NATUREIVol 440130 March 2006 ESSAY Quantum mechanics in the brain Does the enormous computing power of neurons mean consciousness can be explained within a purely neurobiological framework,or is there scope for quantum computation in the brain? Christof Koch and Klaus Hepp The relation between quantum mechanics and higher brain functions,including con- sciousness,is often discussed,but is far from being understood.Physicists,ignorant of modern neurobiology,are tempted to assume a formal or even dualistic view of the mind-brain problem.Meanwhile,cog- nitive neuroscientists and neurobiologists consider the quantum world to be irrelevant to their concerns and therefore do not attempt to understand its concepts.What can we confidently state about the current A thought experiment involving an observer looking at a superimposed quantum relationship between these two fields of system with one eye,and at a succession of faces with the other,challenges the idea scientific inquiry？ that a quantum framework is needed to explain consciousness. All biological organisms must obey the laws ofphysics,both classical and quantum. intact organisms.Most quantum physicists computation seeks to exploit the In contrast to classical physics,quantum view the brain as a classical instrument. parallelism inherent in entangle- mechanics is fundamentally indeterminis- The critical question we are concerned ment by assuring that the system is tic.It explains a range of phenomena that with here is whether any components of the very likely to converge on the computa- cannot be understood within a classical nervous system-a 300-degrees Kelvin tis- tionally desirable result. context:the fact that light or any small par- sue strongly coupled to its environment- This requires that the qubits are well iso- ticle can behave like a wave or particle display macroscopic quantum behaviours, lated from the rest of the system.Coupling depending on the experimental setup such as quantum entanglement,that are key the system to the external world is necessary (wave-particle duality);the inability to to the brain's function. for the preparation of the initial state(the simultaneously determine,with perfect Specific molecular machines and pro- input);for the control of its evolution;and accuracy,both the position and momentum teins have been proposed to implement for the actual measurement (the output). of an object(Heisenberg's uncertainty prin- quantum computations.The best known of However,all these operations introduce ciple);and the fact that the quantum states such proposals is Penrose and Hameroff's 'noise'into the computation(decoherence) of multiple objects,such as two coupled hypothesis that the tubulin components of Although some decoherence can be com- electrons,may be highly correlated even microtubules,filamentous protein poly- pensated for by redundancy and other fault- though the objects are spatially separated, mers that form the cytoskeleton of cells, tolerant techniques,too much is fatal. thus violating our intuitions about locality implement quantum computations. In spite of an intensive search by many (entanglement). laboratories,no scalable large quantum Major philosophical and conceptual Lessons from quantum computers computers are known.The record for quan- problems surround the process of making When kings build,their followers team up tum computation is the factoring of the measurements in quantum mechanics.To in international journals and conferences, number 15 by liquid-state nuclear magnetic illuminate the paradoxical nature of super- confusing the general public about the dis- resonance(NMR)techniques.Qubits anda position-that is,the fact that particles or tinction between science and poetry.But set of universal quantum gates have been quantum bits(qubits)are allowed to exist large quantum systems are notoriously dif- proposed in many different implementa- in a superposition of states-Schrodinger ficult to analyse rigorously,except in highly tions,but all solutions have serious draw- proposed a celebrated thought experi- idealized models or limits.Estimates based backs:photons interact only weakly with ment:a sealed box containing the quan- on the same unrealistic one-particle model, one another;nuclear spins in individual tum superposition of both a dead and a applied to trillions of interacting particles, molecules are few in number in current live cat.When an observer peers inside the show discrepancies often orders of magni- devices,as are trapped atoms or ions.This box,measuring its content,the wave func- tude in the work of different authors.It is paints a desolate picture for quantum com- tion,which describes the probability that therefore better to turn to hard experimen- putation inside the wet and warm brain. the system will be found in any one partic- tal realities and abstract computational Although brains obey quantum mech- ular state,is said to collapse,and the sys- theory to find the neural correlates of anics,they do not seem to exploit any of its tem will be found in one or the other state quantum processes in the brain. special features.Molecular machines,such with known probability. Quantum computations are difficult to as the light-amplifying components of pho The role of the conscious observer in this implement.In its simplest version,a quan- toreceptors,pre-and post-synaptic recep measuring process has been hotly debated tum computer transforms the state of tors and the voltage-and ligand-gated since the early days of quantum mechanics. many two-dimensional qubits using a channel proteins that span cellular mem- It is fair to say,however,that consciousness reversible,linear,probability-conserving branes and underpin neuronal excitability has been only a place holder in a chain of mapping via a sequence ofexternally con- are so large that they can be treated as classi- mathematical formulae,without much rel- trollable quantum gates into a final state cal objects.(Their relative molecular masses evance to the study of neural circuits in with a probabilistic outcome.Quantum range from 20,000 to 200,000;the two main 2006 Nature Publishing Group
