The scope of theoretical methods

Masashi Tawada, Shu Tanaka, Nozomu Togawa

Low-density parity-check (LDPC) codes have previously been considered as combinatorial optimization problems (COPs) in respect to its decoding. However, after defining it as such, none have gone so far as to convert the LDPC code into a quadratic unconstrained binary optimization (QUBO) problem. Thus, a new method is created: one that converts the LDPC code to a QUBO problem, inputs the QUBO problem into Ising machines (computers based on the Ising model that are designed to solve the QUBO problem), obtains the QUBO solution and converts it to a LDPC solution. By utilizing an actual Ising machine, LDPC solutions with code length of 256-bits have been obtained with an accuracy of 93.9% by average annealing time 214.0ms. The benefit of this newfound methodology goes beyond its theoretical imprint of obtaining LDPC solutions more accurately. It has only been a few years since the Ising machine has been developed. Therefore, in formulating this method, one expands the currently scope of studies involving Ising machines, helping current and future researchers unlock its full range of capabilities and possibilities.

Robert Alicki

Franz Schwabl

Wolfgang Mauerer, Manuel Schönberger

The application of quantum computing to data management has attracted growing interest, yet remains constrained by a limited understanding of how the physical behaviour of quantum devices relates to the structure and difficulty of database problems. In particular, evaluating quantum annealing approaches for combinatorial optimisation, which is central to many data management tasks, poses significant challenges beyond the scope of conventional empirical and complexity-theoretic methods.

Philipp Strasberg

Abstract We introduce a theoretical technique known as the two-point measurement scheme, which allows us to derive a variety of quantum fluctuation theorems with the same form as in classical stochastic thermodynamics. Alternatively, we show how to study fluctuations based on a quantum master equation approach combined with counting field or quantum jump trajectory methods. Although quantum fluctuation theorems have the same form as classical fluctuation theorems, they are more limited in their scope and practical applicability. Nevertheless, we study one important theoretical consequence of them, known as the thermodynamic uncertainty relation. This relation is used to discuss the impossibility of Carnot efficiency at finite power. The latter point also naturally connects to the third law of thermodynamics.

Franz Schwabl