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Due to the limited connectivity of gate model quantum devices, logicalquantum circuits must be compiled to target hardware before they can beexecuted. Often, this process involves the insertion of SWAP gates into thelogical circuit, usually increasing the depth of the circuit, achieved bysolving a so-called qubit assignment and routing problem. Recently, a number ofinteger linear programming (ILP) models have been proposed for solving thequbit assignment and routing problem to proven optimality. These models encodethe objective function and constraints of the problem, and leverage the use ofautomated solver technology to find hardware-compliant quantum circuits. Inthis work, we propose constraint programming (CP) models for this problem andcompare their performance against ILP for circuit depth minimization for bothlinear and two-dimensional grid lattice device topologies on a set of randomlygenerated instances. Our empirical analysis indicates that the proposed CPapproaches outperform the ILP models both in terms of solution quality andruntime.

Constraint programming models for depth-optimal qubit assignment and SWAP-based routing