International Journal of Quantum Information

Due to its unique optical properties, nitrogen-vacancy centers in diamond show remarkable advantages in realizing quantum information processing and computation. This paper proposes a scalable quantum computing architecture based on solid-state NV centers. In our scheme, logical qubits are encoded in a decoherence-free subspace (DFS) with Larmor pairs (a pair of the nucleus). And the connection between multiple qubits is assisted by a cantilever probe. Then the high fidelity of the universal quantum gate is achieved by using a series of pulses. Our scheme provides physical feasibility for scalable quantum computing and may pave the way for large-scale quantum computing based on NV centers.

Point cloud modeling is one of the most common types of 3D modeling, and the PointNet algorithm is an effective point cloud classification and segmentation algorithm. We propose the quantum accelerated PointNet algorithm. The proposed algorithm uses quantum computing to realize the three convolutional layers of the PointNet algorithm and uses classical computers to realize the pooling layers, the fully connected layers, and other parts. For a point cloud with $2^n$ points and coordinate values up to $2^q$, when performing the computation of the convolution layer of the PointNet algorithm with convolution kernel weights up to $2^m$, our algorithm changes the computational complexity from $O(2^n)$ on an electronic computer to $O(qm)$ after the quantum computing acceleration. The quantum accelerated PointNet algorithm proposed in this study changes the variables of the polynomial of computational complexity from $2^n$ to the product $qm$, and completely removes the effect of the parameter $n$, which is positively related to the number of points. Therefore, We can conclude that the quantum accelerated PointNet algorithm achieves a certain speedup compared to the classical PointNet algorithm.

Search algorithms based on discrete-time quantum walk (QW) can be considered as alterations of the standard QW: Use a different coin operator that distinguishes target and nontarget vertices, or, mark the target vertices first followed by the standard QW. Two most frequently used marking coins are $-I$ and $D$ the negative identity operator and the negative Grover diffusion operator. We show that search algorithms corresponding to these four combinations can be reduced to two, denoted as $U_I^{\prime }$ and $U_D^{\prime }$, and they are equivalent when searching for nonadjacent multiple targets. For adjacent target vertices, numerical simulations show that the performance of the algorithm $U_D^{\prime }$ highly depends on the density of the underlying graph, and it outperforms $U_I^{\prime }$ when the density is large enough. At last, a generalized stationary state of both search algorithms on the graphs with even-numbered degree is provided.

Quantum coherence and quantum entanglement are two different manifestations of the superposition principle. In this paper, we show that the right choice of basis to be used to estimate coherence is the separable basis. The quantum coherence estimated using the Bell basis does not represent the coherence in the system, since there is a coherence in the system due to the choice of the basis states. We first compute the entanglement and quantum coherence in the two-qubit mixed states prepared using the Bell states and one of the states from the computational basis. The quantum coherence is estimated using the ${\ell }_1$-norm of coherence, the entanglement is measured using the concurrence and the mixedness is measured using the linear entropy. Then we estimate these quantities in the Bell basis and establish that coherence should be measured only in separable basis, whereas entanglement and mixedness can be measured in any basis. We then calculate the teleportation fidelity of these mixed states and find the regions where the states have a fidelity greater than the classical teleportation fidelity. We also examine the violation of the Bell-CHSH inequality to verify the quantum nonlocal correlations in the system. The estimation of the above-mentioned quantum correlations, teleportation fidelity and the verification of Bell-CHSH inequality is also done for bipartite states obtained from the tripartite systems by the tracing out of one of their qubits. We find that for some of these states’ teleportation is possible even when the Bell-CHSH inequality is not violated, signifying that nonlocality is not a necessary condition for quantum teleportation.

Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian master equation are considered in the absence of thermal noise. The continuity equation is derived and Bohmian trajectories are constructed. As a solution of the master equation, we take a single coherent state and compute analytically the relative entropy of coherence, $C_r$, in the energy, position and momentum bases. Although $C_r$ is constant in both the position and the momentum bases, it is a decreasing function of time in the energy basis becoming zero at long times, revealing its role as the preferred basis. Then, quantum coherence is computed for a superposition of two coherent states, a cat state, and also a superposition of two cat states in the energy basis as a function of separation, in the complex plane, between the two superposed states. It is seen that the quantum coherence increases with this separation. Furthermore, quantum coherence of superposition is compared to that of decomposed states in the superposition. Finally, by considering a system of two noninteracting DHOs, the effect of quantum statistics is studied on the coherence of reduced single-particle states, the joint detection probability and the mean square separation of particles. Our computations show that the single-particle coherence for antisymmetric states is always less than that of symmetric ones. Furthermore, boson anti-bunching and fermion bunching is seen in this open system. This behavior of bosons is the matter-wave analogue of photon anti-bunching seen in a modified Hanbury Brown–Twiss (HBT) interferometer.