内容来源：https://www.quantamagazine.org/entanglement-builds-space-time-now-magic-gives-it-gravity-20260603/

内容总结：

量子“魔法”为时空注入引力：最新研究揭示时空弯曲的量子起源

（北京讯） 自爱因斯坦提出广义相对论以来，科学家一直试图理解时空与物质之间相互作用的本质。近日，以弗吉尼亚理工大学曹查尔斯（Charles Cao）为首的多个物理学家团队取得突破性进展，发现了一种被称为“魔法”（Magic）的量子力学特性，正是它赋予了时空弯曲的能力——这为理解引力的量子起源提供了全新视角。

从“缠绕”到“魔法”：破解引力谜题的两把钥匙

1973年，物理学家约翰·惠勒曾用两句话精辟概括广义相对论：“时空告诉物质如何运动，物质告诉时空如何弯曲。”在经典理论中，大质量物体（如恒星）会像保龄球压弯床垫一样，使平坦的时空结构产生凹陷，从而形成引力。然而，当理论延伸至黑洞等极端量子尺度时，这一模型便失效了——黑洞的奇点会将“时空床垫”彻底撕裂。

过去数十年，物理学家利用“全息原理”取得重要进展，发现量子纠缠是构建时空结构的“粘合剂”。通过将三维时空信息编码在二维表面的量子粒子上，科学家成功模拟了时空的形态。然而，这些基于“稳定子码”（Stabilizer Codes）的模型虽然能解释时空如何成型，却始终无法让物质反过来影响时空——就像保龄球放在床垫上却压不出任何凹陷。

“魔法”登场：让时空“活”起来的关键

曹查尔斯团队的研究揭示了谜底：仅靠量子纠缠远远不够，还需要一种更为根本的量子特性——“魔法”。这种特性源自量子计算中的“托佛利门”（Toffoli gate）操作，它使量子态的复杂性呈指数级增长，远超经典计算机的模拟能力。

研究团队发现，当“魔法”被引入量子纠错编码模型后，原本僵硬的时空结构开始获得“弹性”。与之前的稳定子码不同，包含大量“魔法”的新型编码允许描述时空和物质的量子纠缠相互影响，从而使时空能够对物质做出响应、产生弯曲。曹查尔斯形象地将这一特性称为“时空的柔软剂”。

“如果没有‘魔法’，一切都过于简单了，”加州理工学院的约翰·普雷斯基尔（John Preskill）教授说，“而量子时空显然没那么简单。”

引力可能是“不完美”的量子编码结果

研究指出，这一发现不仅解释了引力的起源，更颠覆了我们对时空本质的传统认知。爱因斯坦和惠勒将时空视为具有固定弯曲的大型经典“织物”，而新研究则表明，时空本身可能是最具量子特性的存在之一。“引力的所有熟悉特征，实际上都是某种量子现象的直接体现，”马里兰大学的布莱恩·斯温格尔（Brian Swingle）表示。

一个更为有趣的推论是：引力或许源于量子编码的“不完美”。在完美的量子纠错码中，信息被绝对隔离，时空保持“惰性”；而当编码产生混合时，引力才得以显现。正如清华大学的巴特克·捷赫（Bartek Czech）所言：“这就是牛顿的苹果落地的原因。”

目前，该模型仍处于概念验证阶段（研究团队自评为“五步走完半步”），尚未能完全描述我们所处的现实时空，也未包含时间的维度。但它首次明确了任何量子引力理论都必须满足的一个关键条件：想要时空弯曲，就必须使用具有“魔法”的量子编码。这一方向为在量子计算机上模拟黑洞内部等极端引力现象铺平了道路。

