Kerr Kernel Quantum Learning Machine: A New Approach to Quantum Machine Learning

The Kerr Kernel Quantum Learning Machine is a proposed quantum machine learning scheme that uses quantum Kerr non-linearities for bosonic modes. Unlike most quantum machine learning methods that rely on qubits and circuits, this approach samples quantum probabilities directly in an engineered device.

The kernel matrices are directly sampled through measurements on the device and passed to a standard algorithm SVM implementation. This method, based on superconducting quantum circuits, could offer advantages in processing information in high-dimensional feature Hilbert spaces. However, this is a relatively new field and further research is needed to fully understand and optimize these methods.

What is a Kerr Kernel Quantum Learning Machine?

A Kerr Kernel Quantum Learning Machine is a proposed scheme for quantum machine learning, based on quantum Kerr non-linearities for bosonic modes. This is fundamentally an analogue scheme, unlike much of quantum machine learning which is based on the quantum computer paradigm with qubits and circuits of single and two qubit gates. The approach is more akin to the growing number of analog machine learning schemes based on sampling quantum probabilities in a device engineered directly. In this scheme, kernel matrices are not computed but directly sampled through measurements made on the device. They can then be passed to a standard algorithm SVM implementation.

Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature Hilbert spaces. Kernels are believed to offer particular advantages when they cannot be computed classically, so a kernel matrix with indisputably non-classical elements is desirable, provided it can be generated efficiently in a particular physical machine. Kerr nonlinearities, known to be a route to universal continuous variable (CV) quantum computation, may be able to play this role for quantum machine learning.

The proposed quantum hardware kernel implementation scheme is based on superconducting quantum circuits. The scheme does not use qubits or quantum circuits, but rather exploits the analogue features of Kerr coupled modes. This approach is more akin to the growing number of analog machine learning schemes based on sampling quantum probabilities directly in an engineered device by stochastic quantum control.

How Does the Quantum Kernel Machine Learning Protocol Work?

The quantum kernel machine learning protocol is based on quantum Kerr non-linearities for bosonic modes. This is a fundamentally analogue scheme. Unlike much of quantum machine learning, this scheme is not based on the quantum computer paradigm with qubits and circuits of single and two qubit gates. Instead, it is more akin to the growing number of analog machine learning schemes based on sampling quantum probabilities in a device engineered directly.

In this scheme, kernel matrices are not computed but directly sampled through measurements made on the device. They can then be passed to a standard algorithm SVM implementation. While most such quantum kernel machines are implemented using qubit based circuit architecture, this model employs continuous variable degrees of freedom of electromagnetic field modes.

The data is regarded as being drawn from some unknown statistical distribution. In supervised learning, we are given many examples of the data together with a corresponding label. We use the training set to find an unknown function such that it can classify a new datum with low probability of error. The construction indicates that the correlation matrix must be positive definite if the data is distributed according to a valid probability measure. This feature ensures that the kernel is a valid kernel.

What is the Role of Quantum Kernels?

The passage to quantum kernels begins with parameterised quantum states, either pure or mixed. In the unitary case, we consider states of the form where x is a data element and we call the state the fiducial state in some suitable Hilbert space. In this paper, the Hilbert space is the tensor product space of N bosonic modes of the electromagnetic field.

The key difference between quantum and classical states is that all quantum states are a source of randomness. In the case of pure states, there is always one physical quantity for which the measurement outcomes are completely certain and simultaneously there is at least one physical quantity for which the outcomes are as random as possible given other constraints such as symmetries.

The statistical distance between two parameterised pure states is simply given in terms of the inner product and we take this to define the kernel. More general measures are used for mixed states, but in this paper, we will only use the unitary quantum kernel defined. Clearly, the kernel thus defined is a positive definite function of the data.

How is the Quantum Device Used in the Training?

The point of using an actual quantum device to do the training is that we never need to know the kernel function. It is generated by making appropriate measurements on a quantum device. The measurement data can then be passed to a support vector machine algorithm on a conventional CMOS computer with the von Neumann architecture. This requires a shift in our perspective from algorithms to machines.

There are two ways to do this. One is based on a variational circuit approach with feedback and the other is based on kernel sampling. These are the analogue of the sequential and parallel scenarios. In both cases, we need to specify what to measure.

What is the Future of Quantum Machine Learning?

The future of quantum machine learning is promising, with the development of new methods and approaches such as the Kerr Kernel Quantum Learning Machine. This approach, which is fundamentally an analogue scheme, offers a new way to process information in high-dimensional feature Hilbert spaces, similar to quantum computing.

The use of quantum devices in the training process eliminates the need to know the kernel function, as it is generated by making appropriate measurements on the device. This shift in perspective from algorithms to machines opens up new possibilities for quantum machine learning.

However, it’s important to note that this is a relatively new field, and much research is still needed to fully understand and optimize these methods. The work of researchers like Carolyn Wood, Sally Shrapnel, and G J Milburn at the Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, is crucial in advancing our understanding of quantum machine learning.