© 2006 Nature Publishing Group NATURE|Vol 440|30 March 2006 ESSAY 611 ESSAY Quantum mechanics in the brain Does the enormous computing power of neurons mean consciousness can be explained within a purely neurobiological framework, or is there scope for quantum computation in the brain? Christof Koch and Klaus Hepp The relation between quantum mechanics and higher brain functions, including consciousness, is often discussed, but is far from being understood. Physicists, ignorant of modern neurobiology, are tempted to assume a formal or even dualistic view of the mind–brain problem. Meanwhile, cognitive neuroscientists and neurobiologists consider the quantum world to be irrelevant to their concerns and therefore do not attempt to understand its concepts. What can we confidently state about the current relationship between these two fields of scientific inquiry? All biological organisms must obey the laws of physics, both classical and quantum. In contrast to classical physics, quantum mechanics is fundamentally indeterministic. It explains a range of phenomena that cannot be understood within a classical context: the fact that light or any small particle can behave like a wave or particle depending on the experimental setup (wave–particle duality); the inability to simultaneously determine, with perfect accuracy, both the position and momentum of an object (Heisenberg’s uncertainty principle); and the fact that the quantum states of multiple objects, such as two coupled electrons, may be highly correlated even though the objects are spatially separated, thus violating our intuitions about locality (entanglement). Major philosophical and conceptual problems surround the process of making measurements in quantum mechanics. To illuminate the paradoxical nature of superposition — that is, the fact that particles or quantum bits (qubits) are allowed to exist in a superposition of states — Schrödinger proposed a celebrated thought experiment: a sealed box containing the quantum superposition of both a dead and a live cat. When an observer peers inside the box, measuring its content, the wave function, which describes the probability that the system will be found in any one particular state, is said to collapse, and the system will be found in one or the other state with known probability. The role of the conscious observer in this measuring process has been hotly debated since the early days of quantum mechanics. It is fair to say, however, that consciousness has been only a place holder in a chain of mathematical formulae, without much relevance to the study of neural circuits in intact organisms. Most quantum physicists view the brain as a classical instrument. The critical question we are concerned with here is whether any components of the nervous system — a 300-degrees Kelvin tissue strongly coupled to its environment — display macroscopic quantum behaviours, such as quantum entanglement, that are key to the brain’s function. Specific molecular machines and proteins have been proposed to implement quantum computations. The best known of such proposals is Penrose and Hameroff ’s hypothesis that the tubulin components of microtubules, filamentous protein polymers that form the cytoskeleton of cells, implement quantum computations. Lessons from quantum computers When kings build, their followers team up in international journals and conferences, confusing the general public about the distinction between science and poetry. But large quantum systems are notoriously difficult to analyse rigorously, except in highly idealized models or limits. Estimates based on the same unrealistic one-particle model, applied to trillions of interacting particles, show discrepancies of ten orders of magnitude in the work of different authors. It is therefore better to turn to hard experimental realities and abstract computational theory to find the neural correlates of quantum processes in the brain. Quantum computations are difficult to implement. In its simplest version, a quantum computer transforms the state of many two-dimensional qubits using a reversible, linear, probability-conserving mapping via a sequence of externally controllable quantum gates into a final state with a probabilistic outcome. Quantum computation seeks to exploit the parallelism inherent in entanglement by assuring that the system is very likely to converge on the computationally desirable result. This requires that the qubits are well isolated from the rest of the system. Coupling the system to the external world is necessary for the preparation of the initial state (the input); for the control of its evolution; and for the actual measurement (the output). However, all these operations introduce ‘noise’ into the computation (decoherence). Although some decoherence can be compensated for by redundancy and other faulttolerant techniques, too much is fatal. In spite of an intensive search by many laboratories, no scalable large quantum computers are known. The record for quantum computation is the factoring of the number 15 by liquid-state nuclear magnetic