内容来源：https://www.quantamagazine.org/biology-might-not-be-quantum-but-its-math-is-quantumlike-20260923/

内容总结：

一项新近发表于《量子》杂志的综述指出，尽管生命活动本身可能并不依赖真正的量子效应，但生物系统中复杂的经典网络却能在数学层面模拟量子行为。普林斯顿大学化学家格雷戈里·斯科尔斯及其合作者提出，生命或许并非利用量子相干或纠缠，而是通过演化出的复杂振荡网络，产生与量子系统数学形式相似的“类量子”状态。这些状态虽非真正量子，却遵循希尔伯特空间中的矢量规则，可表现出叠加与干涉等特征。

这一观点为量子生物学提供了新方向。自20世纪30年代以来，科学家一直猜测光合作用的高效性可能源于量子相干，但后续研究表明早期观测到的“拍频”信号源于分子振动共振，而非长寿命量子相干。斯科尔斯因此对生命能否在温暖潮湿的细胞环境中维持量子态持怀疑态度。他转而研究复杂网络如何涌现出可数学描述为量子态的行为，并证明特定振荡器网络能模拟量子比特及其逻辑门。

维也纳量子光学与量子信息研究所的物理学家马库斯·穆勒表示，斯科尔斯的工作展示了类量子行为如何从自然界常见的复杂网络中自然涌现。北卡罗来纳州立大学的量子化学家萨布尔·凯斯认为，这对量子机器学习和复杂系统建模具有应用潜力。但研究人员也提醒，数学上的相似不应被误认为物理上的等同，量子词汇不宜随意用于经典系统描述。

尽管生命可能并非真正量子化，但支配微观世界的数学结构似乎在宏观复杂经典系统中重新浮现，这为理解生命与量子世界的关系提供了新视角。

中文翻译：

生物学或许并非量子性的，但其数学却类量子

Xavi Bou

二十年前，科学家们似乎即将以一种全新的量子视角来理解生物学。

生命的展开跨越了令人难以想象的尺度范围，从一端包裹整个地球的生物圈，到另一端构成细胞的单个生物分子。然而，即便在其最微观的层面，生物学其实也并未真正触及量子领域——在那个领域中，粒子表现为波，彼此纠缠，并同时存在于多种状态的叠加之中。但量子生物学领域的科学家们正在探索，生物体是否可能将量子性推入与生命相关的空间、时间和温度尺度，从而利用其奇异特性。

例如，在光合作用中，生物体利用特化的色素和蛋白质以近乎完美的量子效率捕获光能；它们将几乎每一个入射光子转化为有用的化学能。2007年，新证据表明生命可能通过利用一种称为“相干性”的量子效应来实现这一壮举。这一结果支撑了一个颇具争议的观点：尽管活细胞处于温暖、潮湿且明确属于经典范畴的环境中，它仍能维持——甚至利用——脆弱的量子态。

普林斯顿大学的化学家格雷戈里·斯科尔斯最初对这一结果充满热情。他和同事们随后对进行光合作用的蛋白质和色素开展了实验，得出了类似的结论。但如今，斯科尔斯对量子效应在生命中发挥作用持怀疑态度。事实上，他确信量子生物学的前进方向可能根本与量子无关。斯科尔斯提出，生命或许并非利用真正的量子效应，而是在模仿它们。在过去三年发表的多篇论文中，斯科尔斯及其同事表明，由经典物体构成的复杂网络可以协同产生在数学上模拟量子物体的现象。

不要被迷惑：这些网络所产生的状态并非真正的量子态；它们只是“类量子”的。当许多相互作用的振荡部件汇集成一个集体整体时，这些状态便会涌现，而其行为遵循与量子世界预测相同的数学规律。

“也许最大尺度上的量子生物学，意味着利用35亿年的进化来解决如何获得你本可以从量子系统中得到的功能，”斯科尔斯说。

维也纳量子光学与量子信息研究所的物理学家马库斯·穆勒表示，量子力学基础领域的研究者数十年来一直在探索如何以经典方式重现量子世界的某些方面。穆勒说，斯科尔斯所做的，是展示了类量子行为如何从相对平凡的复杂网络中涌现——而这类网络在自然界中比比皆是。

