Scheme for Implementing Quantum Search Algorithm in a Cluster State Quantum Computer

Jonathan A. Jones, Michele Mosca, Rasmus H. Hansen

Yanhui Wang, Yong Zhang

Using cluster state and single qubit measurement one can perform the one-way quantum computation. Here we give a detailed scheme for realizing a modified Grover search algorithm using measurements on cluster state. We give the measurement pattern for the cluster-state realization of the algorithm and estimated the number of measurement needed for its implementation. It is found that O(2 3n/2 n 2 ) number of single qubit measurements is required for its realization in a cluster-state quantum computer.

John R. Scott, Krishna C. Balram

Understanding the computational overheads imposed by classical control systems on quantum computing platforms becomes critically important as these quantum machines grow in scale and complexity. In this work, we calculate the overheads imposed by the implementation of real-time graph traversal algorithms needed to find computational paths through incomplete cluster states for the implementation of one-qubit gates; a necessary requirement for a realistic implementation of photonic measurement-based quantum computing. By implementing two different algorithms, a global breadth-first search that searches the entire cluster state and an incremental version that traverses a narrow subsection of the cluster state, we analyze the trade-off between the accuracy of finding viable paths and the speed at which this operation can be performed, which constrains the overall photonic clock cycle of the system. We also outline the broader implications of our results for implementing classical control systems for measurement-based photonic quantum computing.

Ivan B. Djordjević

Neil B. Lovett

Quantum computation is a new computational paradigm which can provide fundamentally faster computation than in the classical regime. This is dependent on finding efficient quantum algorithms for problems of practical interest. One of the most successful tools in developing new quantum algorithms is the quantum walk. In this thesis, we explore two applications of the discrete time quantum walk. In addition, we introduce an experimental scheme for generating cluster states, a universal resource for quantum computation. We give an explicit construction which provides a link between the circuit model of quantum computation, and a graph structure on which the discrete time quantum walk traverses, performing the same computation. We implement a universal gate set, proving the discrete time quantum walk is universal for quantum computation, thus confirming any quantum algorithm can be recast as a quantum walk algorithm. In addition, we study factors affecting the efficiency of the quantum walk search algorithm. Although there is a strong dependence on the spatial dimension of the structure being searched, we find secondary dependencies on other factors including the connectivity and disorder (symmetry). Fairly intuitively, as the connectivity increases, the efficiency of the algorithm increases, as the walker can coalesce on the marked state with higher probability in a quicker time. In addition, we find as disorder in the system increases, the algorithm can maintain the quantum speed up for a certain level of disorder before gradually reverting to the classical run time. Finally, we give an abstract scheme for generating cluster states. We see a linear scaling, better than many schemes, as doubling the size of the generating grid in our scheme produces a cluster state which is double the depth. Our scheme is able to create other interesting topologies of entangled states, including the unit cell for topological error correcting schemes.

Jose P. Dumas, Kapil Kumar Soni, Akhtar Rasool