Measurement-based Approaches to Quantum Approximate Optimization

Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near future.

At the same time, as quantum computing hardware continues to improve and incorporate new features such as in-circuit measurement and adaptive control, opportunities arise for novel algorithmic paradigms.

In this work we explore variants of parameterized quantum algorithms related to the measurement-based quantum computing

paradigm. In particular we focus on protocols related to quantum alternating operator ansatze in the context of the quantum approximate optimization algorithm.

We show how a variety of hard problem constraints may be directly incorporated into our protocol to guarantee the feasibility of the solution found and avoid the need for dealing with penalties.

For the construction and analysis of our measurement-based protocols we demonstrate that diagrammatic methods based on the ZX-calculus are particularly useful.

We then compare the resource requirements of our approaches to that of more traditional quantum circuits.

Finally, we discuss opportunities for hybrid approaches lying between measurement-based and gate-model paradigms.