“经典系统可以模拟量子信息的某些关键特征，”萨布雷·凯斯说，他是一位在北卡罗来纳州立大学为复杂系统开发量子计算算法的量子化学家。“这是一个令人兴奋的新方向。”

量子生物学的边界

将生命的奥秘重新解释为量子性质的诱惑，几乎与量子力学本身一样古老。在1929年的一次演讲中，量子先驱尼尔斯·玻尔发表了含糊却引人入胜的论述：量子力学——当时才刚刚开始找到其数学根基——“或许具有决定性的重要意义，尤其是在讨论生命体在我们世界观中的位置时。”

玻尔的同时代人帕斯夸尔·约尔丹花了数十年撰写关于“量子生物学”的著作，主张生命具有一种独特能力，能将量子世界奇异的非确定性放大到宏观尺度，并声称这是人类思维和自由意志的基础。遗传学家兼进化生物学家J.B.S.霍尔丹在1934年的一篇论文中呼应了约尔丹的观点，认为将量子非确定性放大到更大尺度的能力正是生命之所以特殊的原因。（约尔丹于1933年加入纳粹党及其准军事组织，他试图将量子生物学与纳粹主义挂钩，损害了该领域的信誉。）

这些量子生物学的早期倡导者试图用量子尺度上反直觉的物理定律来解释经典尺度上生命令人费解的特性。一个经典粒子在同一时间只能处于一个位置、以一种方式存在；而一个量子粒子则弥散在它可能存在的所有位置和方式之中，仿佛一种可能性的波。这种弥散用波函数来数学描述，波函数如同经典波一样，有波峰和波谷。

在粒子被观测之前，它所有可能的构型实际上同时存在。它们以叠加态堆叠在一起，就像重叠的水波或声波。而如同重叠的波一样，叠加的量子态会相互叠加、相互抵消，或以其他方式相互转化。当叠加态中的量子态具有足够规整的波特性以这种方式相互影响时，它们被称为相干的。相干的量子系统还可以彼此纠缠，本质上融合为一个具有共享波函数的单一统一实体。

量子态是精致脆弱的东西；一旦与外部世界发生碰撞，它们就很容易被破坏。即便极少量的环境噪声，比如热运动引起的原子抖动，也能触发退相干——即坍缩为经典行为。（量子计算机被深度冷却可不仅仅是为了好玩。）而在细胞内部，退相干基本上应该是瞬时发生的——量子性在这样一种环境中不可能存活足够长的时间，从而对生物学产生任何影响。

诚然，即便在细胞中，像氢原子这样极其微小的粒子也可以发生“量子隧穿”，穿越那些原本会减缓或阻止它们通过的能量壁垒。而且有证据表明，某些酶中的隧穿效应可以解释其快速的反应速率。但斯科尔斯说，这并非量子生物学家真正追求的东西。这种隧穿并不涉及长寿命的相干性。其中所涉及的量子性很简单、转瞬即逝，而且某种程度上是不可避免的——即便在一瓶死的化学物质中，一些微小粒子也会隧穿能量壁垒。问题在于，生命能否做到死的化学做不到的事：将量子态保持在相干状态足够长的时间，从而将相干性本身作为一种资源来利用。

光捕获的失望

科学家们最早在20世纪30年代就开始设想量子相干性可以解释光合作用非凡效率的可能性。

光合生物利用称为光捕获复合体的色素和蛋白质阵列来吸收光。当一个光子击中这些复合体之一时，其电磁能被吸收，并将复合体中的一个电子激发到激发态。这个准粒子——称为激子——向反应中心移动，在那里被转化为化学能，从而驱动光合作用的关键步骤。

Xavi Bou

这一过程几乎具有100%的效率：几乎每一个被吸收的光子最终都驱动了光合作用。科学家们曾认为，如果激子在光捕获复合体中的多个分子之间保持量子相干性，它们就能同时探索通往反应中心的多条路径，而不是漫无目的地跳跃并可能迷失方向。