resonance (NMR) techniques. Qubits and a set of universal quantum gates have been proposed in many different implementations, but all solutions have serious drawbacks: photons interact only weakly with one another; nuclear spins in individual molecules are few in number in current devices, as are trapped atoms or ions. This paints a desolate picture for quantum computation inside the wet and warm brain. Although brains obey quantum mechanics, they do not seem to exploit any of its special features. Molecular machines, such as the light-amplifying components of photoreceptors, pre- and post-synaptic receptors and the voltage- and ligand-gated channel proteins that span cellular membranes and underpin neuronal excitability, are so large that they can be treated as classical objects. (Their relative molecular masses range from 20,000 to 200,000; the two main A thought experiment involving an observer looking at a superimposed quantum system with one eye, and at a succession of faces with the other, challenges the idea that a quantum framework is needed to explain consciousness. Q. PAUL/AIP Essay 30.3 jw 27/3/06 10:49 AM Page 611 ©2006 NaturePublishingGroup
ESSAY NATUREIVol 440130 March 2006 dimers of tubulin are around 55,000.) are much more powerful than conventional with the following thought experiment Two key biophysical operations underlie algorithms(based on classical physics),are Visual psychology has caught up with information processing in the brain:chem implemented in the nervous system.The magicians and has devised numerous tech- ical transmission across the synaptic cleft, most famous of these is Shor's procedure for niques for making things disappear.For and the generation of action potentials. factoring large integers for data encryption. instance,if one eye of a subject receives a These both involve However,in the stream ofhighly salient images,a constant thousands ofions and "Many previously mysterious past decade no image projected into the other eye is only neurotransmitter aspects of perception are quantum algorithm seen infrequently.Such perceptual sup molecules,coupled by explainable in terms of of similar power pression can be exploited to study whether diffusion or by the and applicability to consciousness is strictly necessary to the membrane potential neuronal processing." Shor's has been collapse of the wave function that extends across found.And factor- Say an observer is looking at a super- tens of micrometres.Both processes will ing large numbers is not something for imposed quantum system,such as destroy any coherent quantum states.Thus, which the brain has much use. Schrodinger's box with the live and dead spiking neurons can only receive and send Why should evolution have turned to cat,with one eye while his other eye sees a classical,rather than quantum,informa quantum computation,so fickle and capri succession of faces (see figure).Under the tion.It follows that a neuron either spikes at cious,ifclassical neural-network computa- appropriate circumstances,the subject is a particular point in time or it does not,but tions are evidently entirely sufficient to deal only conscious of the rapidly changing is not in a superposition of spike and non- with the problems encountered by nervous faces,while the cat in the box remains spike states. systems? invisible to him.What happens to the cat? The power of quantum mechanics is The conventional prediction would be often invoked for problems that brains solve Food for thought that as soon as the photons from this efficiently.Computational neuroscience is At this point,intrepid students of the mind quantum system encounter a classical a young field and theories of complex point to qualia,the constitutive elements of object,such as the retina of the observer, neural systems,with all the variability ofliv consciousness.The subjective feelings asso- quantum superposition is lost and the cat ing matter,will never reach the precision of ciated with the redness ofred or the painful- is either dead or alive. physical laws of well-isolated simple sys- ness of a toothache are two distinct qualia. This is true no matter whether the tems.It has already been demonstrated, As long as it remains mysterious how the observer consciously saw the cat in the box however,that many previously mysterious physical world gives rise to such sensations or not.If,however,consciousness is truly aspects of perception and action are could one of the more flamboyant interpre necessary to resolve the measurement explainable in terms of conventional neu- tations of quantum mechanics explain con- problem,the animal's fate would remain ronal processing. sciousness?Most provocatively,Roger undecided until that point in time when the Two examples are models for the rapid Penrose has claimed that brains can evalu- cat in the box becomes perceptually domi- recognition ofobjects(for example,animals ate noncomputable functions;that this abil- nant to the observer.This seems unlikely or faces)in natural scenes,with perfor- ity is related to consciousness;that both this but could,at least in principle,be empiri- mance approaching that of human ability and consciousness require a yet-to- cally verified. observers,and the attentional selection of be-discovered theory of quantum gravity The empirical demonstration of slowly objects in cluttered images.The necessary and that microtubules are the sites of the decoherent and controllable quantum bits mathematical operations-such as changes associated quantum gates. in neurons connected by electrical or chem- in synaptic weights,evaluating the inner The