Hierarchies of resources for measurement-based quantum computation

Understand

For certain restricted computational tasks, quantum mechanics provides a provable advantage over any possible classical implementation.

• Several of these results have been proven using the framework of measurement-based quantum computation (MBQC), where non-locality and more generally contextuality have been identified as necessary resources for certain quantum computations.
• Here, we consider the computational power of MBQC in more detail by refining its resource requirements, both on the allowed operations and the number of accessible qubits.
• More precisely, we identify which Boolean functions can be computed in non-adaptive MBQC, with local operations contained within a finite level in the Clifford hierarchy.