中文翻译：

纠缠构建时空，如今“魔力”赋予其引力。
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；反过来，物质反作用于空间，告诉它如何弯曲。”惠勒的这番话精辟地概括了阿尔伯特·爱因斯坦的引力理论——广义相对论。
惠勒的语句也揭示了当今理论家面临的挑战：在构建宇宙模型时——至少是那些能在量子层面成立的模型——让空间与物质按照必然的方式相互作用一直困难重重。
爱因斯坦并未将引力视为一种力，而是时空的几何弯曲。一个流行的类比是：时空结构就像床垫平坦的表面，而像恒星这样的巨大物体则像放在上面的保龄球。保龄球的重量压缩床垫，形成凹陷——物质告诉时空如何弯曲。
在这个类比中，行星就像一个小球。如果它滚得足够靠近保龄球，它的路径就会被床垫上的凹陷改变——时空告诉物质如何运动。
但广义相对论有一个致命缺陷。当恒星死亡并坍缩时，其质量会浓缩成一个难以想象的致密点。床垫上的凹陷被拉伸成深坑，最终几乎撕裂整个床垫。物理学家称这种结构为黑洞。若一个球到达这样的撕裂处，它便不再受床垫结构的引导，这个类比也就失效了；科学家需要一种新理论来理解这一情况以及其他类似的极端情形。
20世纪90年代末，物理学家们迎来了一次运气。他们发现，如果他们将时空想象成纯粹量子粒子的集合，那么原则上他们就能以一种全新的方式描述黑洞——包括撕裂及其所有特征。
理论家们在过去几十年里一直试图理解这种由量子粒子构成的时空究竟如何运作。他们取得了进展：他们发现粒子间的纠缠赋予了时空结构，构建了一个物质可以运动的环境——满足了惠勒第一句话的条件。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。保龄球放在床垫上，却没有留下任何凹痕。
直到现在。包括弗吉尼亚理工大学的查尔斯·曹在内的物理学家们最近确定了量子粒子如何赋予时空弯曲性。在最近的一些工作中，多个团队识别出了量子力学的一个特征，曹称之为“空间柔顺剂”。这是一种衡量量子特性的指标，被称为“魔力”。
“没有魔力，事情就有点过于简单了，”加州理工学院的物理学家约翰·普雷斯基尔说，他也是曹最新论文的合著者。“而且，你知道，量子时空并没有那么简单。”
如何编码一个宇宙
物理学中处处存在着视角转换。例如，观察单摆运动不止一种方式。你可以用绳子末端悬挂重物的高度和水平位移来指定其位置。或者你也可以用绳子的长度和它的角度来描述。这两种视角是等价的；简单的三角方程就能让你从一个视角转换到另一个视角。
50年来，理论家们一直在追寻一种更为深刻的视角转换：一种超越爱因斯坦弯曲时空的、观察宇宙的新方式。
20世纪70年代初，雅各布·贝肯斯坦和斯蒂芬·霍金朝着这个方向迈出了第一步，他们发现可以将一个黑洞（以及落入其中的任何东西）重新解释为一个球形的粒子集合。20世纪90年代末，胡安·马尔达西那、爱德华·威滕等人将这一洞见扩展到了整个宇宙；他们将一个奇特的静态世界描述为一群相互作用的粒子，这些粒子也排列成球体。
在这两种情况下，你都可以用区域表面上的粒子来替代那个三维的时空区域。你可以将这个表面视为二维的，就像被压平成平面地图的地球仪。物理学家将时空的这种双重性质称为全息原理，因为它类似于全息贴纸可以将整个三维场景压缩到平面上而不丢失数据的方式。
