Browsing by Subject "Quantum computation"

Now showing 1 - 4 of 4

Open Access
Mermin polytopes in quantum computation and foundations
(Rinton Press Inc., 2023-06-27) Okay, Cihan; Chung, Ho Yiu; İpek, Selman
Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes β obtained from the Mermin scenario, parametrized by a function β on the set of contexts. Up to combinatorial isomorphism, there are two types of polytopes 0 and 1 depending on the parity of β. Our main result is the classification of the vertices of these two polytopes. In addition, we describe the graph associated with the polytopes. All the vertices of 0 turn out to be deterministic. This result provides a new topological proof of a celebrated result of Fine characterizing noncontextual distributions on the CHSH scenario. 1 can be seen as a nonlocal toy version of A-polytopes, a class of polytopes introduced for the simulation of universal quantum computation. In the 2-qubit case, we provide a decomposition of the A-polytope using 1, whose vertices are classified, and the nonsignaling polytope of the (2, 3, 2) Bell scenario, whose vertices are well-known.
Open Access
Nonlinear schrödinger equation for quantum computation
(World Scientific, 2006) Yalabik, M. C.
Utilization of a quantum system whose time-development is described by the nonlinear Schrödinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of problems. An example of such a system for implementing the logical NOR operation is demonstrated.
Open Access
Persistent currents in mesoscopic loops and networks
(TÜBİTAK, 2003) Kulik, Igor O.
The paper describes persistent (also termed "permanent", or "non-decaying") currents in mesoscopic metallic and macromolecular rings, cylinders and networks. The current arises as a response of system to Aharonov-Bohm flux threading the conducting loop and does not require external voltage to support the current. Magnitude of the current is periodic function of magnetic flux with a period of normal-metal flux quantum Φ 0 = hc/e. Spontaneous persistent currents arise in regular macromolecular structure without the Aharonov-Bohm flux provided the azimuthal periodicity of the ring is insured by strong coupling to periodic background (a "substrate"), otherwise the system will undergo the Peierls transition arrested at certain flux value smaller than Φ 0. Extremely small (nanoscopic, macromolecular) loop with three localization sites at flux Φ = Φ 0/2 develops a Λ-shaped energy configuration suitable to serve as a qubit, as well as at the same as a "qugate" (quantum logic gate) supporting full set of quantum transitions required for universal quantum computation. The difference of the Aharonov-Bohm qubit from another suggested condensed-matter quantum computational tools is in the radiation free couplings in a qubit supporting the scalable, long-lived quantum computation.
Open Access
Quantum computation with persistent-current Aharonov-Bohm qubits and qugates
(Computational Publications, 2003) Kulik, Igor O.
We analyse the possibility of employing mesoscopic or nanoscopic rings of a normal metal in a double degenerate persistent-current state in the presence of the Aharonov-Bohm flux equal to the half flux quantum as entangled quantum bits of information (qu-bits). The third level in a three-state qubit can be effectively used to coherently couple the qu-bit to logical gates for the reversible NOT (in a single qu-bit) and CNOT (in two coupled qu-bits) operations. Further we suggest that a (hypothetic) crystal implementing conducting ring-shaped molecules, or triples of anionic vacancies (similar to F 3-centers in alkali halides) with one trapped electron, in crossed magnetic and electric fields satisfies the requirements of the proposed mechanism and may serve as a new kind of device for universal quantum computation.