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• W2894587555 abstract "Adiabatic Quantum Computing (AQC) is an attractive paradigm for solving hard integer polynomial optimization problems. Available hardware restricts the Hamiltonians to be of a structure that allows only pairwise interactions. This requires that the original optimization to be first converted -- from its polynomial form -- to a quadratic unconstrained binary optimization (QUBO) problem, which we frame as a in algebraic geometry. Additionally, the hardware where such a QUBO-Hamiltonian needs to be embedded -- assigning variables of the to the qubits of the physical optimizer -- is not a complete graph, but rather one with limited connectivity. This problem to hardware graph embedding can also be framed as a of computing a Groebner basis of a certain specially constructed polynomial ideal. We develop a systematic computational approach to prepare a given polynomial optimization for AQC in three steps. The first step reduces an input polynomial optimization into a QUBO through the computation of the Groebner basis of a toric ideal generated from the monomials of the input objective function. The second step computes feasible embeddings. The third step computes the spectral gap of the adiabatic Hamiltonian associated to a given embedding. These steps are applicable well beyond the integer polynomial optimization problem. Our paper provides the first general purpose computational procedure that can be used directly as a $translator$ to solve polynomial integer optimization. Alternatively, it can be used as a test-bed (with small size problems) to help design efficient heuristic quantum compilers by studying various choices of reductions and embeddings in a systematic and comprehensive manner. An added benefit of our framework is in designing Ising architectures through the study of $mathcal Y-$minor universal graphs." @default.
• W2894587555 created "2018-10-12" @default.
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• W2894587555 date "2018-10-02" @default.
• W2894587555 modified "2023-09-27" @default.
• W2894587555 title "A Novel Algebraic Geometry Compiling Framework for Adiabatic Quantum Computations." @default.
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