International Journal of Quantum Information最新文献

In this paper, continuous-time quantum walk is discussed based on the view of quantum probability, i.e. the quantum decomposition of the adjacency matrix A of graph. Regard adjacency matrix A as Hamiltonian which is a real symmetric matrix with elements 0 or 1, so we regard $e^{-itA}$ as an unbiased evolution operator, which is related to the calculation of probability amplitude. Combining the quantum decomposition and spectral distribution $\mu$ of adjacency matrix A, we calculate the probability amplitude reaching each stratum in continuous-time quantum walk on complete bipartite graphs, finite two-dimensional lattices, binary tree, $N$-ary tree and $N$-fold star power $G^{\star N}$. Of course, this method is also suitable for studying some other graphs, such as growing graphs, hypercube graphs and so on, in addition, the applicability of this method is also explained.

Quantum coherence is one of the most fundamental and striking features in quantum physics. Considered the standard coherence (SC), the partial coherence (PC) and the block coherence (BC) as variance of quantum states under some quantum channels (QCs) $\mathrm{\Phi }$, we propose the concept of channel-based coherence of quantum states, called $\mathrm{\Phi }$-coherence for short, which contains the SC, PC and BC, but does not contain the positive operator-valued measure (POVM)-based coherence. By our definition, a state $\rho$ is said to be $\mathrm{\Phi }$-incoherent if it is a fixed point of a QC $\mathrm{\Phi }$, otherwise, it is said to be $\mathrm{\Phi }$-coherent. First, we find the set ${ℐ}(\mathrm{\Phi })$ of all $\mathrm{\Phi }$-incoherent states for some given channels $\mathrm{\Phi }$ and prove that the set ${ℐ}(\mathrm{\Phi })$ forms a nonempty compact convex set for any channel $\mathrm{\Phi }$. Second, we define $\mathrm{\Phi }$-incoherent operations ($\mathrm{\Phi }$-IOs) and prove that the set of all $\mathrm{\Phi }$-IOs is a nonempty convex set. We also establish some characterizations of a $\mathrm{\Phi }$-IO in terms of its Kraus operators. Lastly, we

There is a property called localization, which is essential for applications of quantum walks. From a mathematical point of view, the occurrence of localization is known to be equivalent to the existence of eigenvalues of the time evolution operators, which are defined by coin matrices. A previous study proposed an approach to the eigenvalue problem for space-inhomogeneous models using transfer matrices. However, the approach was restricted to models whose coin matrices are the same in positions sufficiently far to the left and right, respectively. This study shows that the method can be applied to extended models with periodically arranged coin matrices. Moreover, we investigate localization by performing the eigenvalue analysis and deriving their time-averaged limit distribution.

Finding or estimating the lowest eigenstate of quantum system Hamiltonians is an important problem for quantum computing, quantum physics, quantum chemistry, and material science. Several quantum computing approaches have been developed to address this problem. The most frequently used method is variational quantum eigensolver (VQE). Many quantum systems, and especially nanomaterials, are described using tight-binding Hamiltonians, but until now no quantum computation method has been developed to find the lowest eigenvalue of these specific, but very important, Hamiltonians. We address the problem of finding the lowest eigenstate of tight-binding Hamiltonians using quantum walks. Quantum walks is a universal model of quantum computation equivalent to the quantum gate model. Furthermore, quantum walks can be mapped to quantum circuits comprising qubits, quantum registers, and quantum gates and, consequently, executed on quantum computers. In our approach, probability distributions, derived from wave function probability amplitudes, enter our quantum algorithm as potential distributions in the space where the quantum walk evolves. Our results showed the quantum walker localization in the case of the lowest eigenvalue is distinctive and characteristic of this state. Our approach will be a valuable computation tool for studying quantum systems described by tight-binding Hamiltonians.