Qiskit As a Simulation Platform for Measurement-based Quantum Computation

Universal quantum computation is anticipated to provide solutions to classically intractable problems. Measurement-based quantum computation (MBQC) is one of the leading candidates to achieve universal quantum computation. In MBQC, the development of the underlying quantum algorithms is governed by single-qubit measurements on a highly entangled cluster state of qubits. Recent advances in MBQC mainly explore the physical aspects of MBQC (i.e. Physical development of cluster states) and as most of the simulators that exist today are for the gate-based model of quantum computation, and to date, there is no MBQC-dedicated simulator for MBQC-based algorithmic development. This paper exploits a well-maintained, and popular gate-based simulation framework developed by IBM called Qiskit to design MBQC-based quantum algorithms. We implement various gates, including Hadamard, and CNOT gates, to demonstrate the universality of MBQC in Qiskit. We also demonstrate MBCQ-based algorithm development in Qiskit by implementing MBQC-based teleportation protocol and Grover's algorithm. The objective of this exercise is to demonstrate that the existing gate-based simulators can be used for developing MBQC-based quantum designs, which would help the research community in exploring the advantages that MBQC can offer compared to other quantum computation models.