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.
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.
The Measurement Based Quantum Computation (MBQC) model achieves universal quantum computation by employing projective single qubit measurements with classical feedforward on a highly entangled multipartite cluster state. Rapid advances in improving scalability of quantum computing systems have enabled the generation of large cluster states for implementing MBQC on various platforms. This review focuses on three such efforts, each utilizing a different quantum computing technology viz., superconducting qubits, trapped ion qubits and squeezed photon states. MBQC is being increasingly employed on optical platforms which can generate large entangled resource states but lack the ability to perform deterministic entangling gates.
Quantum computers, leveraging the principles of quantum mechanics, hold the potential to surpass classical computers in numerous applications, with implications across various domains. Besides the well-known gate model, Measurement-based Quantum Computation (MBQC) is another promising computational approach to achieve universal quantum computation. In MBQC, large ensembles of qubits are prepared in a highly entangled cluster state, forming the basis for executing quantum computations through sequential measurements. Cluster states are realized using both continuous variables (CV) and discrete variables (DV) techniques. In the CV-based methods, Frequency Domain Multiplexing (FDM), Time Domain Multiplexing (TDM), Spatial Domain Multiplexing (SDM), and hybrid schemes are employed. This paper thoroughly discusses and compares these approaches, elucidating their strengths and limitations. Additionally, the generation of photonic cluster states in DV is explored and some recent results are reported. Some recent state-of-the-art advancements in photonic and superconducting qubits entanglement, which can potentially serve as cluster states, are also presented. Finally, we highlight the approach that exhibits the most promising characteristics for achieving efficient cluster state realization in the context of MBQC.
Measurement-based quantum computing (MBQC) is a powerful model for quantum computation, but dedicated software tools that bridge its theoretical foundations with practical research workflows remain limited. We present Graphix, a software framework for MBQC written in Python that provides a unified environment for developing, integrating, and exploring measurement-based protocols and algorithms. Graphix establishes a modular, extensible, and user-friendly architecture for the compilation and simulation of quantum computations in the MBQC model with abstractions closely aligned with the theoretical formulations of MBQC. Through examples drawn from recent research on MBQC, we demonstrate Graphix's ability to reproduce and extend previous results. Graphix thus provides a software infrastructure for MBQC, supporting education and research while enabling collaborative development and accelerating the transition toward practical implementations.
Simulating the Universal Blind Quantum Computation (UBQC) protocol on gate-based platforms requires updating each measurement basis from earlier outcomes within the same execution. Existing Measurement-Based Quantum Computation (MBQC) simulation tools typically handle this feed-forward outside a single executable quantum program, so they do not natively expose the fixed-graph measurement-by-measurement update order studied here. We address this gap by implementing the flow-based Pauli corrections and a simulation-level UBQC angle-update rule as in-circuit dynamic-circuit primitives in Qiskit. Applied to two-qubit Grover's algorithm on a custom 2×9 flow of 18 qubits, the resulting program achieves deterministic success under both plain MBQC and the UBQC layer. Under the depolarizing-noise setting considered here, the angle-blinding layer remains close to plain MBQC, with only a modest additional gap relative to the dominant MBQC-over-circuit overhead. To show that the construction is not tied only to this Grover-specific pattern, we also verify a G2,5 brickwork-state fragment with representative universal-gate primitives under the same client/server blinding view. Structural blindness for a full algorithmic brickwork resource remains future work, but within this scope the construction provides a concrete dynamic-circuit route toward fixed-graph, privacy-preserving delegated-quantum-computing simulation at the protocol-update level.
Quantum teleportation is the most basic quantum protocol that transfers quantum states between two parties via sharing of quantum entanglement, measurements, and feedforward operations. At first glance, quantum teleportation is simply an identity operation that does not change the quantum states. Quantum teleportation, however, forms the basis for a paradigm of quantum computation called measurement-based quantum computation (MBQC). In the first half of this chapter, we describe continuous-variable (CV) quantum teleportation. In the second half, we explain how to use quantum teleportation in MBQC. There are two important concepts regarding MBQC: cluster state and gate teleportation. Cluster state is a multipartite entangled state that can be used for CV quantum computation, given that we can implement appropriate measurements and feedforward operations on it. Gate teleportation, on the other hand, is a concept that we can “teleport” non-Gaussian operations on the resource state to the input state.
Quantum subroutines, like their classical counterparts, serve as essential components of larger algorithms. They can be realized using gate based architectures or measurement based quantum computation (MBQC), where computation proceeds through adaptive measurements on highly entangled cluster states. In this work, we implement a phase oracle as a reusable subroutine within the MBQC framework using experimentally feasible cluster states. Unlike prior demonstrations of Grover's algorithm in MBQC that omit explicit oracle construction, our approach provides a transparent formulation of the oracle subroutine, including its measurement patterns, byproduct correlations, density-matrix simulations, and corresponding MBQC measurement circuits.