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EINSTEIN once said that God does not play dice, alluding to his scepticism about quantum theory’s ability to describe reality. His opinion is common sense to a realist. Every object and every piece of information should exist in a definite state. Yet quantum mechanics predicts otherwise – that objects could exist in “superpositions”, and a cat could be simultaneously dead and alive.

A century of experiments support quantum physics, yet Einstein’s statement continues to haunt us. If the underlying world is quantum, we do not directly see it that way. Even information from quantum experiments is recorded in a “classical” way – in words on a piece of paper, or as a series of 0s and 1s on a computer. Why then is nature ultimately quantum mechanical?

A clue to this enigma may emerge from some of the most unlikely places, with links to far more practical concerns – the design of cities, the understanding of the economy and the dynamics of human societies. At first this might appear surprising, for these topics seem to have little to do with each other, and much less with quantum theory. Yet, when experts in these fields gathered in September for the World Economic Forum meeting committed to “improving the state of the world”, it emerged that they had much in common.

The topic that permeated many discussions and presentations – those of economists, politicians and social scientists alike – was the struggle to understand systems that are inherently complex. Here we want to argue that not only can quantum theory play a role in this endeavour, but using it in this way presents a surprising opportunity

to put Einstein’s concerns to rest.There are good reasons to be interested

in complex systems. Things would be easy if everything followed simple rules. If, for instance, the housing market alternated between boom and bust each week, then who wouldn’t be an economic expert? Anyone could make the right investments by tracking whether the current week is boom or bust – a feat that requires remembering no more than a single bit of information, just a 0 or 1.

But real-world systems are vastly more complex. Our economy consists of a mind-boggling network of interconnected components. Perturbations in one sector can have immense consequences – as witnessed during the 2008 financial crisis. This culminates in a rich tapestry of behaviour, requiring us to keep track of far more than the single bit of information involved in our simplified example.

This complexity is also a blessing. A world operating in predictable “boom-bust” cycles depending on a single bit would be a boring world indeed. Complex systems form the basis of our society, whose different institutions – schools, courts, factories and so on – work together to move our society beyond that of a simple hunter-gatherer lifestyle. Meanwhile, life itself demands complexity – cells in our

body work in unison to keep us functioning. Without complexity, life could not exist. The fact that our universe turns out to be complex is probably very fortunate for us.

So it is no surprise that the understanding of complex systems was of great interest at the World Economic Forum, where discussions revolved around how to accurately predict and mitigate the next disaster, whether financial, humanitarian or ecological.

Our capacity to answer such questions may be crucial for our survival.

The fundamental principle that underlies the understanding of complex systems is cause and effect. We record information from the past and make use of it to gain greater knowledge in the future. This is illustrated in the movie 21, in which a group of MIT graduates take on the casinos of Las Vegas by playing black-jack. Playing this game with no knowledge of what cards were previously dealt will always give the casino an edge. Yet, by tracking this information players can better predict their future odds of winning, and twist the game in their favour. The systems that were discussed at the World Economic Forum, however, are far more complex, and the amount of relevant past information is immense.

This is where a quantum theory of complexity that we have developed comes in. This may appear paradoxical at first. Whether

Zen and the art of quantum complexity Being two things at once may simplify reality say physicists Mile Gu and Vlatko Vedral

ProfileVlatko Vedral is professor of quantum information theory at the University of Oxford and the National University of Singapore. Mile Gu is assistant professor at the Center for Quantum Information, Tsinghua University, China

“ Complex systems form the basis of our society and life itself demands complexity”

OPINION THE BIG IDEA

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it is a game of cards, or the institutions that underlie the economy, all follow “classical” logic, so how can quantum mechanics help?

It turns out that for many processes, even the optimal classical models are wasteful because they require information from the past that has no bearing on the future. Take,

for example, a simple variation of the boom-bust economy. Instead of a guaranteed boom after every bust, suppose it happens with a probability of 80 per cent. Let X now be the variable that represents whether the previous week was boom or bust. It is clear X is a cause of future events, and thus must be recorded to make beneficial future investments. However, observing only the future, it is not possible to tell with certainty whether the previous week

was a boom or bust, showing some of the information we stored is never reflected in future statistics, and is thus wasted. The potential consequences are dramatic. In 1961, the physicist Rolf Landauer showed that each bit of wasted information also wastes extra energy (incidentally, the environmental heating due to computation was also a big topic at the World Economic Forum meeting).

Einstein’s ideal Quantum logic offers improvement. X need not take on a definite value. We may store the conditions “X = bust” and “X = boom” in a superposition. Thus a quantum computer saves memory by never knowing exactly whether a system is in boom or bust. Yet, surprisingly, we found that a quantum computer can still simulate many physical processes with no loss of accuracy compared to its classical counterparts (Nature Communications, doi.org/ww5). Einstein’s lamentation has become a virtue.

Saving just part of a bit may not sound very significant. But the more complex the process being modelled, the greater the amount of wasted information when using classical logic and assuming a definite reality. The further we are from Einstein’s ideal of a totally classical universe, the less information we require to fully understand the complex processes of everyday life. To a person capable of storing and processing quantum information, the universe could look far simpler. This offers a new paradigm, where our notion of complexity ultimately depends on the information theory we use.

In using quantum theory to understand complexity, we open a rare window of insight into quantum theory itself. If we simulate a process, then every bit of information necessary to make optimal future predictions is a bit of information we must store within our computer. The capacity for quantum computers to record less information without sacrificing predictive power points towards simpler simulations and, ultimately, a simpler view of reality.

The aesthetic of simplicity has an almost universal human appeal. Indeed, in the words of Isaac Newton: “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances,” a statement that has guided scientific development since its inception.

In answer to Einstein, we could say that a god might play dice because of a love of simplicity too. n

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The strange rules of the quantum world offer a simpler view of reality

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