近的一些工作中，多个团队已经确定了量子力学的一个特征，曹称之为“太空织物柔软剂”。这是一种被称为“魔法”的量子性度量。
“Without magic, things are a little too simple,” said John Preskill , a physicist at the California Institute of Technology who contributed to Cao’s newest paper.
“如果没有魔法，事情就有点太简单了，”加州理工学院的物理学家约翰·普雷斯基尔说，他为曹的最新论文做出了贡献。
“And, you know, quantum space-time isn’t quite that simple.”
“而且，你知道，量子时空并不那么简单。”
Perspective shifts abound in physics.
物理学中观点的转变比比皆是。
For instance, there’s more than one way to look at the motion of a pendulum.
例如，观察钟摆运动的方法不止一种。
You might specify its location using the height and the horizontal displacement of the weight hanging at the end of the string.
您可以使用绳子末端悬挂的重物的高度和水平位移来指定其位置。
Or you might use the length of the string and its angle instead.
或者您可以使用绳子的长度及其角度来代替。
The perspectives are equivalent; simple trigonometric equations take you from one perspective to the other.
观点是对等的；简单的三角方程可以带你从一个角度到另一个角度。
For 50 years, theorists have been chasing a far more profound perspective shift: a new way, beyond Einstein’s curved space-time, to look at the universe.
50 年来，理论家一直在追求更深刻的视角转变：一种超越爱因斯坦弯曲时空的新方式来看待宇宙。
In the early 1970s, Jacob Bekenstein and Stephen Hawking took the first step in that direction when they discovered that you could reinterpret a black hole (and anything that had fallen into it) as a spherical collection of particles .
20 世纪 70 年代初，雅各布·贝肯斯坦 (Jacob Bekenstein) 和斯蒂芬·霍金 (Stephen Hawking) 朝这个方向迈出了第一步，他们发现可以将黑洞（以及落入其中的任何物体）重新解释为粒子的球形集合。
In the late 1990s, Juan Maldacena, Edward Witten, and others extended this insight to a whole universe; they described an exotic, static world as a throng of interacting particles, also arranged in a sphere.
20 世纪 90 年代末，胡安·马尔达西纳 (Juan Maldacena)、爱德华·维滕 (Edward Witten) 等人将这一见解扩展到整个宇宙；他们将一个奇特的静态世界描述为一群相互作用的粒子，也排列在一个球体中。
In both cases, you could replace the 3D region of space-time with particles on the region’s surface.
在这两种情况下，您都可以用该区域表面的粒子来替换 3D 时空区域。
You could consider the surface to be 2D, like a globe flattened into a paper map.
您可以将表面视为 2D，就像扁平化为纸质地图的地球仪。
Physicists call this dual nature of space-time the holographic principle, since it resembles the way a holographic sticker can cram a whole 3D scene onto a flat surface without losing data.
物理学家将这种时空的双重性称为全息原理，因为它类似于全息贴纸可以将整个 3D 场景填充到平面上而不丢失数据的方式。
Without magic, things are a little too simple.
如果没有魔法，事情就有点太简单了。
And, you know, quantum space-time isn’t quite that simple.
而且，你知道，量子时空并不是那么简单。
John Preskill, California Institute of Technology
约翰·普雷斯基尔，加州理工学院
Over the last couple of decades, theorists have explored what gives the 3D fabric of space its shape.
在过去的几十年里，理论学家们一直在探索是什么赋予了空间 3D 结构的形状。
Entanglement, a quantum property that links particles to one another, seems to serve as space’s connective tissue.
纠缠是一种将粒子相互连接的量子特性，似乎可以充当空间的结缔组织。
Take, for instance, a wormhole, a theoretical bridge connecting two distant regions of space.
以虫洞为例，它是连接两个遥远空间区域的理论桥梁。
Holographically, a 3D wormhole is equivalent to two entangled sets of particles.
从全息角度来看，3D 虫洞相当于两组纠缠的粒子。
Start snipping the “threads” of entanglement that link one set with the other, and the tunnel connecting the regions gets thinner and thinner.
