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The paradigm of measurement-based quantum computing (MBQC) starts from ahighly entangled resource state on which unitary operations are executedthrough adaptive measurements and corrections ensuring determinism. This is setin contrast to the more common quantum circuit model, in which unitaryoperations are directly implemented through quantum gates prior to finalmeasurements. In this work, we incorporate concepts from MBQC into the circuitmodel to create a hybrid simulation technique, permitting us to split anyquantum circuit into a classically efficiently simulatable Clifford-part and asecond part consisting of a stabilizer state and local (adaptive) measurementinstructions, a so-called standard form, which is executed on a quantumcomputer. We further process the stabilizer state with the graph stateformalism, thus enabling a significant decrease in circuit depth for certainapplications. We show that groups of fully commuting operators can beimplemented using fully-parallel, i.e., non-adaptive, measurements within ourprotocol. In addition, we discuss how such circuits can be implemented inconstant quantum depths by employing quantum teleportation. Finally, wedemonstrate the utility of our technique on two examples of high practicalrelevance: the Quantum Approximate Optimization Algorithm (QAOA) and theVariational Quantum Eigensolver (VQE).

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