在过去的几十年里，理论家们探索了是什么赋予了三维空间结构其形状。纠缠——一种将粒子相互连接起来的量子属性——似乎是空间的结缔组织。以虫洞为例，虫洞是连接两个遥远空间区域的理论桥梁。在全息视角下，一个三维虫洞等价于两个纠缠的粒子集合。开始剪断连接两组粒子的纠缠“线”，连接区域的隧道就会越来越细。剪断最后一根线，连接就会完全消失。
曹在2016年作为加州理工学院的研究生时了解了纠缠与空间之间的联系，特别是通过丹尼尔·哈洛（现为麻省理工学院物理学家）的一篇论文。“查尔斯花了一个月来理解这篇论文，”当时同为研究生的贾森·波拉克说，他现在是锡拉丘兹大学的物理学家。
哈洛部分基于普雷斯基尔等人的工作，确定了从二维视角转换到三维视角所需的数学类型。他需要将空间及其物质——恒星、行星和电子——编码到一堆量子粒子中。那么，为什么不使用量子纠错码呢？
量子纠错码对量子计算至关重要，因为量子计算机通过操控“量子比特”来工作，量子比特是经典比特的量子版本，可以处于0和1的叠加态。量子比特极其脆弱，经常失去叠加态，从而丢失其额外信息。因此，物理学家们想出了通过冗余来保护这些精细信息的方法。通过将一个量子比特的信息分散到许多量子比特中，即使在部分量子比特丢失的情况下也能保存信息。
同类型的冗余也出现在全息理论中。“当你为量子计算设计编码时，你实际上在做（全息理论）早已为你做过的事情，”中国清华大学的物理学家巴特克·捷克说。单个全息位置——一块空间区域及其中的物质——并非仅编码在一组量子粒子中；相反，由于纠缠，它被分散在多个粒子组中。哈洛及其合作者在2014年详细阐述了这在一种编码中如何运作，并在2016年令曹印象深刻的那篇论文中进一步充实了这种关系。
但这些被称为“稳定子码”的编码有一个缺陷。它们将粒子的纠缠分为两类：一类负责空间，另一类负责物质。这种划分是不可逾越的。这种完美的分离在量子计算中是一种优点，因为你希望你的加密数据与外部世界的破坏性影响完美隔离。但在全息理论中，这种完美性没有为两者相互作用留下空间。“我们知道如何构建时空，”捷克说，但“这个时空是惰性的。它什么也不做。”
为了让空间和物质相互作用，曹知道需要一个更复杂的编码。“很明显，除了纠缠之外，还必须存在别的东西，”东北大学的物理学家宁宝说。
魔力成分
曹从摆弄现有的纠错码开始。2020年，他与合作者布拉德·莱基修改了这样一个编码，发现它允许空间发生变化——只是并非因为物质的反应而变化。这不是引力，但这是进步。只是曹和莱基并不完全理解这个改动为何奏效。
第二年，波拉克和他的合作者意识到，如果你真的试图创建一个在量子计算机上执行修改后编码的量子程序，你需要使用一个特定的操作，称为托佛利门，它在特定条件下翻转一个量子比特。
曹注意到了这一点。他刚刚参加了一个量子计算会议，会上研究人员都在热议托佛利门，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。
研究人员此前认为关键因素是纠缠。他们找到了一种在经典计算机上运行软件来模拟量子任务的方法。当该量子任务涉及纠缠量子比特时，与经典计算机相比量子计算机有优势，因为经典程序运行需要很长时间。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。
2004年，当时同在加州理工学院的阿列克谢·基塔耶夫和布拉维伊将研究人员的注意力引向了托佛利门。当一个量子程序使用一组特定的量子操作（包括托佛利门）时，等效的经典程序运行所需的时间要长得多。基塔耶夫和布拉维伊将这些操作引入的复杂性描述为“魔力”。例如，要产生一个量子态所需的托佛利门越多，这个态就越有魔力。
