The most important mathematical work in China’s long history is Jiuzhang suanshu (‘Nine Chapters on the Mathematical Art’), a second BC text compiled by generations of scholars.
Now a novel kind of computer named in its honour has lived up to the reputation of this grand book of mathematics where Jui represents ‘9’ and, because it is the largest digit, also means ‘supreme’.
Developed by a team led by Prof Chao-Yang Lu and Jian-Wei Pan at the University of Science and Technology of China, Hefei, the quantum computer has cracked a problem that seems to lie beyond the reach of the ‘classical’ digital computers that run so much of modern life.
Japan’s Fugaku supercomputer, the world’s most powerful classical computer, would take 600 million years to accomplish what Jiuzhang can do in just 200 seconds, said Prof Lu.
The feat is the most convincing yet of what some call quantum advantage, or quantum supremacy.
In 2019, Google was the first to claim quantum supremacy using a quantum computer called Sycamore, which relies on superconducting circuits, that is, which conduct electricity without resistance at low temperatures.
While conventional computers that inhabit our homes, offices and pockets, encode information in the form of bits, which can take the value of 1 or 0, quantum computers such as Sycamore use ‘qubits’, which can represent both a 1 and a 0 at the same time. They are said to be entangled – think of it like interference – so that they can perform parallel computing.
Even though Sycamore had a relatively modest number of quantum bits (qubits) – just 53 – it could sample the solutions of the ‘random circuit sampling problem’ in a mere 200 seconds, whereas the Google team estimated that Summit supercomputer at Oak Ridge National Laboratory in Tennessee, would take 10,000 years to do the same thing, while full verification would take millions of years.
Prof Lu commented: ‘While Google used superconducting circuits inside an ultracold fridge, we used photons – particles of light – at room temperature. It is nice to demonstrate the quantum advantage using different platforms.’
Quantum advantage, or supremacy, does not necessarily indicate that the quantum computers are yet useful. This is because the problems that they are set are selected to be difficult for classical computers and tend to be more esoteric.
Moreover, it remains possible that classical computers can catch up. After Google’s quantum supremacy claim, for example, IBM proposed a type of calculation that might allow a supercomputer to perform the task Google’s computer completed, casting doubt on the claim.
‘All these claims are based on the current optimal classical algorithm/strategy, which may improve as time goes by,’ commented Prof Lu. ‘Quantum computational advantage, rather than being a one-shot experimental proof, will be the result of a long-term competition between a quantum device and classical simulation.’
Jiuzhang is an analogue machine, that is, a computer which exploits the physical properties of a system to tackle a problem. In this case, the problem is called boson sampling, where bosons are one of the basic classes of particles, which includes photons, which are particles of light.
‘We use photons as bosons, not as qubits,’ said Prof Lu, who reported the feat with colleagues in the journal Science. ‘Strictly, the power of Jiuzhang cannot be expressed in terms of qubits.’
Boson sampling entails calculating the probability distribution of many bosons — in this case, photons — after they encounter a device called a beam splitter, which divides a single beam into divergent beams.
The laser light had been manipulated using its quantum properties (in other words, it had been ‘squeezed’) and, because of quantum effects, if two photons of identical properties (position and polarisation) hit the splitter at the same time, they stuck together and both travelled in the same direction.
Only when you send lots of pulses through the device do reliable interference patterns emerge. Jiuzhang sent laser pulses into a maze of 300 beam splitters, 75 mirrors and 100 detectors capable of spotting a single photon. ‘We detected up to 76 photons,’ said Prof Lu.
With enough photons and beam splitters, Jiuzhang could produce a distribution of numbers of photons that – because the problem scales exponentially – lies beyond the reach of a classical computer to calculate: using Jiuzhang the team achieved within minutes what would take half the age of Earth using the best existing supercomputers.
One advantage of digital computers – and Sycamore too – is that they can be programmed to do different things while Jiuzhang is designed only to do boson sampling. ‘Very tricky point,’ said Prof Lu. ‘Most people think that Jiuzhang is not programmable. But, actually, to some extent it already can be. We will try to make use of some tuning knobs in the incoming light to do something useful in a few months.’
Prof Lu added that boson sampling can also be adapted for machine learning, a popular approach to artificial intelligence. ‘We are performing such an experiment and aiming for applications in machine learning,’ said Prof Lu. Compared with conventional computers, photon-based devices such as Jiuzhang offer advantages because they consume a fraction of the power, have higher throughput and work at the speed of light.
There is a limit to what digital computers can do because the binary numbers on which they depend – ones and zeroes – offer a much more limited palette of mathematical possibilities than the continuous, or analogue, quantities of the real world. In contrast, ’Jiuzhang is an analogue device,’ said Prof Lu.
The first computers were also analogue, that is, physical systems configured to be governed by equations identical to the ones you want to solve. The Science Museum Group collection has various analogue machines, such as the ‘differential analyser’ developed by Douglas Hartree at the University of Manchester, capable of solving differential equations that are fundamental to modelling the world because they describe how things change.
Traditional analogue machines were cumbersome in every sense. They represented the quantity they were computing as the size of some part of the apparatus. If you wanted a more accurate answer, you needed a bigger device: because the information is encoded in a physical way (think of the markings on a slide rule, for example) an extra bit of precision doubles the size of the device.
By contrast, abstracting the input data from an analogue form into a string of ones and zeros allows digital computers to be reprogrammed to perform multiple types of calculations, unlike their purpose-built analogue predecessors. However, analogue devices based on light such as Jiuzhang offer new possibilities for fast, low power parallel computing.
There is a deeper, unresolved, issue with quantum computing. There has been unease about the foundations of quantum theory since Albert Einstein, who helped establish the theory and became one of its most dogged critics. The 2020 physics Nobel prize-winner, Sir Roger Penrose, told me recently that, though successful at some things, ‘current quantum mechanics is wrong.’
Quantum mechanics is wrong because it is incomplete, explained Prof Peter Coveney of UCL, who helped organise a quantum computer event in 2019 at the Science Museum. ‘When it comes to quantum computers, for example, it does not explain how you go from the entangled/interference/superposition of zeroes and ones in a qubit to a single output value, a one or a zero.’
Prof Lu commented: ‘quantum mechanics is 120 years old but some of the very fundamental issues still bother us today.’