One Way Quantum Computation

Abstract

The one-way quantum computer, introduced by Raussendorf and Briegel, offers fundamentally different approach to quantum computation: rather than applying sequences of coherent multi-qubit gates, the entire computation is driven by adaptive single-qubit measurements on a pre-entangled resource state called a cluster state. This work presents a self-contained study of the model, developing the stabilizer formalism as the natural language for tracking cluster state evolution under measurement, and demonstrating universality through measurement patterns on both linear and two-dimensional cluster states. The role of adaptive measurement, necessary for non-Clifford operations, and the resulting parallelization advantage over the circuit model are analyzed through the Clifford group. The physical interpretation of X and Z measurements as quantum wires and cluster-shaping operators is also discussed. Finally, we briefly comment on a practical flexibility of the model: since entangling operations and measurements on disjoint qubits commute, the cluster state can be grown and consumed incrementally, removing the need to maintain a large entangled state in memory throughout the computation and making the one-way model well suited to experimental platforms such as optical lattices