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**1 - 2**of**2**### Towards a Cost Metric for Nearest Neighbor Constraints in Reversible Circuits

"... Abstract. This work in progress report proposes a new metric for estimating nearest neighbor cost at the reversible circuit level. This is in contrast to existing literature where nearest neighbor constraints are usually considered at the quantum circuit level. In order to define the metric, invest ..."

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Abstract. This work in progress report proposes a new metric for estimating nearest neighbor cost at the reversible circuit level. This is in contrast to existing literature where nearest neighbor constraints are usually considered at the quantum circuit level. In order to define the metric, investigations on a state-of-the-art reversible to quantum mapping scheme have been conducted. From the retrieved information, a proper estimation to be used as a cost metric has been obtained. Using the metric, it becomes possible for the first time to optimize a reversible circuit with respect to nearest neighbor constraints.

### Determining the Minimal Number of SWAP Gates for Multi-dimensional Nearest Neighbor Quantum Circuits

"... Abstract Motivated by the promises of signicant speed-ups for certain problems, quantum computing received signicant attention in the past. While much progress has been made in the development of synthesis methods for quantum circuits, new physical developments constantly lead to new constraints to ..."

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Abstract Motivated by the promises of signicant speed-ups for certain problems, quantum computing received signicant attention in the past. While much progress has been made in the development of synthesis methods for quantum circuits, new physical developments constantly lead to new constraints to be addressed. The limited interaction distance between the respective qubits (i.e. nearest neighbor optimization) has already been considered intensely. But with the emerge of multi-dimensional quantum architectures, new physical requirements came up for which only a few automatic synthesis solutions exist yet all of them of heuristic nature. In this work, we propose an exact scheme for nearest neighbor optimization in multidimensional quantum circuits. Although the complexity of the problem is a serious obstacle, our experimental evaluation shows that the proposed solution is sucient to allow for a qualitative evaluation of the respective optimization steps. Besides that, this enabled an exact comparison to heuristical results for the rst time.