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The researchers ran a model for portfolio optimization on Canadian company D-Wave's 2,000-qubit quantum annealing processor.

Consultancy firm KPMG, together with a team of researchers from the Technical University of Denmark (DTU) and a yet-to-be-named European bank, has been piloting the use of quantum computing to determine which stocks to buy and sell for maximum return, an age-old banking operation known as portfolio optimization.

The researchers ran a model for portfolio optimization on Canadian company D-Wave's 2,000-qubit quantum annealing processor, comparing the results to those obtained with classical means. They foundthat the quantum annealer performed better and faster than other methods, while being capable of resolving larger problems although the study also indicated that D-Wave's technology still comes with some issues to do with ease of programming and scalability.

The smart distribution of portfolio assets is a problem that stands at the very heart of banking. Theorized by economist Harry Markowitz as early as 1952, it consists of allocating a fixed budget to a collection of financial assets in a way that will produce as much return as possible over time. In other words, it is an optimization problem: an investor should look to maximize gain and minimize risk for a given financial portfolio.

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As the number of assets in the portfolio multiplies, the difficulty of the calculation exponentially increases, and the problem can quickly become intractable, even to the world's largest supercomputers. Quantum computing, on the other hand, offers the possibility of running multiple calculations at once thanks to a special quantum state that is adopted by quantum bits, or qubits.

Quantum systems, for now, cannot support enough qubits to have a real-world impact. But in principle, large-scale quantum computers could one day solve complex portfolio optimization problems in a matter of minutes which is why the world's largest banks are already putting their research team to work on developing quantum algorithms.

To translate Markowitz's classical model for the portfolio selection problem into a quantum algorithm, the DTU's researchers formulated the equation into a quantum model called a quadratic unconstrained binary optimization (QUBO) problem, which they based on the usual criteria used for the operation such as budget and expected return.

When deciding which quantum hardware to pick to test their model, the team was faced with a number of options: IBM and Google are both working on a superconducting quantum computer, while Honeywell and IonQ are building trapped-ion devices; Xanadu is looking at photonic quantum technologies, and Microsoft is creating a topological quantum system.

D-Wave's quantum annealing processor is yet another approach to quantum computing. Unlike other systems, which are gate-based quantum computers, it is not possible to control the qubits in a quantum annealer; instead, D-Wave's technology consists of manipulating the environment surrounding the system, and letting the device find a "ground state". In this case, the ground state corresponds to the most optimal portfolio selection.

This approach, while limiting the scope of the problems that can be resolved by a quantum annealer, also enable D-Wave to work with many more qubits than other devices. The company's latest devicecounts 5,000 qubits, while IBM's quantum computer, for example, supports less than 100 qubits.

The researchers explained that the maturity of D-Wave's technology prompted them to pick quantum annealing to trial the algorithm; and equipped with the processor, they were able to embed and run the problem for up to 65 assets.

To benchmark the performance of the processor, they also ran the Markowitz equation with classical means, called brute force. With the computational resources at their disposal, brute force could only be used for up to 25 assets, after which the problem became intractable for the method.

Comparing between the two methods, the scientists found that the quality of the results provided by D-Wave's processor was equal to that delivered by brute force proving that quantum annealing can reliably be used to solve the problem. In addition, as the number of assets grew, the quantum processor overtook brute force as the fastest method.

From 15 assets onwards, D-Wave's processor effectively started showing significant speed-up over brute force, as the problem got closer to becoming intractable for the classical computer.

To benchmark the performance of the quantum annealer for more than 25 assets which is beyond the capability of brute force the researchers compared the results obtained with D-Wave's processor to those obtained with a method called simulated annealing. There again, shows the study, the quantum processor provided high-quality results.

Although the experiment suggests that quantum annealing might show a computational advantage over classical devices, therefore, Ulrich Busk Hoff, researcher at DTU, who participated in the research, warns against hasty conclusions.

"For small-sized problems, the D-Wave quantum annealer is indeed competitive, as it offers a speed-up and solutions of high quality," he tells ZDNet. "That said, I believe that the study is premature for making any claims about an actual quantum advantage, and I would refrain from doing that. That would require a more rigorous comparison between D-Wave and classical methods and using the best possible classical computational resources, which was far beyond the scope of the project."

