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There are many important works about the construction of universal quantum logic gates which are key elements in quantum computation. However, most of them focus on quantum transformations on the same degree of freedom (DOF) of quantum systems. We propose a CNOT gate performed on the polarization DOF and spatial mode DOF of one photon system assisted by a quantum dot in double-side optical microcavities. This hyper CNOT gate is implemented by using spin selective photon reflection from the cavity, without auxiliary spatial modes or polarization modes. This interface can also be used to construct a hyper photonic Bell-state analyzer. The high fidelities of the hyper CNOT gates may be achieved with low side leakage and cavity loss. [ABSTRACT FROM AUTHOR]

Quantum hidden problem being one of the most important quantum computation problems has been widely investigated. Our purpose in this paper is to prove the independent or partial independent of the reduced state derived from the quantum query with the oracle implementation. We prove that if without bias on implementation functions the subgroup state is independent of evaluation functions using the group representation. This result is also used to improve the quantum query success probability. [ABSTRACT FROM AUTHOR]

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm. [ABSTRACT FROM AUTHOR]

The quantum no-cloning theorem and no-deleting theorem may be the most important quantum features for quantum communications or quantum computations. In this paper, we concentrate typical properties of random quantum evolution. We obtain that universal random evolutions change the generic unknown pure states into their orthogonal states approximately. Moreover, typical random evolutions distort the von Neumann entropy with constants. These results are extended to mixed states with a stronger orthogonal preparation ability. These typical characters are very important for quantum information retrieving or various quantum tasks. [ABSTRACT FROM AUTHOR]

The critical merits acquired from quantum computation require running in parallel, which cannot be benefited from previous multi-level extensions and are exact our purposes. In this paper, with qutrit subsystems the general quantum computation further reduces into qutrit gates or its controlled operations. This extension plays parallizable and integrable with same construction independent of the qutrit numbers. The qutrit swapping as its basic operations for controlling can be integrated into quantum computers with present physical techniques. Our generalizations are free of elevating the system spaces, and feasible for the universal computation. [ABSTRACT FROM AUTHOR]

Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing. [ABSTRACT FROM AUTHOR]