problem of consciousness and its ical synapses,or the discovery of an efficient product between presynaptic activity and neuronal correlates is beginning to emerge quantum algorithm for computations per- synaptic weight,multiplication and station- in outlines.The content of consciousness is formed by the brain,would do much to ary nonlinearities-are available to neu rich and highly differentiated.It is associ- bring these speculations from the'far-out rons.Indeed,there is an embarras de richesse ated with the firing activity of a very large to the mere 'very unlikely:Until such of computational primitives implemented number of neurons spread all over the cor- progress has been made,there is little rea- by synapses,dendrites and neurons.That is tex and associated satellites,such as the son to appeal to quantum mechanics to not to suggest that we understand how thalamus.Thus,any one conscious percept explain higher brain functions,including brains compute.But so far,there seems to be or thought must be expressed in a wide consciousness no need for quantum skyhooks. flung coalition of neurons firing together The reason for the unprecedented com- Even if quantum gates exist within the con Christof Koch is in the Division of Biology and putational power of nervous systems is fines of neurons,it remains totally nebulous the Division of Engineering and Applied Sci- their high degree of parallelism.For how information of relevance to the organ- ence,216-76,California Institute of Technol- instance,filter-like operations in retinal or ism would get to these quantum gates. ogy,Pasadena,California 91125,USA. cortical cells in the visual stream are per- Moreover,how would it be kept coherent Klaus Hepp and Christof Koch are at the formed simultaneously on an entire image across the milli-and centimetres separating Institute of Neuroinformatics,the University and thus are not limited by the tyranny of individual neurons when synaptic and spik- of Zurich and ETH.Zurich.Switzerland. a single processor.Furthermore,unlike the ing processes,the primary means of neu von Neumann architecture of the pro- ronal communication on the perceptual FURTHER READING grammable digital computer,the brain Hepp,K in Quantum Future:Lecture Notes in Physics timescale,destroy quantum information? (eds Blanchard,P.&Jadczyk,A.)517,92-104(1998). intermixes memory elements in the form It is far more likely that the material basis Koch,C.Biophysics of Computation:Information of modifiable interconnections within the of consciousness can be understood within Processing in Single Neurons (Oxford Univ.Press,New computational substrate,the neuronal York1999). a purely neurobiological framework,with- Koch.C.ne Ouest for Conscrousness.A U∩ membrane.Thus,no separate memory out invoking any quantum-mechanical Neurobiological Approach (Roberts,Colorado,2004) fetch'and 'store'cycles are necessary. deus ex machina. Nielsen,M.Chuang,I.Quontum Computation ond Much of the hope that quantum mechan We challenge those who call upon con Quantum Information (Cambridge Univ.Press, Cambridge,2002). ics works in the brain is pinned to the sup- sciousness to carry the burden of the mea- Penrose,R.The Emperor's New Mind (Oxford Univ position that quantum algorithms,which surement process in quantum mechanics Press,Oxford 1989). 612 2006 Nature Publishing Group
© 2006 Nature Publishing Group ESSAY NATURE|Vol 440|30 March 2006 612 ESSAY dimers of tubulin are around 55,000.) Two key biophysical operations underlie information processing in the brain: chemical transmission across the synaptic cleft, and the generation of action potentials. These both involve thousands of ions and neurotransmitter molecules, coupled by diffusion or by the membrane potential that extends across tens of micrometres. Both processes will destroy any coherent quantum states. Thus, spiking neurons can only receive and send classical, rather than quantum, information. It follows that a neuron either spikes at a particular point in time or it does not, but is not in a superposition of spike and nonspike states. The power of quantum mechanics is often invoked for problems that brains solve efficiently. Computational neuroscience is a young field and theories of complex neural systems, with all the variability of living matter, will never reach the precision of physical laws of well-isolated simple systems. It has already been demonstrated, however, that many previously mysterious aspects of perception and action are explainable in terms of conventional neuronal processing. Two examples are models for the rapid recognition of objects (for example, animals or faces) in natural scenes, with performance approaching that of human observers, and the attentional selection of objects in cluttered images. The necessary mathematical operations — such as changes in synaptic weights, evaluating the inner product between presynaptic activity and synaptic weight, multiplication and stationary nonlinearities — are available to neurons. Indeed, there is an embarras de richesse of computational primitives implemented by synapses, dendrites and neurons. That is not to suggest that we understand how brains compute. But so far, there seems to be no need for quantum skyhooks. The reason for the unprecedented computational power of nervous systems is their high degree of parallelism. For instance, filter-like operations in retinal or cortical cells in the visual stream are performed simultaneously on an entire image and thus are not limited by the tyranny of a single processor. Furthermore, unlike the von Neumann architecture of the programmable