DTU's team also flagged some scalability issues, highlighting that as the portfolio size increased, there was a need to fine-tune the quantum model's parameters in order to prevent a drop in results quality. "As the portfolio size was increased, a degradation in the quality of the solutions found by quantum annealing was indeed observed," says Hoff. "But after optimization, the solutions were still competitive and were more often than not able to beat simulated annealing."

SEE: The EU wants to build its first quantum computer. That plan might not be ambitious enough

In addition, with the quantum industry still largely in its infancy, the researchers pointed to the technical difficulties that still come with using quantum technologies. Implementing quantum models, they explained, requires a new way of thinking; translating classical problems into quantum algorithms is not straightforward, and even D-Wave's fairly accessible software development kit cannot be described yet as "plug-and-play".

The Canadian company's quantum processor nevertheless shows a lot of promise for solving problems such as portfolio optimization. Although the researchers shared doubts that quantum annealing would have as much of an impact as large-scale gate-based quantum computers, they pledged to continue to explore the capabilities of the technology in other fields.

"I think it's fair to say that D-Wave is a competitive candidate for solving this type of problem and it is certainly worthwhile further investigation," says Hoff.

KPMG, DTU's researchers and large banks are far from alone in experimenting with D-Wave's technology for near-term applications of quantum computing. For example, researchers from pharmaceutical company GlaxoSmithKline (GSK) recently trialed the use of different quantum methods to sequence gene expression, and found that quantum annealingcould already compete against classical computersto start addressing life-sized problems.

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Are quantum computers good at picking stocks? This project tried to find out - ZDNet

The different strategies toward quantum machine learningThey say you should start an article with a cool fancy image. Google 72 qubits chip Sycamore Google

There is a strong hope (and hype) that Quantum Computers will help machine learning in many ways. Research in Quantum Machine Learning (QML) is a very active domain, and many small and noisy quantum computers are now available. Different approaches exist, for both long term and short term, and we may wonder what are their respective hopes and limitations, both in theory and in practice?

It all started in 2009 with the publications of the HHL Algorithm [1] proving an exponential acceleration for matrix multiplication and inversion, which triggered exciting applications in all linear algebra-based science, hence machine learning. Since, many algorithms were proposed to speed up tasks such as classification [2], dimensionality reduction [3], clustering [4], recommendation system [5], neural networks [6], kernel methods [7], SVM [8], reinforcement learning [9], and more generally optimization [10].

These algorithms are what I call Long Term or Algorithmic QML. They are usually carefully detailed, with guarantees that are proven as mathematical theorems. We can (theoretically) know the amount of speedup compared to the classical algorithms they reproduce, which are often polynomial or even exponential, with respect to the number of input data for most of the cases. They come with precise bounds on the results probability, randomness, and accuracy, as usual in computer science research.

While they constitute theoretical proof that a universal and fault-tolerant quantum computer would provide impressive benefits in ML, early warnings [11] showed that some underlying assumptions were very constraining.

These algorithms often require loading the data with a Quantum Random Access Memory, or QRAM [12], a bottleneck part without which exponential speedups are much more complex to obtain. Besides, they sometimes need long quantum circuits and many logical qubits (which, due to error correction, are themselves composed of many more physical qubits), that might not be arriving soon enough.

When exactly? When we will reach the Universal Fault-Tolerant Quantum Computer, predicted by Google in 2029, or by IonQ in only 5 years. More conservative opinion claim this will not happen before 20+ years, and some even say we will never reach that point. Future will tell!

More recently, a mini earthquake amplified by scientific media has cast doubt on the efficiency of Algorithm QML: the so-called dequantization papers [13] that introduced classical algorithms inspired from the quantum ones to obtain similar exponential speedups, in the field of QML at least. This impressive result was then hindered by the fact that the equivalent speedup only concerns the number of data, and comes at a cost of a terrible polynomial slowdown with respect to other parameters for now. This makes these quantum-inspired classical algorithms currently unusable in practice [14].

In the meantime, something very exciting happened: actual quantum computers were built and became accessible. You can play with noisy devices made of 5 to 20 qubits, and soon more. Quite recently Google performed a quantum circuit with 53 qubits [15], the first that could not be efficiently simulable by a classical computer.

Researchers have then been looking at new models that these noisy intermediate scale quantum computers (NISQ) could actually perform [16]. They are all based on the same idea of variational quantum circuits (VQC), inspired by classical machine learning.

