JUWELS Booster -- A Supercomputer for Large-Scale AI Research

Kesselheim, Stefan; Herten, Andreas; Krajsek, Kai; Ebert, Jan; Jitsev, Jenia; Cherti, Mehdi; Langguth, Michael; Gong, Bing; Stadtler, Scarlet; Mozaffari, Amirpasha; Cavallaro, Gabriele; Sedona, Rocco; Schug, Alexander; Strube, Alexandre; Kamath, Roshni; Schultz, Martin; Riedel, Morris; Lippert, Thomas

doi:10.48550/arxiv.2108.11976

Cited by 2 publications

(2 citation statements)

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“…For this case, the CoP is improving even more rapidly compared to TSP and also here for the BPP with 6 and 7 items the solutions using slack variables (61 and 78 qubits) is beyond range of what can be simulated with quantum computer simulators. The largest simulations up to 43 qubits were performed on JUWELS Booster [52] as they required more than 1/8 PiB of distributed memory and took more than one million core hours. Finally, figure 16(c) shows the CoP for the KP with 5 to 41 items (5 to 41 qubits) with increments of two (same number of qubits).…”

Section: The Copmentioning

confidence: 99%

Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Montañez-Barrera,

Willsch,

Maldonado-Romo

et al. 2024

Quantum Sci. Technol.

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Solving combinatorial optimization problems of the kind that can be codiﬁed by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.

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Section: The Copmentioning

confidence: 99%

Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Montañez-Barrera,

Willsch,

Maldonado-Romo

et al. 2024

Quantum Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…where | • | denotes the L1-norm and w represents the weights (see the following section for how the weights are chosen). In practice, we use the implementation of the BFGS algorithm from TensorFlow Probability [60] running on the NVIDIA A100 GPUs of JUWELS Booster [94,95]. If necessary, a suitable initial value for the BFGS algorithm is obtained from Newton-LB applied to the case in which only some elements of #f are used to ensure #x = #f .…”

Section: Hampiepmentioning

confidence: 99%