An introduction to measurement based quantum computation

Abstract

In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms.

22 pages, 15 figures. Section 6.2 replaced

References in corpus (11)

• Measurement-based quantum computation with cluster states
• Improved Simulation of Stabilizer Circuits
• Cluster-state quantum computation
• Valence Bond Solids for Quantum Computation
• Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state
• Fault-tolerant quantum computation with cluster states
• Unified derivations of measurement-based schemes for quantum computation
• Both Toffoli and Controlled-NOT need little help to do universal quantum computation
• Computation by measurements: a unifying picture
• Quantum computing via measurements only
• Two-qubit Projective Measurements are Universal for Quantum Computation

Cited by in corpus (56)

• Quantum computational chemistry
• Measurement-based quantum computation
• OpenQASM 3: A broader and deeper quantum assembly language
• Determinism in the one-way model
• Generalized Flow and Determinism in Measurement-based Quantum Computation
• A random walk approach to quantum algorithms
• Parallelizing Quantum Circuits
• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator
• Speed limits and locality in many-body quantum dynamics
• Port-based teleportation in arbitrary dimension
• On the simulation of quantum circuits
• State preparation by shallow circuits using feed forward
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)
• Efficient multi port-based teleportation schemes
• Quantum supremacy in constant-time measurement-based computation: A unified architecture for sampling and verification
• Optimal computation with non-unitary quantum walks
• Optimal Multi-port-based Teleportation Schemes
• Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator
• Hybrid quantum-classical circuit simplification with the ZX-calculus
• On the Need for Large Quantum Depth
• Minimal informationally complete measurements for probability representation of quantum dynamics
• Quantum Depth in the Random Oracle Model
• Physical Realization of Measurement Based Quantum Computation
• Computational Distinguishability of Quantum Channels
• A Framework for Heterotic Computing
• Quantum mutual information and quantumness vectors for multi-qubit systems
• Hybrid Exchange Measurement-Based Qubit Operations in Semiconductor Double Quantum Dot Qubits
• Optimal parallel quantum query algorithms
• The Hadamard gate cannot be replaced by a resource state in universal quantum computation
• Hilbert Space Representations of Decoherence Functionals and Quantum Measures
• Partial Multipartite Entanglement in the Matrix Product State Formalism
• Twisted graph states for ancilla-driven quantum computation
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• Generalised Clifford groups and simulation of associated quantum circuits
• The Influence of Experimental Imperfections on Photonic GHZ State Generation
• Overcoming experimental limitations in a non-linear two-qubit gate through postselection
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Bases in diagrammatic quantum protocols
• Test of Quantumness with Small-Depth Quantum Circuits
• Hybrid Decision Trees: Longer Quantum Time is Strictly More Powerful
• Space-time Peer-to-Peer Distribution of Multi-party Entanglement for Any Quantum Network
• GHZ transform (I): Bell transform and quantum teleportation
• Towards a Pattern Language for Quantum Algorithms
• The Universe and The Quantum Computer
• The basic principles to construct a generalized state-locking pulse field and simulate efficiently the reversible and unitary halting protocol of a universal quantum computer
• Projecting onto Qubit Irreps of Young Diagrams
• Computational Perspectives on Bell Inequalities and Many-body Quantum Correlations
• Offloading Quantum Computation by Superposition Masking
• Covert Quantum Internet
• Quantum Computing Using Crossed Atomic Beams
• Building a fusion-based quantum computer using teleported gates
• Robust Multipartite Entanglement Without Entanglement Breaking
• One-Way Quantum Computer Simulation
• Teleportation-based quantum homomorphic encryption scheme with quasi-compactness and perfect security