Abstract
This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables.
Highlights
We address Constrained Optimization Problems (COPs), where in addition to the constraints Fj there is an objective to be minimized over the feasible configurations
RESULTS we report results of our experiments using D-Wave hardware for solving LDPC problems
We have outlined a general approach for coping with intrinsic issues related to the practical use of quantum annealing
Summary
D-Wave Systems manufactures a device [1,2,3,4] that uses quantum annealing (QA) to minimize the dimensionless energy of an Ising model E(s|h, J ) = hisi + Ji,j sisj. We have spin variables si ∈ {−1, 1} indexed by the vertices V(G) of a graph G fixed by the device with allowed pairwise interactions given by the edges E(G) of this graph, and where the hi and. Similar ideas were generalized to full quantum computation [7, 8]. The quantum annealing process minimizes the Ising energy by evolving the ground state of an initial Hamiltonian H0 =
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