开始剪断连接一组与另一组的纠缠“线”，连接这些区域的隧道变得越来越细。
Cut the final thread, and the connection dissolves entirely.
切断最后一根线，连接就完全消失了。
Cao learned about the link between entanglement and space as a graduate student at Caltech in 2016, most notably through a paper by Daniel Harlow , a physicist now at the Massachusetts Institute of Technology.
2016 年，曹在加州理工学院读研究生时了解了纠缠与空间之间的联系，最引人注目的是通过现任麻省理工学院物理学家丹尼尔·哈洛 (Daniel Harlow) 的一篇论文。
“Charles spent a month understanding the paper,” said Jason Pollack , then a fellow graduate student, now a physicist at Syracuse University.
“查尔斯花了一个月的时间来理解这篇论文，”当时的研究生、现在是雪城大学的物理学家杰森·波拉克 (Jason Pollack) 说。
Harlow, building in part on the work of Preskill and others, had identified the type of math required to shift perspectives from 2D to 3D.
哈洛在一定程度上以普雷斯基尔等人的工作为基础，确定了将视角从 2D 转变为 3D 所需的数学类型。
He needed to encode a space and its matter — stars and planets and electrons — into a bunch of quantum particles.
他需要将空间及其物质——恒星、行星和电子——编码成一堆量子粒子。
So why not use a quantum error-correcting code?
那么为什么不使用量子纠错码呢？
Quantum error-correcting codes are crucial to quantum computing because quantum computers work by manipulating “qubits,” quantum versions of bits that can exist in superpositions of 0s and 1s.
量子纠错码对于量子计算至关重要，因为量子计算机通过操纵“量子位”来工作，“量子位”是可以以 0 和 1 的叠加形式存在的量子版本。
Qubits are extremely delicate, frequently losing their superposition and therefore their extra information.
量子位非常脆弱，经常会失去其叠加态，从而失去额外的信息。
And so physicists have worked out ways to protect this delicate information through redundancy.
因此，物理学家找到了通过冗余来保护这些敏感信息的方法。
By spreading out one qubit’s information among many qubits, they can preserve it even if some of the qubits are lost.
通过将一个量子位的信息分散到许多量子位中，即使某些量子位丢失，他们也可以保留它。
Charles Cao, a physicist at Virginia Tech, calls magic “the fabric softener of space.”
弗吉尼亚理工大学的物理学家查尔斯·曹将魔法称为“太空织物柔软剂”。
The same type of redundancy shows up in holography .
全息术中也出现了相同类型的冗余。
“When you design codes for quantum computing, you’re doing the same kind of thing that [holography] already did for you,” said Bartek Czech, a physicist at Tsinghua University in China.
中国清华大学的物理学家 Bartek Czech 表示：“当你为量子计算设计代码时，你所做的事情与[全息术]已经为你所做的事情是一样的。”
A single holographic location — a region of space and the matter in it — is not encoded in just one set of quantum particles; rather, it is spread across many sets, due to their entanglement.
单个全息位置——空间区域和其中的物质——不仅仅被编码在一组量子粒子中；而是被编码在一组量子粒子中。相反，由于它们的纠缠，它分布在许多集合中。
Harlow and collaborators detailed how this works in a code in 2014 , and he further fleshed out the relationship in the 2016 paper that impressed Cao.
Harlow 和他的合作者在 2014 年的代码中详细说明了这一点是如何工作的，他在 2016 年的论文中进一步充实了这种关系，这给曹留下了深刻的印象。
But these codes, known as “stabilizer codes,” had a shortcoming.
但这些被称为“稳定器代码”的代码有一个缺点。
They divided the entanglement of the particles into two types: one responsible for space and another responsible for matter.
他们将粒子的纠缠分为两种类型：一种负责空间，另一种负责物质。
And the divide was unbridgeable.
分歧是不可逾越的。
Such a perfect split is a virtue in quantum computing, since you want your encrypted data to stay perfectly isolated from the corrupting influence of the outside world.
