Abstract: In this paper, we study ZpZp[u]-additive codes, where p is prime and u 2 = 0. In particular, we determine a Gray map from ZpZp[u] to Z α+2β p and study generator and parity check matrices for these codes. We prove that a Gray map Φ is a distance preserving map from (ZpZp[u],Gray distance) to (Z α+2β p ,Hamming distance), it is a weight preserving map as well. Furthermore we study the ...

We present benchmarks of the parity transformation for Quantum Approximate Optimization Algorithm (QAOA). analyse gate resources required to implement a single QAOA cycle real-world scenarios. In particular, we consider random spin models with higher order terms, as well problems predicting financial crashes and finding ground states electronic structure Hamiltonians. For studied our findings i...

We introduce parity quantum optimization with the aim of solving problems consisting arbitrary $k$-body interactions and side conditions using planar chip architectures. The method introduces a decomposition problem graph terms generalized closed cycles hypergraph. Side in form hard constraints can be included as open containing involved conditions. mapping thus circumvents need to translate qu...

Instances of logical cryptanalysis, circuit verification, and bounded model checking can often be succinctly represented as a combined satisfiability (SAT) problem where an instance is a combination of traditional clauses and parity constraints. This paper studies how such combined problems can be efficiently solved by augmenting a modern SAT solver with an xor-reasoning module in the DPLL(XOR)...

The parity-preserving UA(1)×Ua(1) massive QED3 is ultraviolet finiteness – exhibits vanishing β-functions, associated to the gauge coupling constants (electric and pseudochiral charges) Chern–Simons mass parameter, all anomalous dimensions of fields as well parity anomaly free at orders in perturbation theory. proof independent any regularization scheme it based on quantum action principle comb...

Today, the use of CMOS technology for the manufacture of electronic ICs has faced many limitations. Many alternatives to CMOS technology are offered and made every day. Quantum-dot cellular automata (QCA) is one of the most widely used. QCA gates and circuits have many advantages including small size, low power consumption and high speed. On the other hand, using special digital gates called re...

We present a complete classification of quantum stabilizer gates in terms of the functions they generate assuming the ability to swap qubits and use ancillary workspace. Because we view these stabilizer circuits as subroutines of some general quantum computation, we insist that any ancilla qubits used during the computation must not change in an input-dependent manner. This is the first attempt...