Quantum computing is one of the most exciting areas of research in physics, occupying with researchers across the globe developing it. By exploiting the exotic properties of quantum mechanics, such as entanglement and superposition, quantum computers have the potential to solve problems that would be impossible with a standard computer or even a supercomputer. Today, researchers dream of future quantum computers discovering better materials, creating new medicines, solving complicated equations, and more.

However, the quantum computers of today are still in their infancy; few qubits can be controlled at a time to which few quantum gates can be applied. Though these limitations vary depending on the quantum hardware that is used, classical computers still outclass current quantum computers in several aspects. An exciting opportunity to go beyond this limitation is given by hybrid algorithms. The idea is to pair a classical computer’s processor and a quantum co-processor in a feedback loop to solve hard optimisation problems, in particular minimizing the expectation value of a given quantum operator. In this way, one exploit the strengths of both platforms without the limitations of either. Companies and scientists around the world are working on hybrid methods with the goal of enabling new discoveries in fields such as material science, fundamental physics, chemistry, and drug design. At the Institute for Quantum Computing at the University of Waterloo, Prof. Christine Muschik leads a group dedicated to using hybrid quantum computing in new and exciting ways.

Currently, almost all quantum computers use the so-called circuit model of computing. The initial qubits, representing the input state of the computation, are acted upon by single- and -multi-qubit gates to produce the output qubits, which encode the output state of the computation. This is similar to how a classical computer operates. the measurement-based model of quantum computing is an exciting alternative. Here, the input qubits are entangled with a large number of ancillary qubits, forming a so-called graph state. Then, single-qubit measurements are performed on the ancillary qubits; due to the entanglement in the graph state, these measurements affect the states of the unmeasured qubits. The remaining qubits at the end of the measurement process encode the output of the computation. Measurement-based approaches have been applied to several problems, but often many ancillary qubits in the graph state are required. By collaborating with Prof. Wolfgang Dür from University of Innsbruck, Prof. Karl Jansen from DESY, and PhD student Abdulrahim Al Balushi from IQC, MSc student Ryan Ferguson along with post-doc Luca Dellantonio and Prof. Christine Muschik were able to innovate by marrying the measurement-based approach with hybrid quantum computing for the first time ever.

By using the measurement-based approach in a feedback loop with a classical computer, they invented a new way of tackling hard optimization problems. Their method is extremely resource efficient: their graph state is small because they custom tailor it to the specific problem at hand. Additionally, their optimisation-feedback loop method has no analogy in the traditional circuit model and as a result it can produce states not easily accessible by the circuit model. Their novel framework for hybrid computing has a lot to offer quantum software developers and experimentalists: it provides an entirely new way to think about optimization algorithms, it offers high error tolerance, and it can be run on photonic quantum co-processors. This last point is particularly interesting since it is notoriously difficult to perform quantum gates on photonic platforms, whereas entangling qubits and measurements can be done quite easily. Therefore, their framework removes the need for single- and multi-qubit gates and enables a new generation of photonic hybrid computers. These exciting results were published in Physics Review Letters 126 220501 (2021).

In summary, this new computing method opens the door for new algorithms and experiments that bring us closer to near-term applications and discoveries. Christine’s group is now looking for further models to apply the hybrid measurement-based optimizer on to highlight its advantages over the circuit model. They also hope for an experimental realization of their method will come in the near future.