The main difference with algorithmic QML is that the circuit is not implementing a known classical ML algorithm. One would simply hope that the chosen circuit will converge to successfully classify data or predict values. For now, there are several types of circuits in the literature [17] and we start to see interesting patterns in the success. The problem itself is often encoded in the loss function we try to decrease: we sum the error made compared to the true values or labels, or compared to the quantum states we aim for, or to the energy levels, and so on, depending on the task. Active research tries to understand why some circuits work better than others on certain tasks, and why quantumness would help.

Another core difference is that many providers [18, 19, 20] allow you to program these VQC so you can play and test them on actual quantum computers!

In recent years, researchers have tried to find use cases where Variational QML would succeed at classical problems, or even outperforms the classical solutions [21, 22]. Some hope that the variational nature of the training confers some resilience to hardware noise. If this happens to be the case, it would be beneficial not to wait for Error Correction models that require many qubits. One would only need Error Mitigation techniques to post-process the measurements.

On the theoretical side, researchers hope that quantum superposition and entangling quantum gates would project data in a much bigger space (the Hilbert Space of n qubits has dimension 2^n) where some classically inaccessible correlations or separations can be done. Said differently, some believe that the quantum model will be more expressive.

It is important to notice that research on Variational QML is less focused on proving computational speedups. The main interest is to reach a more expressive or complex state of information processing. The two approaches are related but they represent two different strategies. Unfortunately, less is proven compared to Algorithmic QML, and we are far from understanding the theoretical reasons that would prove the advantage of these quantum computations.

Of course, due to the limitations of the current quantum devices, experiments are often made on a small number of qubits (4 qubits in the above graph) or on simulators, often ideal or limited to 30+ qubits. It is hard to predict what will happen when the number of qubits will grow.

Despite the excitement, VQC also suffers from theoretical disturbance. It is proven that when the number of qubits or the number of gates becomes too big, the optimization landscape will be flat and hinder the ability to optimize the circuit. Many efforts are made to circumvent this issue, called Barren Plateaus [23], by using specific circuits [24] or smart initialization of the parameters [25].

But Barren Plateaus are not the only caveat. In many optimization methods, one must compute the gradient of a cost function with respect to each parameter. Said differently, we want to know how much the model is improved when I modify each parameter. In classical neural networks, computing the gradients is usually done using backpropagation because we analytically understand the operations. With VQC, operations become too complex, and we cannot access intermediate quantum states (without measuring and therefore destroying them).

The current state-of-the-art solution is called the parameter shift rule [27, 28] and requires to apply the circuit and measure its result 2 times for each parameter. By comparison, in classical deep learning, the network is applied just once forward and once backward to obtain all thousand or millions gradients. Hopefully, we could parallelize the parameter shift rule on many simulators or quantum devices, but this could be limited for a large number of parameters.

Finally, researchers tend to focus more and more on the importance of data loading into a quantum state [29], also called feature map [30]. Without the ideal amplitude encoding obtained with the QRAM, there are doubts that we will be able to load and process high dimensional classical data with an exponential or high polynomial factor. Some hope remains on data independent tasks such as generative models [21, 31] or solving partial differential equations.

Note that the expression Quantum Neural Networks has been used to show the similarities with classical Neural Networks (NN) training. However they are not equivalent, since the VQC dont have the same hidden layers architecture, and neither have natural non linearities, unless a measurement is performed. And theres no simple rule to convert any NN to a VQC or vice versa. Some now prefer to compare VQC to Kernel Methods [30].

We now have a better understanding of the advantages and weaknesses of the two main strategies towards quantum machine learning. Current research is now focused on two aspects:

Finally, and most importantly, improve the quantum devices! We all hope for constant incremental improvements or a paradigm shift in the quality of the qubits, their number, the error correction process, to reach powerful enough machines. Please physicists, can you hurry?

PS: lets not forget to use all this amazing science to do good things that will benefit everyone.

Jonas Landman is a Ph.D. student at the University of Paris under the supervision of Prof. Iordanis Kerenidis. He is Technical Advisor at QC Ware and member of QuantX. He has previously studied at Ecole Polytechnique and UC Berkeley.

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How and when quantum computers will improve machine learning? - Medium