On The Fundamental Flaws of Qubit Concept for General- Purpose Quantum Computing

For general-purpose quantum computing, the addition rules must be imposed and implemented first. An examination of this condition shows that the use of qubits is fundamentally flawed. The reasons are elaborated here. When two qubits are used for an addition operation of two bits, it is not the four states in superposition that are relevant for the addition. Rather it is the four symbolic substitution rules that are derived after the two qubits are collapsed that are to be used as a processor. This fundamental quantum processor possesses the capabilities of executing four instructions and a storage of two data. Thus general-purpose quantum computing is shown to be rule-based, rather than logic-gate (or truth-table) based and with implemented spatial relations. The consequence of replacing the 4 states in superposition with four symbolic substitution rules brings the addition operation into the architecture of one-dimensional cellular automaton with a dual-bit in each cell. They are equivalently transformed into a 16 specific right-nearest neighbor interaction rules for each cell. When the quantum processors are not connected correctly in cellular automata with relaxed long range spatial relations, a new kind of science appears and explained.