2007年，加州大学伯克利分校的格雷厄姆·弗莱明利用来自一种细菌的色素和蛋白质光捕获复合体检验了这一想法。他和同事们用极快的激光脉冲泵浦这些色素和蛋白质以产生激子，然后用后续脉冲对其进行探测。这揭示了同步的“拍频”信号，在当时看来似乎是激子通过量子相干性相互干涉的证据。包括斯科尔斯在内的其他研究人员也进行了类似实验，发现了类似的拍频——甚至在室温下进行的实验中也是如此。

但就在量子生物学开始蓄势之际，它撞上了一堵墙。经过更仔细的审查，弗莱明团队所描述的那类拍频信号，结果反映的并非量子相干性，而是振动的分子键之间的共振。这种共振是一种有趣的效应，科学家们至今仍在研究，但它并非长寿命、长程的量子相干性。

“人们很失望，”格拉斯哥大学的光生物学家理查德·科格德尔说。“如果这背后真的有什么东西，如果真的存在某种此前无人意识到的生物学特殊之处，那将会非常令人兴奋。”

研究人员曾假设量子效应在多种生物现象中发挥作用——包括帮助鸟类导航的磁感应，以及更具推测性的人类意识——但实证支持程度不一。然而在目前，对于任何具有生物学功能的长寿命量子相干性，仍然没有确凿的证据。

斯科尔斯越来越怀疑，在生命中放大相干性和纠缠等效应究竟是否可能。“正是这种放大才让人觉得了不起。而真正的量子世界并不会那样放大，”他说。

在2023年12月的一次会议上，斯科尔斯就推动该领域发展需要什么进行了一次对话。他回忆说，回到酒店房间后，他记下了一个想法：也许量子生物学中的“量子”根本不来自量子力学，而是从横跨巨大复杂网络的波状涟漪中涌现出来的。

“我现在确信，你可以获得变革性的效应，但它们会来自经典系统对你用量子系统所能做的事情的模仿，”斯科尔斯说。“如果你分辨不出区别，那还有关系吗？”

类量子态的世界

斯科尔斯想知道，复杂网络中特殊同步态的出现——比如鸟群或鱼群——是否可能产生类量子行为。

剥离量子态中的物理内容，剩下的数学对象是一个向量——一组有序排列的数字，就像数学可能性空间中某个位置的坐标。量子态在一种称为希尔伯特空间的特殊向量空间中表示。

希尔伯特空间中的向量遵循特定规则。其中一条规则是，任意两个态可以相加，结果也是一个有效向量，归一化后将产生一个有效的量子态。这在数学上正是量子叠加所表达的。如果态之间具有规整的相位关系，使它们能够干涉——根据对齐方式而叠加或抵消——那么它们就是相干的。希尔伯特空间中向量的坐标包含对应于这种波峰波谷对齐方式的信息，称为波的相位。

Xavi Bou

瑞典林奈大学的数学家安德烈·赫连尼科夫在20世纪90年代开始借用量子力学的数学来建模概率时，注意到了量子干涉与经典世界之间的联系。他的核心思想是，概率性结果——在神经科学和经济学等不同领域中——可以像叠加态中的量子态一样自我干涉。

2024年，斯科尔斯找到了一种方法，设计出振荡器的复杂网络，使其产生涌现态——即同步行为的稳定模式，就像一群人齐声拍手——这些状态可以在数学上描述为希尔伯特空间中的向量。具体而言，他表明可以构建网络来产生涌现态，这些态在数学上模拟最简单的量子单元：量子比特，它有两个态（如1或0），并且可以存在于两者的叠加态中。

“这严格地源于图的数学结构，”普渡大学的计算机科学家伊桑·迪基说。“如果你以某些并非不合理的方式构建图，它们恰好会涌现出这个非常优美、非常优雅的数学对象，它模拟——或几乎逼近——一个量子对象。”

重新定义量子生物学

截然不同的物理可以支撑相似的数学形式。飞行中棒球的抛物线弧和仙人掌刺尖端的抛物线弧都可以用二次方程来描述，但两者由不同的力所塑造。因此，经典世界与量子世界之间的数学联系不应被误认为是物理联系。

