TY  - CONF
AU  - Sensebat, Orkun
AU  - Willsch, Dennis
AU  - Bode, Mathis
AU  - Michielsen, Kristel
TI  - Quantum Annealers and Partial Differential Equations: The Gate-Based Encoding Approach
M1  - FZJ-2025-00611
PY  - 2024
AB  - Representing Partial Differential Equations (PDEs) on Quantum Annealers (QAs) is not obvious. The first step of solving a PDE on a QA is to discretize it. We used finite differences. Next, a Quadratic Unconstrained Binary Optimization (QUBO) model is obtained that is equivalent to an Ising model. Finally, the QUBO coefficients are computed using an encoding in terms of the qubits to represent the variables. The conventional choice for this encoding is a binary encoding. A challenge is that the accessible size of systems is constrained due to the limited number of qubits. In other words, it becomes impossible to achieve a non-zero convergence probability. We addressed this challenge by developing a novel encoding, the gate-based encoding (GBE), to replace the conventionally used binary encoding. This aims to overcome the problem of exponentially scaling coefficients of binary encoding. GBE utilizes the structure of the discretized operators to construct a circuit that results in QUBO weights of comparative magnitude for each bit in the final bit-string, thus overcoming the exponentially rising weight given to the leading digits in the conventionally used binary encoding. GBE allows to successfully solve problems with larger encoding lenths for all problem sizes and solvers, e.g., 21 vs. 17 for the hybrid solver with our test setup. This is also emphasized by the significantly higher success probability for all encoding lengths compared to binary encoding. The cost of GBE is the higher number of variables
T2  - ISC High Performance 2024
CY  - 12 May 2024 - 16 May 2024, Hamburg (Germany)
Y2  - 12 May 2024 - 16 May 2024
M2  - Hamburg, Germany
LB  - PUB:(DE-HGF)24
UR  - https://juser.fz-juelich.de/record/1037283
ER  -