Extended Quantum XOR Gate in Terms of Two-Spin Interactions

Considerations of feasibility of quantum computing lead to the study of multispin quantum gates in which the input and output two-state systems (spins) are not identical. We provide a general discussion of this approach and then propose an explicit two-spin interaction Hamiltonian which accomplishes the quantum XOR gate function for a system of three spins: two input and one output. PACS numbers: 03.65.Bz, 89.80.+h, 02.20.Sv, 76.70.Fz – 1 – The size of semiconductor computer components is still quite far from atomic dimensions. They will soon reach [1] linear dimensions of about 0.25μm. This is 2500 Å, well above the sizes at which quantummechanical effects will be important. It has become clear, however, that as the miniaturization continues, atomic dimensions will be reached, perhaps, with technology different from today’s semiconductors. Then, quantum-mechanical effects will have to be considered in computer operation. Lead by this expectation, some early works [2-4] considered how quantum mechanics affects the foundations of computer science. Questions such as limitations on “classical” computation due to quantum fluctuations, etc., have been raised. A more “active” approach, initiated recently by many authors [4-30] is to attempt to harness the quantum nature of components of atomic dimensions for more efficient computation and design. This ambitious program involves many interesting scientific concepts new to both Computer Science and Physics. In order to answer whether quantum computation is feasible and useful, several issues must be addressed. Is quantum computation faster than classical computation? Can quantum computational elements be built and combined with other quantum and/or classical components? What will be the “design” rules for quantum computer components in order to perform Boolean logic operations on quantum bits (qubits) such as the up and down spin states of a spin2 particle?