Scalable quantum computing based on stationary spin qubits in coupled quantum dots inside double-sided optical microcavities

Quantum logic gates are the key elements in quantum computing. Here we investigate the possibility of achieving a scalable and compact quantum computing based on stationary electron-spin qubits, by using the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics. We design the compact quantum circuits for implementing universal and deterministic quantum gates for electron-spin systems, including the two-qubit CNOT gate and the three-qubit Toffoli gate. They are compact and economic, and they do not require additional electron-spin qubits. Moreover, our devices have good scalability and are attractive as they both are based on solid-state quantum systems and the qubits are stationary. They are feasible with the current experimental technology, and both high fidelity and high efficiency can be achieved when the ratio of the side leakage to the cavity decay is low.Comment: 12 pages, 5 figures, one colum

Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities

We present some compact quantum circuits for a deterministic quantum computing on electron-spin qubits assisted by quantum dots inside single-side optical microcavities, including the CNOT, Toffoli, and Fredkin gates. They are constructed by exploiting the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a single-side optical microcavity as a result of cavity quantum electrodynamics. Our universal quantum gates have some advantages. First, all the gates are accomplished with a success probability of 100% in principle. Second, our schemes require no additional electron-spin qubits and they are achieved by some input-output processes of a single photon. Third, our circuits for these gates are simple and economic. Moreover, our devices for these gates work in both the weak coupling and the strong coupling regimes, and they are feasible in experiment.Comment: 13 pages, 6 figures, a single column. The negligible error on the schematic figures for some PBSs in Opt. Express 22, 593-607 (2014) is correcte

Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers

It is desirable to implement an efficient quantum information process demanding fewer quantum resources. We designed two compact quantum circuits for determinately implementing four-qubit Toffoli and Fredkin gates on single-photon systems in both the polarization and spatial degrees of freedom (DoFs) via diamond nitrogen-vacancy (NV) centers in resonators. The gates are heralded by the electron spins associated with the diamond NV centers. In contrast to the ones with one DoF, our implementations reduce the quantum resource and are robust against the decoherence. Evaluations of fidelities and efficiencies of our gates show that our schemes may be implemented with current technology.Comment: 9 pages,5 figure

Optimal synthesis of multivalued quantum circuit

Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the optimization of generic multivalued quantum circuits. The multivalued quantum Shannon decompositions (QSD) are improved so that the circuits obtained are asymptotically optimal for all dimensionality d. The syntheses of uniformly multifold controlled $R_y$ rotations are also optimized to make the circuits further simplified. Moreover, the theoretical lower bound of complexity for multivalued quantum circuits is investigated, and a quantity known as efficiency index is proposed to evaluate the efficiency of synthesis of various quantum circuits. The algorithm for qudit circuits given here is an efficient synthesis routine which produces best known results for all dimensionality d, and for both cases the number of qudit n is small and that is asymptotic. The multivalued quantum circuits are indeed more efficient than the binary quantum circuits. The facts, the leading factor of the lower bound of complexity for qudit circuits is small by a factor of d-1 in comparison to that for qubit circuits and the asymptotic efficiency index is increased with the increase of dimensionality d, reveal the potential advantage of qudit circuits over generic qubit circuits. The generic n-qudit circuits with $d\geq5$ and generic two-ququart circuits synthesized by the algorithm given here are practical circuits which are more efficient than the most efficient qubit circuits.Comment: 7 pages, 2 figures, 6 table

Synthesis of Multivalued Quantum Logic Circuits by Elementary Gates

We propose the generalized controlled X (GCX) gate as the two-qudit elementary gate, and based on Cartan decomposition, we also give the one-qudit elementary gates. Then we discuss the physical implementation of these elementary gates and show that it is feasible with current technology. With these elementary gates many important qudit quantum gates can be synthesized conveniently. We provide efficient methods for the synthesis of various kinds of controlled qudit gates and greatly simplify the synthesis of existing generic multi-valued quantum circuits. Moreover, we generalize the quantum Shannon decomposition (QSD), the most powerful technique for the synthesis of generic qubit circuits, to the qudit case. A comparison of ququart (d=4) circuits and qubit circuits reveals that using ququart circuits may have an advantage over the qubit circuits in the synthesis of quantum circuits.Comment: 9 pages, 14 figures, 2 tables. Expanded version of quant-ph/1105.548

Decomposition of orthogonal matrix and synthesis of two-qubit and three-qubit orthogonal gates

The decomposition of matrices associated to two-qubit and three-qubit orthogonal gates is studied, and based on the decomposition the synthesis of these gates is investigated. The optimal synthesis of general two-qubit orthogonal gate is obtained. For two-qubit unimodular orthogonal gate, it requires at most 2 CNOT gates and 6 one-qubit Ry gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit Ry and Rz gates in the worst case.Comment: 7 pages,5 figure

Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities

Constructing compact quantum circuits for universal quantum gates on solid-state systems is crucial for quantum computing. We present some compact quantum circuits for a deterministic solid-state quantum computing, including the CNOT, Toffoli, and Fredkin gates on the diamond nitrogen-vacancy centers confined inside cavities, achieved by some input-output processes of a single photon. Our quantum circuits for these universal quantum gates are simple and economic. Moreover, additional electron qubits are not employed, but only a single-photon medium. These gates have a long coherent time. We discuss the feasibility of these universal solid-state quantum gates, concluding that they are feasible with current technology.Comment: 12 pages, 6 figures. To appear i

Correlation dynamics of a two-qubit system in a Bell-diagonal state under non-identical local noises

The property of quantum correlation has been studied in recent years, especially for the quantum and classical correlations affected by environment. The dynamics of quantum and classical correlations in two-qubit system under identical local noise channels have been investigated recently. Here we will consider the dynamics of quantum and classical correlations when the local noise channels of two sides are not identical. We investigate the dynamics of quantum and classical correlations with three types of local noise channels in both Markovian and non-Markovian conditions, and show the decay rules of quantum and classical correlations with different types and parameter times of local noise channels.Comment: 11 pages, 5 figure

Elementary gates for ternary quantum logic circuit

In this article the elementary gates for ternary quantum logic circuit are studied. We propose the ternary controlled X (TCX) gate or ternary controlled Z (TCZ) gate as two-qutrit elementary gate, which is universal when assisted by arbitrary one-qutrit gates. It is primitive, efficient and easy to implement. Based on Cartan decomposition, we also give the one-qutrit elementary gates. Then the synthesis of some important ternary gates is investigated and the scheme of physical implementation for these ternary gates is discussed. Finally we extend these elementary gates to more general qudit case, so it provides a unified description for the synthesis of the binary and multi-valued quantum circuits.Comment: 8 pages, 13 figures, small modification to Fig.1

Implementations of more general solid-state (SWAP)1/m^{1/m} and controlled-(swap)1/m^{1/m} gates

Universal quantum gates are the core elements in quantum information processing. We design two schemes to realize more general (SWAP)$^{1/m}$ and controlled--(swap)$^{1/m}$ gates (for integer $m\geq1$) by directing flying single photons to solid--state quantum dots. The parameter $m$ is easily controlled by adjusting two quarter--wave plates and one half--wave plate. Additional computational qubits are not required to construct the two gates. Evaluations of the gates indicate that our proposals are feasible with current experimental technology.Comment: 20 page,7 figure