See also [42, Chapter 6] for a general introduction. To define quantum gates, we first need to specify the quantum replacement of an n-bit datum. Will Not Be Covered. Sufficiency of two-qubit gates for quantum computation 3. • Logic design (classical and quantum) attempts to find circuit structures for needed operations that are > Functionally correct > Independent of physical technology > Low-cost, e.g. In the framework of mathematical logic, such a logical structure can be expressed via a subset of Description Logic (DL) statements. An example from quantum mechanics will be used to illustrate how the principle of modularity can be encoded within our framework. First, we setup a locale for the inputs to the search problem. 14 Quantum Circuits • Example 1: Quantum Half Adder > Compute the sum and carry for two qubits x 1,x 0 |y ¯ carry |x 1 |x 0D |y |x 1 sum Toffoli gate CNOT gate D at in at in Control in Data out … uses the minimum number of qubits or gates. XOR gate: role in universality, entanglement, error-correction 5. Lets us start with discussing logic for computational purpose. mechanics, e.g. Deutsch’s three-qubit generalization of the Toffoli gate 2. However, the Hilbert-space structure of the qubits permits many quantum gates that are not induced by classical ones. Quantum logic gates. Open image in new window. For example, a relative phase shift is a 1 qubit gate given … In particular, we prove that both classical logic and quantum logic are sound and … quantum logic, which represen t “genuine logics” according to the standard way of thinking of the logi cal tradition, can be characterized by con venient abstraction from the physical models. We give an equivalent proof for the classical logic which turns out to have disjoint distributive and nondistributive ortholattices. for minimal quantum logic will be proposed. That is, we assume \(N=2^n\) items in total. We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. 1 Introduction Quantum logic has been introduced in the early 1930s by John von Neumann in his famous treatise on the mathematical foundations of quantum mechanics [15]. Universal Quantum Logic Gates (1989, 1995-) ----- p.12 1. In the DL parlance, logical structure among predicates (red oval nodes) is commonly known as T-box, whereas logical structure connecting entities (or entity tuples) to the … Implementation of two-qubit gates – the linear ion trap scheme C. Multi-valued and … The ... Other examples of quantum logic gates derived from classical ones are the Toffoli gate and the Fredkin gate. Here n is the number of qubits used to represent the items. In that work, he proposed to regard projection … The paper uses Grover’s algorithm as the main example illustrating quantum Hoare logic. Birkhoff & von Neumann, The Logic of Quantum Mechanics, 1936. Universality of two-qubit gates: proof sketch 4. B. We largely follow its approach in this paper. For example, cardiologist )physician )doctor, and similarly, Mother_of )Parent_of)Blood_relation. Using non-classical logics to solve ‘paradoxes’ in quantum.