关于生命中的量子效应，既有严肃研究也有奇思妙想，历史颇为复杂。渥太华大学的物理学家易卜拉欣·卡里米认为，研究人员应对这种数学联系过于当真保持谨慎。他称赞斯科尔斯的新框架优雅，并认为它可能有用，但他认为量子词汇不应出现在经典系统附近。卡里米指出，干涉并非什么神秘或量子的事物。它不过是波行为方式的一个特征。

研究人员希望更好地理解经典系统何时以及如何能够模拟量子数学。这些知识可能有助于厘清关于生命中量子效应的争议性主张——包括在大脑中的那些。

在热衷于将生命与量子领域联系起来的研究人员中，大脑长期以来一直是强烈关注和激烈争论的焦点。例如，1989年，罗杰·彭罗斯复活了关于量子物理是自由意志基础的老旧观点；他提出意识源于大脑中称为微管的蛋白质丝网络中的量子效应。很少有神经科学家认真对待这一观点。

在这样的背景下，当赫连尼科夫邀请马克斯·普朗克学会恩斯特·斯特伦曼研究所的神经生理学家沃尔夫·辛格参加一个关于类量子建模的研讨会时，辛格最初持怀疑态度。

辛格及其同事在2025年表明，将振荡引入一种特定的简单神经网络可以使其更高效、更稳健。辛格说，利用干涉本质上给了网络一个可以利用的新维度：时间。这是因为振荡的相位编码了关于事件在时间上如何相对于彼此组织的信息。研讨会之后，辛格说他“对一些现实世界现象也许用他们在量子物理中使用的描述技术来描述会更好这一事实印象深刻。”

Xavi Bou

类量子态还为有意设计网络提供了概念蓝图——这些网络可以是任何东西，从电路到神经元再到由弹簧耦合的物理摆——从而利用叠加和干涉来进行计算。在后续工作中，斯科尔斯及其同事表明，可以将类量子比特连接在一起以产生更大的网络，这些网络也是类量子态，并展示了如何设计一个网络来模拟“逻辑门”的量子版本——一种用于执行简单计算的电路。

迪基和他的博士联合导师凯斯相信，类量子态在量子机器学习和复杂系统建模中具有“强大的实际应用潜力”。但这些应用面临局限：当你开始将类量子比特连接在一起时，底层网络的复杂性会急剧膨胀。要完美模拟量子逻辑门，“你需要无限的资源，物理资源，”斯科尔斯说。

迪基在斯科尔斯工作的基础上，确定了产生类量子态的网络特性，并正在努力寻找计算上高效的方法来产生它们。他还在2026年发表了研究，展示了如何设计网络来产生比斯科尔斯原始框架所允许的更多种类的量子态。

就斯科尔斯而言，他感兴趣的是理解经典世界中类量子态的极限。他正在努力确定经典系统是否可能有意义地模拟纠缠。

即便生物学最终并不像研究人员曾经希望的那样具有量子性，生命世界与量子领域之间可能仍然存在有趣的——且可能具有启发性的——平行之处。尽管量子叠加随着尺度的增大而消散，但支配存在中最小、最简单之物的数学的某些方面，似乎在我们所知的最庞杂、最复杂的经典系统中重新浮现。

