Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and the low success probability of finding a global optimal measurement output. Each measurement round requires preparing the quantum system and applying quantum operations and measurements with high-precision control in the physical layer. These issues result in extremely high-cost measurements with a low probability of success at the end of the measurement rounds. Here, we define a novel measurement for quantum computations called dense quantum measurement. The dense measurement strategy aims at fixing the main drawbacks of standard quantum measurements by achieving a significant reduction in the number of necessary measurement rounds and by radically improving the success probabilities of finding global optimal outputs. We provide application scenarios for quantum circuits with arbitrary unitary sequences, and prove that dense measurement theory provides an experimentally implementable solution for gate-model quantum computer architectures.
@cite_57: The quantum approximate optimization algorithm (QAOA) has been recently introduced as a heuristic digital quantum computing scheme to solve combinatorial optimization problems with shallow circuits. We present a scheme to parallelize this approach for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest neighbor interactions. The optimization protocol consisting of single qubit operations that encode the optimization problem while all interactions are problem-independent pair-wise CNOT gates among nearest neighbors. This allows for a parallelizable implementation in quantum devices with a square lattice geometry. The basis of this proposal is a lattice gauge model which also introduces additional parameters and protocols for QAOA to improve the efficiency.
In @cite_57 , the authors studied the implementation of QAOA with parallelizable gates. The work introduced a scheme to parallelize the QAOA for arbitrary all-to-all connected problem graphs in a layout of qubits. The proposed method was defined by single qubit operations and the interactions were set by pair-wise CNOT gates among nearest neighbors. As the work concluded, this structure allows for a parallelizable implementation in quantum devices with a square lattice geometry.