摘要：A powerful new idea about how the laws of physics work could bring breakthroughs on everything from quantum gravity to consciousness, says researcher Chiara Marletto

“QUANTUM supremacy” is a phrase that has been in the news a lot lately. Several labs worldwide have already claimed to have reached this milestone, at which computers exploiting the wondrous features of the quantum world solve a problem faster than a conventional classical computer feasibly could. Although we aren’t quite there yet, a general-purpose “universal” quantum computer seems closer than ever – a revolutionary development for how we communicate and encrypt data, for virtual reality, artificial intelligence and much more.

These prospects excite me as a theoretical physicist too, but my colleagues and I are captivated by an even bigger picture. The quantum theory of computation originated as a way to deepen our understanding of quantum theory, our fundamental theory of physical reality. By applying the principles we have learned more broadly, we think we are beginning to see the outline of a radical new way to construct laws of nature.

It means abandoning the idea of physics as the science of what’s actually happening, and embracing it as the science of what might or might not happen. This “science of can and can’t” could help us tackle some of the big questions that conventional physics has tried and failed to get to grips with, from delivering an exact, unifying theory of thermodynamics and information to getting round conceptual barriers that stop us merging quantum theory with general relativity, Einstein’s theory of gravity. It might go even further and help us to understand how intelligent thought works, and kick-start a technological revolution that would make quantum supremacy look modest by comparison.

Since the dawn of modern physics in Galileo Galilei and Isaac Newton’s times, physics has progressed using broadly the same approach. At its core are exact laws of motion: equations that describe how a system evolves in space and time from a given set of initial conditions. Think Newton’s laws of motion describing billiard balls on a table, or his universal law of gravitation explaining how apples fall to the ground and Earth moves around the sun.

“Physical laws are our manual to the universe, and the best laws are exact”

The word “exact” is important here. If you were to buy a device such as a washing machine, a manual stating how to use it approximately, plus or minus some error, would be pretty useless. Physical laws are our tentative manual to the universe, and the best laws are exact ones, too: they are easier to test and discard when they clash with evidence.

At least initially, quantum theory changed nothing about this traditional approach. At the heart of the theory when it was first formulated in the 1920s is an exact equation of motion, the Schrödinger equation, which determines how quantum systems evolve. The big difference from the classical world is that this equation tells us that quantum objects obey Heisenberg’s uncertainty principle. This states that certain quantum properties are incompatible, meaning they can’t be measured simultaneously to arbitrarily high accuracy: if you have one property perfectly focused, you must lose sight of the other. Position and velocity are one such pair, so if you have an electron’s position, say, perfectly in focus, it must be in a quantum “superposition” of all its possible velocities. The values of an electron’s quantum-mechanical spin along two different axes are another incompatible pair.

Examining the nature of the uncertainty principle back in the 1980s led quantum computing pioneer David Deutsch to a radical insight. The best way to think about an electron in a certain spin state, for example, is as a “qubit” – an entity that can instantiate one bit of information in multiple ways that can’t all be sharp, or in focus, at the same time. What’s important about this qubit – the essence of its quantumness – isn’t the trajectories it follows in space and time, but the transformations you can and can’t perform on it. For instance, you can’t copy all the information reliably from a single qubit, but all that information about its incompatible properties exists, and can be used to perform quantum computations.

Actual to counterfactual

These rules of “can” and “can’t” surrounding qubits and their incompatible variables make them much more powerful than classical bits, and underlie the promise of quantum computers and quantum supremacy. More fundamentally, however, they tell us that, rather than always focusing on what happens (the actual), you can lay the foundations of a physical theory on what could or couldn’t be (the counterfactual), and explain the actual in terms of the counterfactual.

Now comes the daring leap: what if these “can and can’t” properties were key to the whole of physics? Instead of starting from initial conditions and exact dynamical laws, you might express physics in terms of laws of possible and impossible transformations, and derive other laws of motion from these.

This counterfactual approach isn’t an entirely new mode of thinking in physics. The first and second laws of thermodynamics, as conceived in the 19th century, set powerful counterfactual constraints. You can, for example, construct a “heat engine” that converts heat to useful work, but you can’t convert heat completely into useful work, or create energy out of nothing.

Thermodynamics is a formidable tool: its principles allow us to make predictions about systems with large numbers of particles, for instance, whose dynamical laws are intractable. Generalising this logic, the science of can and can’t allows us to formulate new principles and improve on existing ones (see “A new thermodynamics“) – and, perhaps surprisingly, express more phenomena in terms of exact physical laws.

Information is a crucial example. What physical property makes a computer bit capable of containing information? Not that it is in a particular state, 0 or 1, but that you can, once it has been set to 0, set it to 1, and vice versa – and also that you can copy its value to another physical system, if it too is made of bits. These properties are counterfactuals that the traditional physical approach of explaining everything with dynamical laws struggles to handle.

The science of can and can’t allows us to express exact physical laws capturing the regularities that allow bits to exist in the universe. What’s more, these laws explain classical bits – the state of a traffic light or a neuron in the brain – just as well as qubits. You don’t need to worry about underlying laws of motion, whether quantum or classical or anything else. Far from being irreconcilable, quantum and classical information are unified by general overarching principles about how you can and can’t manipulate it.

That bodes well for making progress on merging quantum theory and general relativity. Notoriously, these theories, our best current guides to the universe, are fundamentally incompatible. While quantum theory requires masses to display Heisenberg uncertainty, general relativity doesn’t allow it. In terms of information theory, gravity is fundamentally a classical entity – one that can support only bits, not qubits.

