It is shown that a multiboson (k-boson) algebra can be conveniently utilized to generate a k-dimensional computational basis. The single qukit logical operators are given ∀k and two different constructions of the CNOT gate are presented.
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary representation in usual computational basis. This decomposition may be simplified greatly with the help of the properties of the finite-dimensional multiple-quantum operator algebra spaces of a quantum system and the specific properties of a given quantum algorithm. As elementary building blocks of quantum computation, the two-qubit diagonal gates and one-qubit gates may be constructed physically with one- and two-body interactions in a two-state quantum system and hence could be conveniently realized experimentally. The present work will be helpful for implementing generally any N-qubit quantum computation in those feasible two-state quantum systems and determining conveniently the time evolution of these systems in course of quantum computation.
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. Realization of the B gate is illustrated with an example of charge-coupled superconducting qubits for which the B gate is seen to be generated in shorter time than the CNOT gate.
Abstract Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.
Fewer-qubit quantum logic gate, serving as a basic unit for constructing universal multiqubit gates, has been widely applied in quantum computing and quantum information. However, traditional constructions for fewer-qubit gates often utilize a multipulse protocol, which inevitably suffers from serious intrinsic errors during the gate execution. In this paper, we report an optimal model about universal two- and three-qubit cnot gates mediated by excitation to Rydberg states with easily accessible van der Waals interactions. This gate depends on a global optimization to implement amplitude- and phase-modulated pulses via genetic algorithm, which can facilitate the gate operation with fewer optical pulses. Compared to conventional multipulse piecewise schemes, our gate can be realized by simultaneous excitation of atoms to the Rydberg states, saving the time for multipulse switching at different spatial locations. Our numerical simulations show that a single-pulse two- (three-) qubit cnot gate is possibly achieved with a fidelity of 99.23% (90.39%) for two qubits separated by $7.10\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$ when the fluctuation of Rydberg interactions is excluded. Our work is promising for achieving fast and convenient multiqubit quantum computing in the study of neutral-atom quantum technology.