英文来源：

Biology Might Not Be Quantum, but Its Math Is Quantumlike
Xavi Bou
Two decades ago, scientists seemed on the verge of understanding biology in a new, quantum way.
Life unfolds over an incomprehensible span of scales, from our planet-enveloping biosphere at one end, to individual cell-building biomolecules at the other. Even at its most microscopic, though, biology doesn’t really reach down to the quantum realm, in which particles act like waves, become entangled with one another, and exist in superpositions of multiple states at once. But scientists in the field of quantum biology are searching for ways that organisms might be able to push quantumness into the space, time, and temperature domains relevant to life, to make use of its strange properties.
In photosynthesis, for example, organisms use specialized pigments and proteins to harvest light with nearly perfect quantum efficiency; they convert almost every incoming photon into useful chemical energy. In 2007, new evidence suggested that life might accomplish this feat by taking advantage of a quantum effect called coherence. The result buoyed the controversial idea that, despite being a warm, wet, and decidedly classical environment, a living cell could maintain — and even exploit — fragile quantum states.
Gregory Scholes, a chemist at Princeton University, was initially enthusiastic about the result. He and colleagues followed up with experiments on photosynthesizing proteins and pigments and came away with similar conclusions. But today, Scholes is skeptical that quantum effects play a role in life. In fact, he’s convinced that the way forward for quantum biology might not be quantum at all. Rather than taking advantage of genuine quantum effects, Scholes proposes, life might be imitating them instead. In several papers published over the past three years, Scholes and colleagues have shown that complex networks of classical objects can conspire to produce phenomena that mathematically mimic quantum objects.
Don’t be fooled: The states that these networks produce are not truly quantum; they’re only “quantumlike.” They arise when many interacting, oscillating parts add up to a collective whole whose behavior obeys the same mathematics that makes predictions about the quantum world.
“Maybe quantum biology, at the biggest scales, means using 3 1/2 billion years of evolution to work out how to get the functionality that you could get from quantum systems,” Scholes said.
Researchers in the foundations of quantum mechanics have been exploring how to classically re-create certain aspects of the quantum world for decades, said Markus Müller, a physicist at the Institute for Quantum Optics and Quantum Information in Vienna. What Scholes has done, Müller said, is show how quantumlike behavior can emerge from relatively unremarkable complex networks — of the sort that abound in nature.
“Classical systems can mimic some of the key features of quantum information,” said Sabre Kais, a quantum chemist developing quantum computing algorithms for complex systems at North Carolina State University. “This is an exciting new direction.”
The Bounds of Quantum Biology
The temptation to recast life’s mysteries as quantum in nature is about as old as quantum mechanics itself. In a 1929 lecture, the quantum pioneer Niels Bohr made the vague but enticing statement that quantum mechanics, which at the time was just starting to find its mathematical footing, “may perhaps be of decisive importance, particularly in the discussion of the position of living organisms in our picture of the world.”
Bohr’s contemporary Pascual Jordan spent several decades writing on Quantenbiologie, or quantum biology, arguing that life has a unique ability to amplify the strange indeterminism of the quantum world to macroscopic scales, and claiming this as the basis of human thought and free will. J.B.S. Haldane, a geneticist and evolutionary biologist, echoed Jordan in a 1934 paper arguing that the ability to scale up quantum indeterminacy was what made life special. (Jordan, who joined the Nazi Party and its paramilitary forces in 1933, damaged the credibility of quantum biology by attempting to link it to Nazism.)
These early proponents of quantum biology sought explanations for the puzzling properties of life at the classical scale in the counterintuitive laws of physics at the quantum scale. A classical particle can be in only one place, in one way, at a time; a quantum particle is smeared out across all the places and ways it could potentially be, in a kind of wave of possibility. This smear is described mathematically by a wave function which, like a classical wave, has peaks and troughs.
Until a particle is observed, all of its possible configurations effectively exist at once. They’re stacked up in superposition, like overlapping waves of water or sound. And like overlapping waves, stacked quantum states add up, cancel one another out, or otherwise transform each other. When quantum states in superposition have tidy enough wave properties to affect each other this way, they’re called coherent. Coherent quantum systems can also become entangled with each other, essentially merging into a single, unified entity with a shared wave function.
Quantum states are delicate things; they’re easily destroyed when jostled against the outside world. Even a tiny amount of environmental noise, like the atomic jiggle of heat, can trigger decoherence, a collapse into classical behavior. (Quantum computers aren’t supercooled just for fun.) And in the interior of a cell, decoherence should be basically instantaneous — quantumness shouldn’t survive long enough in such an environment to have any bearing on biology.
