Swap Minimization in Nearest Neighbour Quantum Circuits: An ILP Formulation

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“…, |V |} which represents the node location of logical qubit q ∈ Q at layer ℓ ∈ L ′ . Since ILP is less flexible than CP (e.g., due to linearity restrictions) the ILP models from the literature [10,3,9] must introduce additional variables to properly model the problem. In our models, it is sufficient to constrain the values of x qℓ from one layer to the next.…”

“…In the more general case, however, this is no longer true. 3 Our model for general architectures is similar to that for linear array architectures, however, instead of using absolute value constraints we use table constraints. The table constraint specifies the list of tuples (solutions) to which a vector of variables can be fixed.…”

“…A variety of techniques have been proposed for solving this problem in the literature, including both exact and heuristic approaches. Exact methods typically involve the use of search-based solvers leveraging smart inference techniques that, given enough time, will find and prove the optimal solution [4,3,10,9,14]. Alternatively, heuristic methods (which have, until recently, been the focus of previous work) sacrifice completeness in favor of rapidly producing high quality circuits [8,15,6]; these methods tend to scale more effectively to larger problem instances as well.…”

“…The first model is designed for linear array quantum device topologies, while the second can be used to solve problems involving more general architectures. We conduct an empirical analysis of the ILP models proposed by Boccia et al [3] and Nannicini et al [10] using circuit depth minimization as our objective function. We demonstrate, through empirical evaluation using different solvers, that our CP models outperform these existing ILP approaches in terms of solution quality and runtime for depth minimization.…”