曹了解了魔力和托佛利门后，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。2020年，他们研究了对应于一个名为反德西特空间的奇特宇宙的粒子集合。该小组发现这些粒子具有高度的魔力。他们想知道，对于这些粒子所代表的反德西特空间来说，这种魔力会起到什么作用？
曹——与阿利奥夏·哈马等人合作，并在现为加州大学圣巴巴拉分校的奚冬的工作基础上——几年后找到了答案。他们证明，魔力赋予了空间弹性。换句话说，魔力与空间的弯曲能力相关。因此，魔力与引力相关。“如果你有其一，”宁宝说，“你就总有另一个。”
到2026年初，曹和他的合作者已经掌握了所有拼图。他们知道魔力使空间弯曲。他们也知道了量子编码是从托佛利门获得魔力的。因此，曹、普雷斯基尔等人创建了新一代编码，以接替哈洛等人十年前专注于将编码空间与编码物质分开的稳定子码。这个新编码使用了大量的托佛利门。这些门使编码具有魔力，从而让（负责）空间的纠缠和（负责）物质的纠缠能够相互影响。
“这非常酷，因为在量子引力中，我们并不期望背景是固定的，”并未参与此项工作的亚利桑那州立大学物理学家辛西娅·基勒说。“它应该会波动。”
魔力的基本性质特别引起了像斯温格尔这样的物理学家的兴趣，他们希望利用它在量子计算机上模拟广义相对论失效情况下的引力行为。“如果我们需要高魔力，那么我们本质上就需要量子计算机，”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。”
源自量子性的引力
原则上，纠缠和魔力足以让未来的物理学家在量子计算机上模拟空间。但曹的新编码仍需要大量工作。
在丹佛举行的美国物理学会年度峰会上谈论该编码时，曹开玩笑说，他是唯一一位并非真正在研究量子引力的演讲者。这是因为他的编码仍然非常笼统。它没有描述我们生活的这种空间，没有捕捉到爱因斯坦描述的特定反应，也没有包含时间的流逝。
这个编码更像是关于量子引力理论应该采取何种总体形状的一个概念验证。如果你想要你的空间弯曲，就用一个充满魔力的编码。“这让你得到了引力的前身，”曹说。“你满足了一个必要条件。目前，我们处在5步中的0.5步。”
但即使在这个早期阶段，这项研究计划也凸显了任何量子引力理论都应具有的一些惊人特征。
爱因斯坦和惠勒认为时空是一个巨大、无特征的床垫结构，具有固定的弯曲和褶皱——一个典型的经典物体。但现在物理学家们了解到，量子力学的两个决定性特征——纠缠和魔力——对应于空间的两个决定性特征——形状和弹性。这表明空间本身就是可想象的最具量子性的事物之一。“引力的所有熟悉方面实际上都是某种量子现象的直接体现，”斯温格尔说。
这也表明引力源于不完美的量子编码。非魔力的编码产生惰性、无引力的空间，因为它们完美地保护了编码信息。曹和合作者已经证明，引力源于编码信息的混合。因此，编码必然是不精确的，因此，通过通常方式测量一小部分量子粒子，时空内部发生的某些方面无法被完美地恢复。这种近似——对于量子计算机来说意味着编码写得很差——是“牛顿的苹果砸在他头上的原因，”捷克说。
就曹而言，他觉得这个特性很有吸引力。他说，量子纠错和量子计算是人类的活动。他认为没有理由认为引力应该迎合我们对完美的偏见。

