| measurement-based quantum computation | |
|---|---|
| Name | Measurement-based quantum computation |
| Other names | One-way quantum computer |
| Field | Quantum computing |
| Introduced | 2001 |
| Inventor | Robert Raussendorf and Jim Harrington* (concept formalized by Raussendorf and Hans J. Briegel) |
| Key concepts | Cluster state, Graph state, Adaptive measurement |
| Notable implementations | Optical quantum computing, Ion trap quantum computer |
measurement-based quantum computation
Measurement-based quantum computation (MBQC) is a model of quantum computation in which universal computation is achieved by a sequence of local quantum measurements on a highly entangled many-qubit resource state, typically a cluster state or graph state. MBQC matters in Quantum Physics and Quantum computing because it separates entanglement generation from logical processing, enabling alternative approaches to fault tolerance, resource accounting, and experimental architectures distinct from gate-based models like the Quantum circuit model.
MBQC was introduced in the early 2000s by Robert Raussendorf and Hans J. Briegel with the formulation known as the one-way quantum computer (2001). The approach built on prior work in entanglement theory, stabilizer formalism and cluster states introduced by Briegel and colleagues. MBQC clarified the role of single-qubit measurement and classical feed-forward in driving quantum information processing, contrasting with unitary quantum gate synthesis in the Quantum circuit model. Historical connections include the development of stabilizer codes by Daniel Gottesman, the Pauli group formalism, and contemporaneous progress in linear optics quantum computing by Knill, Laflamme and Milburn (KLM).
The canonical resource for MBQC is the cluster state, a particular instance of a graph state defined on a lattice or graph where qubits are prepared in |+⟩ states and entangling controlled-Z gates are applied along edges. Graph states are described within the stabilizer formalism and are closely related to error-correcting codes such as surface codes when embedded on two-dimensional lattices. Resource characterizations include measures like entanglement width and localizable entanglement; in many proofs of universality, two-dimensional cluster states on square lattices or hexagonal lattices serve as universal resources. Extensions include AKLT states and other many-body states shown to be universal under local measurements, linking MBQC to condensed matter physics and quantum many-body theory.
Computation proceeds by single-qubit projective or generalized POVM measurements in bases determined by the computational task. Measurement outcomes are stochastic; classical feed-forward of outcomes is used to adapt subsequent measurement bases to correct byproduct operators (elements of the Pauli group). Adaptive measurement schemes implement logical gates (e.g., rotations, entangling gates) through patterns of measurements and basis choices, with deterministic protocols relying on the stabilizer structure. Nonadaptive and teleportation-based variants relate to quantum teleportation and measurement-driven circuit identities developed by Gottesman and others.
MBQC is universal: families of resource states and measurement patterns can simulate any computation in the BQP complexity class. Equivalences between MBQC and the Quantum circuit model have been established via translation procedures; conversely, MBQC gives alternative proofs of universality using minimal measurement sets. MBQC variants include deterministic one-way computation, measurement-only proposals, and hybrid schemes combining gates and measurements. Complexity-theoretic analyses link MBQC to concepts such as classical simulation hardness of certain stabilizer circuits augmented by non-Clifford measurements and to resource theories of magic states (e.g., magic-state distillation).
Fault-tolerant MBQC integrates quantum error correction by embedding error-correcting codes into resource states or by performing measurements that realize syndrome extraction. Notable approaches include using surface code cluster states for topologically protected MBQC and schemes based on topological quantum computation ideas where measurement patterns realize logical operations with protection against local noise. Threshold theorems for MBQC adapt circuit-model techniques and analyze adversarial and stochastic noise models; practical considerations include measurement errors, loss (important in optical implementations), and imperfect entangling operations.
MBQC has been pursued in diverse platforms: linear optical quantum computing with photonic cluster states demonstrated via spontaneous parametric down-conversion and integrated photonics; ion trap quantum computers generating graph states via multi-qubit gates; superconducting qubits forming small-scale cluster states; and experiments in neutral atoms and Rydberg atoms creating entangled lattices. Notable experimental milestones include small-scale teleportation-based gates, demonstration of universal single-qubit rotations via measurement, and generation of four- and eight-qubit cluster states in optics and trapped ions. Industrial and academic groups active in MBQC research include teams at University of Oxford, University of Innsbruck, University of Vienna, Institute for Quantum Computing (IQC), and companies developing photonic quantum processors.
MBQC illuminates computational complexity by partitioning resource preparation and classical control, framing resource states as substrates whose preparation complexity affects overall cost. Applications explored include quantum simulation of many-body systems, measurement-based implementations of quantum algorithms (e.g., quantum Fourier transform, phase estimation), and subroutines for quantum error correction and state injection for non-Clifford gates. MBQC connects conceptually and technically to the Quantum circuit model, adiabatic quantum computing via resource-state constructions, and to topological quantum computing through topological cluster-state schemes. The model remains a fertile area linking theoretical computer science, experimental quantum engineering, and fundamental Quantum Physics.
Category:Quantum computing Category:Quantum information theory