这种完美的分割是量子计算的一个优点，因为您希望加密的数据完全隔离，免受外界的破坏性影响。
But in holography, that perfection left no room for the two to interact.
但在全息术中，这种完美没有给两者留下互动的空间。
“We knew how to build a space-time,” Czech said, but “this space-time was inert.
“我们知道如何构建时空，”捷克说，但“这个时空是惰性的。
It didn’t do anything.”
它什么也没做。”
To get space and matter to interact, Cao knew he needed a more sophisticated code.
为了让空间和物质相互作用，曹知道他需要更复杂的代码。
“It was clear that something else beyond entanglement had to be there,” said Ning Bao , a physicist at Northeastern University.
“很明显，除了纠缠之外，还必须存在其他东西，”东北大学物理学家鲍宁说。
Cao started by playing around with existing error-correcting codes.
曹首先尝试了现有的纠错码。
In 2020, he and a collaborator, Brad Lackey, tweaked one such code and found that it allowed space to change — just not in response to matter.
2020 年，他和一位合作者 Brad Lackey 调整了一个这样的代码，发现它允许空间改变——只是不是对物质做出反应。
It wasn’t gravity, but it was progress.
这不是重力，而是进步。
Except that Cao and Lackey didn’t fully understand why the tweak worked.
只是曹和拉基并没有完全理解为什么这个调整会起作用。
M.C.
MC
Escher’s 1959 woodcut Circle Limit III has the geometry of a holographic world: A whole universe fits inside a spherical surface.
埃舍尔 1959 年的木刻《圆极限 III》具有全息世界的几何形状：整个宇宙都装在一个球面内。
In holography, you can learn about what’s happening in the interior by studying the surface itself.
在全息术中，您可以通过研究表面本身来了解内部发生的情况。
The next year, Pollack and his collaborators realized that if you actually tried to create a quantum program that executed the tweaked code on a quantum computer, you’d need to use a particular operation known as a T gate, which rotates a qubit.
第二年，波拉克和他的合作者意识到，如果你真的尝试创建一个在量子计算机上执行调整后的代码的量子程序，你需要使用一种称为 T 门的特殊操作，它会旋转一个量子位。
Cao took notice.
曹注意到了。
He had just attended a quantum computing conference where researchers were buzzing about gates like these, in part because they are the key to making quantum computers more powerful than classical computers.
他刚刚参加了一次量子计算会议，会上研究人员对此类门议论纷纷，部分原因是它们是使量子计算机比经典计算机更强大的关键。
Researchers had previously thought the key was entanglement.
研究人员此前认为关键在于纠缠。
They had worked out a way of running software on a classical computer that would mimic a quantum task.
他们找到了一种在经典计算机上运行模拟量子任务的软件的方法。
When that quantum task involved entangling qubits, quantum computers had an advantage over classical computers, as the classical program took ages to run.
当量子任务涉及纠缠量子位时，量子计算机比经典计算机具有优势，因为经典程序需要很长时间才能运行。
But then physicists discovered a way of speeding things up; it turned out that certain classical algorithms could mimic certain entangling operations even on a laptop.
但后来物理学家发现了一种加快速度的方法；事实证明，某些经典算法甚至可以在笔记本电脑上模拟某些纠缠操作。
In 2004, Alexei Kitaev and Sergey Bravyi, both then at Caltech, brought researchers’ attention to quantum operations known as non-Clifford gates, which include the T gate.
2004 年，当时就职于加州理工学院的阿列克谢·基塔耶夫 (Alexei Kitaev) 和谢尔盖·布拉维 (Sergey Bravyi) 引起了研究人员对被称为非克利福德门（包括 T 门）的量子运算的关注。
When a quantum program uses these operations, the equivalent classical program takes much, much longer to run.
当量子程序使用这些操作时，等效的经典程序需要运行更长的时间。
Kitaev and Bravyi described the complexity that these operations introduce as “magic.” The more non-Clifford gates you need to produce a quantum state, the more magical that state is.