英文来源：

Entanglement Builds Space-Time. Now “Magic” Gives It Gravity.
In 1973, John Archibald Wheeler described the relationship between space and matter in two sentences: “Space acts on matter, telling it how to move. 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.
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.
Einstein cast gravity not as a force but as the geometric bending of space and time. 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. The weight of the bowling ball compresses the mattress, forming a dimple — matter tells space-time how to curve.
In this analogy, a planet is like a smaller ball. 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.
But general relativity has a fatal flaw. When a star dies and collapses, its mass is concentrated into an unimaginably dense point. The dimple in the mattress stretches into a deep depression, one that essentially rips all the way through. Physicists call this arrangement a black hole. 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.
In the late 1990s, physicists had a stroke of luck. 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.
Theorists have spent the last few decades trying to understand exactly how a space-time constructed from such quantum particles could work. 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. But the origin of Wheeler’s second statement remained mysterious; in their models, matter didn’t tell space how to curve. The bowling ball sat atop the mattress without making a dent.
Until now. Physicists including Charles Cao at Virginia Tech have recently determined how quantum particles could give space-time its bendiness. 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.”
“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. “And, you know, quantum space-time isn’t quite that simple.”
How To Code a Universe
Perspective shifts abound in physics. For instance, there’s more than one way to look at the motion of a pendulum. You might specify its location using the height and the horizontal displacement of the weight hanging at the end of the string. Or you might use the length of the string and its angle instead. The perspectives are equivalent; simple trigonometric equations take you from one perspective to the other.
Mark Belan/Quanta Magazine
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.
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. 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.
In both cases, you could replace the 3D region of space-time with particles on the region’s surface. You could consider the surface to be 2D, like a globe flattened into a paper map. 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.
Over the last couple of decades, theorists have explored what gives the 3D fabric of space its shape. Entanglement, a quantum property that links particles to one another, seems to serve as space’s connective tissue. Take, for instance, a wormhole, a theoretical bridge connecting two distant regions of space. Holographically, a 3D wormhole is equivalent to two entangled sets of particles. Start snipping the “threads” of entanglement that link one set with the other, and the tunnel connecting the regions gets thinner and thinner. Cut the final thread, and the connection dissolves entirely.
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. “Charles spent a month understanding the paper,” said Jason Pollack, then a fellow graduate student, now a physicist at Syracuse University.
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. He needed to encode a space and its matter — stars and planets and electrons — into a bunch of quantum particles. So why not use a quantum error-correcting code?
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. Qubits are extremely delicate, frequently losing their superposition and therefore their extra information. And so physicists have worked out ways to protect this delicate information through redundancy. By spreading out one qubit’s information among many qubits, they can preserve it even if some of the qubits are lost.
The same type of redundancy shows up in holography. “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. 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. 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.
But these codes, known as “stabilizer codes,” had a shortcoming. They divided the entanglement of the particles into two types: one responsible for space and another responsible for matter. And the divide was unbridgeable. 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. But in holography, that perfection left no room for the two to interact. “We knew how to build a space-time,” Czech said, but “this space-time was inert. It didn’t do anything.”
To get space and matter to interact, Cao knew he needed a more sophisticated code. “It was clear that something else beyond entanglement had to be there,” said Ning Bao, a physicist at Northeastern University.
The Magic Ingredient
Cao started by playing around with existing error-correcting codes. 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. It wasn’t gravity, but it was progress. Except that Cao and Lackey didn’t fully understand why the tweak worked.
M.C. Escher
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 Toffoli gate, which flips a qubit under certain circumstances.
Cao took notice. He had just attended a quantum computing conference where researchers were buzzing about Toffoli gates, in part because they are the key to making quantum computers more powerful than classical computers.
Researchers had previously thought the key was entanglement. They had worked out a way of running software on a classical computer that would mimic a quantum task. When that quantum task involved entangling qubits, quantum computers had an advantage over classical computers, as the classical program took ages to run. 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.
In 2004, Alexei Kitaev and Bravyi, both then at Caltech, brought researchers’ attention to Toffoli gates. When a quantum program uses a particular group of quantum operations, including Toffoli gates, the equivalent classical program takes much, much longer to run. Kitaev and Bravyi described the complexity that these operations introduce as “magic.” The more Toffoli gates you need to produce a quantum state, for example, the more magical that state is.
After Cao learned about magic and Toffoli gates, he joined forces with Brian Swingle and Christopher White, both researchers at the University of Maryland. In 2020, they studied collections of particles equivalent to an exotic universe called an anti-de Sitter space. The group found that the particles were highly magical. What would the role of this magic be, they wondered, for the anti-de Sitter space the particles represented?
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. They showed that magic gave space its springiness. Magic, in other words, is connected to space’s ability to bend. And therefore magic is connected to gravity. “If you have one,” Bao said, “you always have the other.”
By early 2026, Cao and his collaborators had all the pieces. They knew that magic made space bend. And they knew that quantum codes got their magic from Toffoli gates. 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. This new code used lots of Toffoli gates. The gates made the code magical, letting the entanglement for space and the entanglement for matter affect each other.
“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. “It should fluctuate.”
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. “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.”
Gravity From Quantumness
In principle, entanglement and magic could be enough for future physicists to simulate space on a quantum computer. But Cao’s new code still needs a lot of work.
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. That’s because his code is still extremely general. 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.
The code is more of a proof of concept of the general shape that a theory of quantum gravity should take. If you want your space to bend, use a magical code. “This gets you a precursor of gravity,” Cao said. “You satisfy one of the necessary conditions. Right now, we are at step 0.5 of 5.”
But even at this early stage, the research program highlights some surprising features that any theory of quantum gravity should have.
Einstein and Wheeler thought of space-time as a large, featureless fabric existing with fixed bends and folds — a typical classical object. 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. This suggests that space itself is one of the most quantum things imaginable. “All the familiar aspects of gravity are actually a very direct manifestation of something quantum,” Swingle said.
It also suggests that gravity results from imperfect quantum encoding. Non-magical codes produce inert, gravity-free spaces because they protect their encoded information perfectly. Cao and collaborators have shown that gravity comes from the mixing of the encoded information. 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. This approximation, which would indicate a poorly written code for a quantum computer, is “the reason Newton’s apple fell on him,” Czech said.
Cao, for his part, finds the feature appealing. Quantum error correction and quantum computing are human pursuits, he said. He sees no reason that gravity should accommodate our prejudice for perfection.