digital computer, the brain intermixes memory elements in the form of modifiable interconnections within the computational substrate, the neuronal membrane. Thus, no separate memory ‘fetch’ and ‘store’ cycles are necessary. Much of the hope that quantum mechanics works in the brain is pinned to the supposition that quantum algorithms, which are much more powerful than conventional algorithms (based on classical physics), are implemented in the nervous system. The most famous of these is Shor’s procedure for factoring large integers for data encryption. However, in the past decade no quantum algorithm of similar power and applicability to Shor’s has been found. And factoring large numbers is not something for which the brain has much use. Why should evolution have turned to quantum computation, so fickle and capricious, if classical neural-network computations are evidently entirely sufficient to deal with the problems encountered by nervous systems? Food for thought At this point, intrepid students of the mind point to qualia, the constitutive elements of consciousness. The subjective feelings associated with the redness of red or the painfulness of a toothache are two distinct qualia. As long as it remains mysterious how the physical world gives rise to such sensations, could one of the more flamboyant interpretations of quantum mechanics explain consciousness? Most provocatively, Roger Penrose has claimed that brains can evaluate noncomputable functions; that this ability is related to consciousness; that both this ability and consciousness require a yet-tobe-discovered theory of quantum gravity and that microtubules are the sites of the associated quantum gates. The problem of consciousness and its neuronal correlates is beginning to emerge in outlines. The content of consciousness is rich and highly differentiated. It is associated with the firing activity of a very large number of neurons spread all over the cortex and associated satellites, such as the thalamus. Thus, any one conscious percept or thought must be expressed in a wideflung coalition of neurons firing together. Even if quantum gates exist within the confines of neurons, it remains totally nebulous how information of relevance to the organism would get to these quantum gates. Moreover, how would it be kept coherent across the milli- and centimetres separating individual neurons when synaptic and spiking processes, the primary means of neuronal communication on the perceptual timescale, destroy quantum information? It is far more likely that the material basis of consciousness can be understood within a purely neurobiological framework, without invoking any quantum-mechanical deus ex machina. We challenge those who call upon consciousness to carry the burden of the measurement process in quantum mechanics with the following thought experiment. Visual psychology has caught up with magicians and has devised numerous techniques for making things disappear. For instance, if one eye of a subject receives a stream of highly salient images, a constant image projected into the other eye is only seen infrequently. Such perceptual suppression can be exploited to study whether consciousness is strictly necessary to the collapse of the wave function. Say an observer is looking at a superimposed quantum system, such as Schrödinger’s box with the live and dead cat, with one eye while his other eye sees a succession of faces (see figure). Under the appropriate circumstances, the subject is only conscious of the rapidly changing faces, while the cat in the box remains invisible to him. What happens to the cat? The conventional prediction would be that as soon as the photons from this quantum system encounter a classical object, such as the retina of the observer, quantum superposition is lost and the cat is either dead or alive. This is true no matter whether the observer consciously saw the cat in the box or not. If, however, consciousness is truly necessary to resolve the measurement problem, the animal’s fate would remain undecided until that point in time when the cat in the box becomes perceptually dominant to the observer. This seems unlikely but could, at least in principle, be empirically verified. The empirical demonstration of slowly decoherent and controllable quantum bits in neurons connected by electrical or chemical synapses, or the discovery of an efficient quantum algorithm for computations performed by the brain, would do much to bring these speculations from the ‘far-out’ to the mere ‘very unlikely’. Until such progress has been made, there is little reason to appeal to quantum mechanics to explain higher brain functions, including consciousness. ■ Christof Koch is in the Division of Biology and the Division of Engineering and Applied Science, 216-76, California Institute of Technology, Pasadena, California 91125, USA. Klaus Hepp and Christof Koch are at the Institute of Neuroinformatics, the University of Zürich and ETH, Zürich, Switzerland. FURTHER READING Hepp, K. in Quantum Future: Lecture Notes in Physics (eds Blanchard, P. & Jadczyk, A.) 517, 92–104 (1998). Koch, C. Biophysics of Computation: Information Processing in Single Neurons(Oxford Univ. Press, New York, 1999). Koch, C. The Quest for Consciousness: A Neurobiological Approach (Roberts, Colorado, 2004). Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2002). Penrose, R. The Emperor’s New Mind (Oxford Univ. Press, Oxford 1989). “Many previously mysterious aspects of perception are explainable in terms of neuronal processing.” Essay 30.3 jw 27/3/06 10:49 AM Page 612 ©2006 NaturePublishingGroup