Some results from the combinatorial approach to quantum logic

Richard J. Greechie

Naoki Takeuchi, Masashi Aono, Nobuyuki Yoshikawa

Among advanced paradigms in the physics of computing, adiabatic quantum-flux-parametron (AQFP) logic is interesting, in that it can easily introduce stochastic processes by exploiting naturally occurring thermal fluctuations. This study proposes using AQFP logic to implement stochastic-local-search solvers. Experiments show that AQFP circuits can find solutions to simple logical constraint-satisfaction problems when moderate thermal fluctuations are applied. This result indicates the possibility of superconducting digital circuits dedicated to solving combinatorial optimization problems.

Shanzhen Gao

Xu Xu

Marek A. Perkowski, Martin Lukáč, Paweł Kerntopf +7 more

A new approach to synthesis of quantum logic circuits has been presented in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). The approach is based on the following principles: (1) design of (complex) gates using approach that links evolutionary, combinatorial and human interaction approaches, (2) design of circuits with these gates using evolutionary and search methods, (3) macro-generation of complex gates to lower level quantum primitives, (4) applying technology-related optimizing tautological transforms that take realistic quantum layout constraints, (5) calculating realistic costs related to quantum realization, (6) synthesis of incompletely specified functions. 1.

Kadi̇r Emi̇r, David Kruml, Jan Paseka +1 more

The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as minimalistic; solely the aspect of mutual exclusiveness is taken into account. In fact, an orthogonality space is simply a set endowed with a symmetric and irreflexive binary relation. If the rank is at least 4 and if a certain combinatorial condition holds, these relational structures can be shown to give rise in a unique way to Hermitian spaces. In this paper, we focus on the finite case. In particular, we investigate orthogonality spaces of rank at most 3.