Mapping quantum circuits to shallow-depth measurement patterns based on graph states

Kurzfassung

The paradigm of measurement-based quantum computing (MBQC) departs from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to some final measurement. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to divide any quantum circuit in a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state dressed with local (adaptive) measurements - a so-called standard form. We further treat the stabilizer state through the graph state formalism, thus enabling a significant decrease in circuit depth for certain applications. We show that groups of fully commuting operators can be implemented through fully-parallel, i.e.~non-adaptive measurements within our protocol. Finally, we demonstrate the utility of our technique using an example with high practical relevance -- the variational quantum eigensolver (VQE).