Kitaev 和 Bravyi 将这些操作带来的复杂性描述为“魔法”。产生量子态所需的非克利福德门越多，该态就越神奇。
After Cao learned about magic and non-Clifford gates, he joined forces with Brian Swingle and Christopher White, both researchers at the University of Maryland.
在曹了解了魔法和非克利福德门之后，他与马里兰大学的研究人员布莱恩·斯温格尔和克里斯托弗·怀特联手。
In 2020, they studied collections of particles equivalent to an exotic universe called an anti-de Sitter space.
2020 年，他们研究了相当于称为反德西特空间的奇异宇宙的粒子集合。
The group found that the particles were highly magical .
研究小组发现这些粒子非常神奇。
What would the role of this magic be, they wondered, for the anti-de Sitter space the particles represented?
他们想知道，对于粒子所代表的反德西特空间来说，这种魔法将发挥什么作用？
Cao — in partnership with Alioscia Hamma and others and building on work from Xi Dong , now at the University of California, Santa Barbara — found the answer a few years later.
几年后，曹与 Alioscia Hamma 等人合作，在加州大学圣塔芭芭拉分校的习东的工作基础上找到了答案。
They showed that magic gave space its springiness .
他们表明魔法赋予了空间弹性。
Magic, in other words, is connected to space’s ability to bend.
换句话说，魔法与空间的弯曲能力有关。
And therefore magic is connected to gravity.
因此魔法与重力有关。
“If you have one,” Bao said, “you always have the other.”
“如果你有一个，”鲍说，“你总会有另一个。”
By early 2026, Cao and his collaborators had all the pieces.
到 2026 年初，曹和他的合作者已经掌握了所有的部分。
They knew that magic made space bend.
他们知道魔法可以使空间弯曲。
And they knew that quantum codes got their magic from non-Clifford gates.
他们知道量子密码的魔力来自非克利福德门。
So Cao, Preskill, and others created a next-generation code to succeed the stabilizer codes Harlow and others had focused on a decade before, when they split encoded space from encoded matter.
因此，曹、普雷斯基尔和其他人创建了下一代代码，以继承哈洛和其他人十年前关注的稳定器代码，当时他们将编码空间与编码物质分开。
This new code used lots of non-Clifford gates.
这个新代码使用了大量非 Clifford 门。
The gates made the code magical, letting the entanglement for space and the entanglement for matter affect each other.
大门让密码变得神奇，让空间的纠缠和物质的纠缠相互影响。
“This is pretty cool, because in quantum gravity, we don’t expect the background is fixed,” said Cynthia Keeler , a physicist at Arizona State University who was not involved in the work.
“这非常酷，因为在量子引力中，我们不希望背景是固定的，”亚利桑那州立大学的物理学家辛西娅·基勒（Cynthia Keeler）说，她没有参与这项工作。
“It should fluctuate.”
“应该会波动。”
The essential nature of magic especially intrigues physicists like Swingle, who hope to use it on a quantum computer to simulate how gravity behaves in situations where general relativity fails.
魔法的本质尤其引起像斯温格尔这样的物理学家的兴趣，他们希望在量子计算机上使用它来模拟广义相对论失效的情况下重力的行为。
“If we need high magic, then we intrinsically need a quantum computer,” Swingle said, “because there’s no other way, in general, to get at that kind of question.”
“如果我们需要高级魔法，那么我们本质上就需要一台量子计算机，”斯温格尔说，“因为一般来说，没有其他方法可以解决这类问题。”
In principle, entanglement and magic could be enough for future physicists to simulate space on a quantum computer.
原则上，纠缠和魔法足以让未来的物理学家在量子计算机上模拟空间。
But Cao’s new code still needs a lot of work.
但曹的新代码仍然需要大量工作。
During a talk about it at the American Physical Society’s annual summit in Denver, Cao joked that he was the only speaker who wasn’t actually studying quantum gravity.
在丹佛举行的美国物理学会年度峰会上，曹开玩笑说，他是唯一一个没有真正研究量子引力的演讲者。
That’s because his code is still extremely general.