“The ‘universal constructor’ is an all-powerful 3D printer that can be used to make anything possible”

To unify the theories, we need to treat quantum and classical information on the same footing – and the science of can and can’t does just that. My colleague Vlatko Vedral and I have already done preliminary work using its principles to constrain existing and future proposals for quantum gravity. They can also be used to make predictions in contexts where both theories matter, but neither fully applies, such as in the interior of black holes or in the first moment of the big bang.

The potential advantages don’t stop there, however. Can/can’t rules about the manipulation of information don’t depend on the existence of subjective beings to observe what is happening. They can therefore give us an objective handle on other properties based on information that, in the traditional approach, seem only subjectively defined and thus out of the reach of physics.

The most interesting property of this type is knowledge: the kind of resilient information brought about by evolution and created in our brains when we think. In the can and can’t picture, knowledge is described not in terms of subjective features of knowing about things, but simply as information that can enable its own survival. On this basis, we can attempt to formulate exact physical laws about how knowledge is created, or whether it is finite or unbounded – questions that are beyond traditional physics.

Being capable of producing knowledge is a characteristic trait of conscious entities, so an exact theory of knowledge, fully rooted within physics, would be an essential stepping stone towards a theory of consciousness or general artificial intelligence. It might give us new tools to look for alien life too. At present, we are limited to searching for life elsewhere in the cosmos by looking for its chemical signatures, even though we have no guarantee it is based on the same chemistry as the life we do know. A physical theory of knowledge is likely to provide more generally applicable predictions.

But is it true?

As yet, these ideas are all theoretical, but there are promising avenues to test them. One concerns the phenomenon known as entanglement, a type of correlation between different particles or qubits that is stronger than any classical correlation between the properties of two objects. Vedral and I have shown that the science of can and can’t predicts what transformations are possible for two qubits interacting with another object that may or may not obey quantum theory, such as a macroscopic biomolecule, or even gravity. As a result, we can test for the presence of elusive quantum effects in an unknown system by setting up an experiment in which this “mystery” object is the only channel of interaction between the two qubits. If the mystery object can entangle the qubits, then we can conclude that it must have some quantum features, in a way that is independent of the laws of motion governing the unknown system.

Several groups are now trying to test this experimentally, having the qubits be two quantum masses and the unknown system be gravity. If entanglement were to be observed, it would be the first empirical refutation of classical theories of gravity, including general relativity, as well as the first test of the principles of the science of can and can’t.

That is an exciting prospect, even if making such experiments work is challenging and probably still a few years away yet. But let’s circle back to where we started, with the idea of the technological breakthroughs we anticipate on the back of a universal quantum computer. In the 1940s, mathematician John von Neumann pointed out that the universal computer, one capable of all physically permitted computations, isn’t the most universal machine that can be programmed. He conceived the “universal constructor”, a machine that can perform all physically possible transformations – essentially an all-powerful 3D printer that, provided with the requisite knowledge, can be programmed to produce anything that is physically possible.

Von Neumann never managed to develop a physical basis for his universal constructor, let alone engineer one. The science of can and can’t, when fully developed, is the best candidate for the theory that underlies the universal constructor. That is why the collection of research projects aiming to implement the science of can and can’t is called the Constructor Theory Programme. Originally proposed by David Deutsch, it is now being pursued by my group at the University of Oxford, and our collaborators at the Centre for Quantum Technologies in Singapore, and the Institute for Scientific Interchange and Italian National Metrology Institute, both in Turin.

Our hope is that constructor theory will be critical for the technological revolution after quantum computation, just as thermodynamics helped spur the original industrial revolution, or Alan Turing’s ideas about universal computation informed the information-technology revolution.

Will it be? The honest answer is that it is too soon to tell. Science is tentative: the faster we make errors, the more chances we have to make progress. Physics is full of open problems that are too often swept under the carpet. Far from being undesirable, they are rich opportunities to find the next breakthrough. There is no guarantee that the science of can and can’t will succeed, but it will teach us a lot of new physics by solving some of those problems. It already has. There’s a saying that “the best way to predict the future is to invent it”. The science of can and can’t is one of our most promising bets to invent the future.

A NEW THERMODYNAMICS

Thermodynamics is all about things you can and can’t do. One consequence of the second law of thermodynamics, for instance, is that when heat is generated, say through friction on a flywheel, you can’t reverse the energy transfer and convert the heat back entirely into useful work, say to drive a piston. This seems to clash with the reversible laws governing the microscopic particles of the flywheel and piston, which say that if a forward motion is allowed, so is its reverse.

The standard way of explaining away this contradiction is to say that thermodynamic laws are “emergent” approximations of what is going on at microscopic scales. They are valid only in a statistical sense for large numbers of particles: the reversible, microscopic laws of motion are the fundamental laws.

One consequence is that the laws of thermodynamics as they stand are insufficient to build engines made of just a few particles, a stumbling block on the way to developing nanomachines. These could have a plethora of applications, from repairing cells in our bodies to removing harmful chemicals from the atmosphere.

CYCLING BACKWARDS

The “science of can and can’t” approach that my colleagues and I are developing (see main story) takes a different path. It says that a thermodynamic transformation is possible when it can be brought about on a system to an arbitrarily high accuracy, with an arbitrarily small error, by an entity that operates in a cycle, reliably.

So, for example, a mechanical stirrer can increase the temperature of an otherwise isolated mass of water by increasing the kinetic energy of its molecules. But here, reversing the trajectory doesn’t perform the inverse operation of cooling the water: that requires a refrigerator, a cyclic machine that goes far beyond just the stirrer’s atoms running backwards.

So being able to transform something doesn’t always mean that its reverse transformation is possible – and irreversibility formulated in terms of possibility and impossibility doesn’t clash with time-reversal-symmetric laws. In the science of can and can’t, it is possible to formulate an upgraded second law of thermodynamics that is valid, exactly, at all scales, and regardless of the dynamical laws the particles are following.

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