It’s true that, even in a cell, very, very small particles like hydrogen atoms can “quantum tunnel,” popping up beyond energetic barriers that would otherwise slow them down or prevent them from crossing. And there’s evidence that tunneling in certain enzymes could explain their speedy reaction rates. But that’s not really what quantum biologists are after, Scholes said. There’s no long-lived coherence involved in this kind of tunneling. The quantumness involved is simple, fleeting, and kind of unavoidable — even in a flask of dead chemicals, some tiny particles will tunnel through energetic barriers. The question is whether life can do what dead chemistry can’t: hold quantum states in coherence long enough to use coherence itself as a resource.
A Light-Harvesting Letdown
Scientists first toyed with the idea that quantum coherence could explain the remarkable efficiency of photosynthesis as early as the 1930s.
Photosynthetic organisms use arrays of pigments and proteins called light-harvesting complexes to soak up light. When a photon strikes one of these complexes, its electromagnetic energy is absorbed and boosts an electron in the complex into an excited state. This quasiparticle — called an exciton — heads toward a reaction center, where it is transformed into chemical energy that can perform the key steps of photosynthesis.
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The process is nearly 100% efficient: Almost every single photon absorbed ends up powering photosynthesis. Scientists thought that if excitons maintained quantum coherence across multiple molecules in the light-harvesting complex, they could simultaneously explore several routes to the reaction center, rather than hopping around haphazardly and potentially getting lost.
In 2007, Graham Fleming of the University of California, Berkeley tested this idea using a light-harvesting complex of pigments and proteins from a bacterium. He and his colleagues pumped the pigments and proteins with extremely fast pulses of laser light to generate excitons, then probed them with follow-up pulses. This revealed synchronized “beats” that, at the time, seemed like evidence that excitons were interfering with each other via quantum coherence. Other researchers, including Scholes, performed similar experiments and found similar beats — even in experiments conducted at room temperature.
But just as quantum biology started to build momentum, it hit a wall. Upon closer examination, beats like the ones that Fleming’s team described turned out to reflect not quantum coherence, but a resonance between wiggling molecular bonds. The resonance was an interesting effect that scientists are still working out, but it wasn’t long-lived, long-range quantum coherence.
“People were disappointed,” said Richard Cogdell, a photobiologist at the University of Glasgow. “It would be exciting if there really was something to this, and there was something special about biology that no one had realized before.”
Researchers have hypothesized that quantum effects are at play in a variety of biological phenomena — including the magnetic sense that helps birds navigate and, more speculatively, human consciousness — with varying degrees of empirical support. But at this point, there’s still no definitive proof for any long-lived quantum coherence with a biological function.
Scholes has grown skeptical that scaling up effects such as coherence and entanglement in life is possible at all. “It’s that scale-up that gets the wow factor. And the real quantum world isn’t going to scale up like that,” he said.
At a conference in December 2023, Scholes had a conversation about what needed to happen to advance the field. He recalls returning to his hotel room and jotting down an idea: Maybe the “quantum” in quantum biology doesn’t come from quantum mechanics at all, but emerges out of wavelike ripples across huge, complex networks.
“I’m now convinced that you could get transformative effects, but they would come from classical systems mimicking what you can do with quantum systems,” Scholes said. “Does it matter if you can’t tell the difference?”
A World of Quantumlike States
Scholes wondered if the emergence of special synchronized states in complex networks, like flocks of birds or schools of fish, might produce quantumlike behavior.
Strip away the physics from a quantum state, and the mathematical object you’re left with is a vector — an ordered list of numbers that acts like coordinates for a location in a mathematical space of possibilities. Quantum states are represented in a particular kind of vector space called a Hilbert space.
Vectors in Hilbert space follow specific rules. One of those rules says that any two states can be added together, and the result will also be a valid vector that, once normalized, will yield a valid quantum state. This is, mathematically, what quantum superposition gets at. States are coherent if they have neat phase relationships that allow them to interfere — adding up or canceling out, depending on how they line up. The coordinates of a vector in Hilbert space include information that corresponds to this alignment of peaks and troughs, called a wave’s phase.