那是因为他的代码仍然非常通用。
It doesn’t describe the kind of space in which we live, doesn’t capture the particular reactions Einstein described, and doesn’t include the ticking of time.
它没有描述我们生活的空间类型，没有捕捉爱因斯坦描述的特定反应，也不包括时间的滴答声。
The code is more of a proof of concept of the general shape that a theory of quantum gravity should take.
该代码更多的是对量子引力理论应采取的一般形式的概念证明。
If you want your space to bend, use a magical code.
如果你想让你的空间弯曲，请使用神奇的代码。
“This gets you a precursor of gravity,” Cao said.
“这让你得到了引力的前兆，”曹说。
“You satisfy one of the necessary conditions.
“你满足了必要条件之一。
Right now, we are at step 0.5 of 5.”
现在，我们处于 5 步中的 0.5 步。”
But even at this early stage, the research program highlights some surprising features that any theory of quantum gravity should have.
但即使在这个早期阶段，该研究项目也强调了任何量子引力理论都应该具有的一些令人惊讶的特征。
Einstein and Wheeler thought of space-time as a large, featureless fabric existing with fixed bends and folds — a typical classical object.
爱因斯坦和惠勒认为时空是一种巨大的、无特征的织物，存在着固定的弯曲和折叠——一种典型的经典物体。
But now physicists are learning that the two defining features of quantum mechanics, entanglement and magic, correspond to the two defining features of space, its shape and its flexibility.
但现在物理学家们发现，量子力学的两个定义特征，即纠缠和魔力，对应于空间的两个定义特征：形状和灵活性。
This suggests that space itself is one of the most quantum things imaginable.
这表明空间本身是可以想象到的最量子化的事物之一。
“All the familiar aspects of gravity are actually a very direct manifestation of something quantum,” Swingle said.
“引力的所有熟悉的方面实际上都是量子事物的非常直接的表现，”斯温格尔说。
It also suggests that gravity results from imperfect quantum encoding.
它还表明引力是由不完美的量子编码产生的。
Non-magical codes produce inert, gravity-free spaces because they protect their encoded information perfectly.
非魔法代码会产生惰性、无重力的空间，因为它们完美地保护了其编码信息。
Cao and collaborators have shown that gravity comes from the mixing of the encoded information.
曹和合作者已经证明，引力来自编码信息的混合。
So by necessity, the encoding must be approximate, and therefore some aspects of what’s going on in the space-time can’t be perfectly recovered by measuring a subset of the quantum particles in the usual way.
因此，必然地，编码必须是近似的，因此时空中发生的事情的某些方面无法通过以通常的方式测量量子粒子的子集来完美地恢复。
This approximation, which would indicate a poorly written code for a quantum computer, is “the reason Newton’s apple fell on him,” Czech said.
捷克说，这种近似表明量子计算机的代码编写得很糟糕，这就是“牛顿的苹果落在他身上的原因”。
Cao, for his part, finds the feature appealing.
曹则认为这个功能很有吸引力。
Quantum error correction and quantum computing are human pursuits, he said.
他说，量子纠错和量子计算是人类的追求。
He sees no reason that gravity should accommodate our prejudice for perfection.
他认为重力没有理由容纳我们对完美的偏见。
Correction: June 3, 2026 Charles Cao was a graduate student at Caltech, and he later held a postdoctoral position at the University of Maryland.
更正：2026 年 6 月 3 日 Charles Cao 是加州理工学院的研究生，后来在马里兰大学担任博士后职位。
The article previously called the gates that introduce magic Toffoli gates and conflated them with a simpler gate called the T gate.
文章之前将介绍神奇的 Toffoli 门的门称为“Toffoli 门”，并将它们与一种称为“T 门”的更简单的门混为一谈。
Toffoli gates and T gates are both a part of a wider category called non-Clifford gates, all of which introduce magic.
托弗里门和 T 门都是称为非克利福德门的更广泛类别的一部分，所有这些门都引入了魔法。
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