&Bullet; *physics* 14, 79

Machine quantum learning techniques accelerate the task of classifying data provided by a small network of quantum sensors.

Quantum technologies are growing rapidly, driven by the interaction between science, government, start-ups and large companies such as Google, IBM, Microsoft and Amazon. Quantum communication systems, including quantum cryptographic networks, have been used on a large scale; Quantum metrology schemes, such as atomic clocks, provide the state of the art for high-precision measurements; and quantum computers are entering an early industrial age. Still, the “quantum jungle” of available devices and protocols remains difficult to navigate, and researchers still have to work to identify the most promising avenues to quantum technologies that can be socially beneficial. Now shows a collaboration between two teams at the University of Arizona – under the direction of Zheshen Zhang respectively [1] . With the help of a machine learning algorithm, the team classifies data from a network of interlinked sensors (Fig. 1). By comparing their schema with a schema with classical data processing, they show that entanglement can increase both the accuracy and the speed of the classification. The work paves the way for a wide range of quantum-enhanced classification methods that could be made possible by quantum technologies in the near future.

There are good reasons to be optimistic about the future of quantum computers. But building a universal, fault-tolerant quantum computer – one that can correct errors due to imperfections in its operation or environmental disturbances – is a daunting task. Fault tolerant quantum computers that can be scaled to solve meaningful problems are still a decade away (plus or minus infinity, given the uncertainty inherent in such predictions). In the meantime, however, the field of quantum simulation is advancing. Devices known as variation quantum self solvers hold promise for solving difficult problems in quantum chemistry [2, 3] and to perform data classification tasks [4] . The performance of these quantum devices can be further increased by integrating techniques that originate from the emerging field of machine learning. But can this potential be realized with the quantum hardware available in the near future, ie noisy medium-scale quantum devices (NISQ)? [5] ? And can quantum machine learning algorithms offer a real advantage over the powerful, classic machine learning methods that are already available?

The work of Zhang, Zhuang and co-workers explores a path for quantum-enhanced data processing that results from the connection of quantum machine learning with the most established quantum technologies: quantum sensors and metrology. A well-known example of such technologies is the quantum logic clock, which was first developed by Nobel Prize winner David Wineland and colleagues [6] . Through the use of quantum computation methods, including the manipulation of entanglement, this type of watch achieves unprecedented precision in measuring time – it is by many criteria the most accurate measuring instrument ever made by humans. Related techniques have advanced the measurement of other quantities (electric and magnetic fields, mass, acceleration, and more) and are approaching levels of precision near the ultimate limits set by the laws of quantum mechanics.

The combination of techniques from the mature field of quantum measurement technology with techniques from quantum computing is therefore particularly promising. Recent theoretical and experimental work has shown the potential of using quantum machine learning techniques to directly process “quantum data” captured by quantum measurement and sensing devices and optimize tasks such as measurement, discrimination and data classification. Such direct processing has advantages over the processing of classical data with quantum techniques, which require an interface called quantum random access memory (qRAM) that loads classical data into a quantum computer [7] . However, this technology is still in its infancy.

The work of Zhang and Zhuang’s teams focuses on a particularly fascinating case – a network of quantum sensors. The use of quantum information processing techniques to combine and analyze the quantum outputs of multiple sensors holds great promise for realizing a quantum advantage. The potential gain arises from a fundamental characteristic of quantum measurement technology: the advantage of the coherent processing of sensor data scales as the square root of the dimension of the so-called Hilbert space, which represents the quantum states recorded by the network. Since the dimension of this Hilbert space scales exponentially with the number of analyzed states, the quantum advantage for a quantum sensor network scales exponentially with the number of sensors.

The teams are conducting the first experimental study that applies quantum machine learning to quantum sensor networks, which provides a compelling indication of a quantum advantage. The authors construct a sensor network that generates entangled states and encodes such states in high-frequency signals. They then design a quantum protocol to classify these signals based on certain characteristics of their amplitude-phase relationship. One such protocol, known as supervised learning and supported by an entangled quantum network, uses variation optimization techniques (analogous to training a deep neural network) to identify an optimal quantum measurement for analyzing the states and classifying the quantum data.

The authors examine a framework that can be generalized to data classification problems in many other physical domains. You analyze an experimental setup in which a classic signal in the quantum sensors generates a quantum state. Then they compare the optimal signal-discriminating measurements for two cases. In the first, the states generated by the quantum sensors are measured individually and the measurement results are processed in the classic way. In the second, the states generated by the sensors are processed by a quantum network that performs entanglement operations between the states generated by the various sensors. In both cases, the measurements are optimized by variation techniques in order to minimize the classification error using the established support vector machine (SVM) method. SVM classifies data about the quantum states by finding optimal “hyperplanes” that separate the states in a vector space. The researchers found that the quantum SVM significantly reduces the error rate of the classification compared to the error rate of a classic SVM.

This first experimental demonstration is carried out with only three quantum sensors – a tiny “quantum step” for the tiny “quantum feet” offered by current technologies. However, the method can easily be extended to a higher number of sensors and, given the exponential scaling, promises a dramatic increase in the performance of large sensor networks. Importantly, such an improvement can be achieved with quantum information processors that contain hundreds or thousands of quantum logic gates – those that may be available in the near future.

Zhang, Zhuang, and co-workers decided to explore the quantum jungle by following a path that straddles the boundary between quantum sensing and quantum machine learning. The beautiful “quantum fruits” that they discovered show that this path deserves further exploration.

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