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Combinatorial optimization problems whose search space is a set of permutations introduce significant difficulty for quantum computation. The traditional approach to encoding apermutation is to represent the matrix elements of a permutation matrix using qubits. This results inan N**2 encoding for elements of the symmetric group over N elements. The group size grows asNlog(N), so valid states become a vanishingly small fraction of the entire search space as N grows. Efficient permutation encodings that only require Nlog(N) qubits can be constructed using sorting networks. Constructing the objective functions for permutation-based problems such as the Traveling Salesman Problem can be automated with symbolic logic. The resulting objective functions contain many higher order terms. Handling these with QAOA in the circuit model creates an opportunity to use heuristics for phase polynomials. Teams: Join the meeting now Meeting ID: 249 207 579 967 Passcode: 6GC6qy6B Host: Luis Pedro Garcia-Pintos (T-4) |