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Andrei Khrennikov, a mathematician at Linnaeus University in Sweden, noticed a connection between quantum interference and the classical world in the 1990s when he began borrowing mathematics from quantum mechanics to model probabilities. His idea, essentially, was that probabilistic outcomes — in fields as different as neuroscience and economics — can interfere with themselves like quantum states in superposition.
In 2024, Scholes found a way to design complex networks of oscillators such that they produced emergent states — stable patterns of synchronized behavior, like a crowd that claps in time — that could be mathematically described as vectors in a Hilbert space. Specifically, he showed that networks can be constructed to produce emergent states that mathematically mimic the simplest quantum unit: a qubit, which has two states (like 1 or 0) and can exist in a superposition of both.
“This strictly arises from the mathematical structure of the graph,” said Ethan Dickey, a computer scientist at Purdue University. “If you build graphs in certain ways which are not that unreasonable, they happen to pop up with this very nice, very elegant mathematical object that simulates — or almost approaches — a quantum object.
Redefining Quantum Biology
Very different physics can underlie similar mathematical forms. Both the parabolic arc of a flying baseball and the parabolic arc at the tip of a cactus spine can be described using quadratic equations, but the two are fashioned by different forces. So a mathematical connection between the classical and quantum worlds shouldn’t be mistaken for a physical one.
There’s a complicated history of both serious research and fanciful speculation about quantum effects in life. Ebrahim Karimi, a physicist at the University of Ottawa, thinks researchers should be careful about putting too much stock in this mathematical link. He praises Scholes’ new framework for its elegance and says it could be useful, but he thinks quantum vocabulary doesn’t belong anywhere near classical systems. Interference isn’t anything mysterious or quantum, Karimi pointed out. It’s simply a feature of how waves behave.
Researchers want to gain a better understanding of when and how classical systems can mimic quantum math. That knowledge could be helpful for sorting out contentious claims about quantum effects in life — including in the brain.
Among researchers keen to connect life to the quantum realm, the brain has long been a focus of intense interest and plenty of heated debate. In 1989, for instance, Roger Penrose revived old ideas about quantum physics as the basis for free will; he proposed that consciousness arises from quantum effects in the brain, in networks of protein filaments called microtubules. Few neuroscientists take this view seriously.
Given that context, Wolf Singer, a neurophysiologist at the Ernst Strüngmann Institute of the Max Planck Society, was initially skeptical when Khrennikov invited him to a workshop on quantumlike modeling.
Singer and colleagues showed in 2025 that introducing oscillations into a particular kind of simple neural network makes them more efficient and robust. Singer said that using interference essentially gave the network a new dimension to work with: time. This was because the phase of an oscillation encodes information about how events are structured in time relative to each other. After the workshop, Singer said he was “impressed by the fact that some real-world phenomena are maybe better described using the description techniques they use in quantum physics.”
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Quantumlike states also provide a conceptual blueprint for intentionally engineering networks — which could be anything from electrical circuits to neurons to physical pendulums coupled by springs — that can take advantage of superposition and interference to compute. In follow-up work, Scholes and his colleagues showed that it’s possible to wire together quantumlike bits to produce bigger networks, which are also quantumlike states, and demonstrated how a network could be designed to mimic the quantum version of a “logic gate,” a circuit used to perform a simple computation.
Dickey and his doctoral co-supervisor, Kais, believe quantumlike states have “strong potential for practical applications” in quantum machine learning and in modeling complex systems. But those applications face limitations: The complexity of the underlying network blows up when you start wiring quantumlike bits together. To perfectly mimic quantum logic gates, “you need to have infinite resources, physical resources,” Scholes said.
Dickey has built on Scholes’ work to pin down network properties that produce quantumlike states and is working to find computationally efficient ways to produce them. He also published work in 2026 showing how networks can be designed to produce more kinds of quantum states than Scholes’ original framework allowed.
For his part, Scholes is interested in understanding the limits of quantumlike states in the classical world. He’s working to determine whether it’s possible for classical systems to meaningfully mimic entanglement.
Even if biology is ultimately not as quantum as researchers once hoped, there may still be interesting — and potentially illuminating — parallels between the living world and the quantum realm. Although quantum superpositions dissolve with increasing scale, aspects of the math that governs the smallest, simplest stuff of existence seem to resurface in the most sprawling, complex classical systems we know.