Consider a function f and a corresponding unitary u. The oneway or measurement based quantum computer mbqc is a method of quantum computing that first prepares an entangled resource state, usually a. One particularly interesting model to study, in view of recent progress in manipulating ultracold fermion gases, is the fermionic version of measurementbased quantum computation mbqc, which implements full quantum computation with only singlesite measurements on a. Selfguaranteed measurementbased quantum computation. Miyake, quantum computational capability of a twodimensional valence bond solid phase, arxiv. The oneway or measurement based quantum computer mbqc is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it.
Quantum computation by measurement use an entangled quantum state j ias computational resource. In this thesis, we describe the oneway quantum computer, a scheme of universal quantum computation that consists entirely of onequbit measurements on a. Pdf measurementbased quantum computation beyond the one. Two principal schemes of measurement based computation are teleportation quantum computation tqc and the socalled cluster model or oneway quantum computer 1wqc. It is oneway because the resource state is destroyed by the measurements. Author links open overlay panel vincent danos ellie. Introduction to measurement based quantum computation. This is in direct analogy to the tendency of lattices to observe criticality in spin systems. Measurementbased quantum computation and undecidable. Solid state spin can be used as a qubit for implementing cluster states. November 28th 2007 mark tame qteq quantum technology at queens queens university, belfast. Hybrid architecture for encoded measurementbased quantum. Selfguaranteed measurementbased quantum computation michal hajdusek beyond iid, 28 july 2017 joint work with masahito hayashi arxiv.
Clear separation between classical and quantum parts of computation. Martin pei for being, quite simply, an excellent collaborator. The new paradigm of measurementbased quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in. We establish a connection between measurementbased quantum computation and the field of mathematical logic. Computational depth complexity of measurementbased quantum. We show that the computational power of an important class of quantum states called graph states, representing resources for measurementbased quantum computation, is reflected in the expressive power of classical formal logic languages defined on the underlying mathematical. Hierarchy of universal entanglement in 2d measurement. A particularly exciting paradigm is that of measurementbased quantum computation, where the processing of quantum information takes place by. Measurementbased quantum computation on cluster states robert raussendorf, daniel e. Nielsen1,3, 1institute for quantum information, california institute of technology, pasadena, california 91125, usa 2center for theoretical physics, massachusetts institute of technology, cambridge, massachusetts 029, usa. We give a detailed account of the oneway quantum computer, a scheme of quantum computation that. The main mbqc framework was proposed by rassendorf and briegel in the \oneway quantum computer 2 using the cluster state 5. Jsps queeng university belfast japan society for the promotion of science. An introduction to measurement based quantum computation.
Measurementbased quantum computation with qubit and. This thesis explores extensions of the measurementbased model for quantum computation in qubit and continuousvariable systems. Measurementbased models provide an intriguing new framework for thinking about quantum computation. In this article we discuss a number of recent developments in. This is in contrast with the more traditional circuit model which is based on unitary operation. A number of models of quantum computation exist, including the now wellstudied quantum circuit model. We will describe these schemes and show how they are able to perform universal quantum computation. There are several resource states which allow for universal quantum computation, e. Measurementbased and universal blind quantum computation anne broadbent 1, joseph fitzsimons,2, elham kashe. This work adds confidence to the analogy and highlights new features of what we require for universal resources for measurementbased quantum computation. The input is a gatemodel description of a quantum computation. However, this method is only useful in a quantum circuit setup, so we must instead discuss possible correction methods for a resource state.
Universal resources for measurementbased quantum computation authors. We also propose an mbqcbased dimension witness and analyze it in different noisy and noiseless scenarios. Computational depth complexity of measurementbased quantum computation. 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. We also discuss the analogy between thermodynamics and oneway computation in this context. Measurementbased quantum computation beyond the one. Therein, the entire quantum computation consists of a spatiotemporal pattern of onequbit measurements on an entangled multiqubit quantum state, the cluster state.
Measurementbased quantum computation beyond the oneway model. Measurementbased quantum computing is a universal quantum computation paradigm in which an initial clusterstate provides the quantum resource, while the iteration of sequential measurements and. While quantum computers can achieve dramatic speedups over the classical computers familiar to us, identifying the origin of this quantum advantage in physical systems remains a major goal of quantum information science. We give a detailed account of the oneway quantum computer, a scheme of quantum computation that consists entirely of onequbit measurements on a particular class of entangled states, the cluster states. The choice of basis for later measurements may depend on earlier. Information written onto j i, processed and read out by onequbit measurements only. Clusterandgraphstates wehaveseenintheabovethatwithalineararrayofclusterstates,arbitrary rotationcanbeachieved. Contextuality also plays a role in measurementbased quantum computation mbqc. Measurementbased quantum computation with mechanical oscillators related talks. John watrous and daniel gottesman, for being the instructors wose provided me with more than anyone else the conceptual framework necessary. Measurementbased quantum computation and the clifford hierarchy.
Quantum computation in a nutshell naive measurement only gives one fk at a time exploit quantum parallelism. If an mbqc on qubits evaluates a nonlinear boolean function in which case the computation is classically universal with high probability of success, this computation is also contextual 11. Contextuality as a resource for measurementbased quantum computation beyond qubits to cite this article. Good design of measurement may reveal properties of f e. Symmetry protection of measurementbased quantum computation in ground states centre for engineered quantum systems, school of physics the university of sydney, australia dominic else, stephen bartlett, and andrew doherty 1. In the measurementbased model, quantum computation is driven by singlesite measurements on a large entangled quantum state known as a cluster state. In measurementbased quantum computation one starts with an entangled resource state. Sarvepalli university of british columbia qpl nijmegen, october 2011. Pdf measurementbased quantum computation relies on the ability to carry out singlequbit measurement and the creation of cluster state. Measurementbased quantum computation relies on the ability to carry out singlequbit measurement and the creation of cluster state.
Measurementbased quantum computation 10th canadian summer school on qi dan browne dept. For measurementbased schemes, the hardware consists of a multiparticle quantum system in an algorithmindependent state and a classical computer. A particularly exciting paradigm is that of measurementbased quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a. Measurementbased quantum computation nature physics. A useful tool here is measurementbased quantum computation mqc, a computational framework utilizing the quantum entanglement found in manybody resource states. Measurementbased quantum correlations for quantum information. Quantum circuits are still widely used as a convenient formalism for describing quantum computation, and they provide a framework for the structure of quantum algorithms and the physical realization of quantum computers. Shors factoring algorithm 1807082088687404805951656164405905566278102516769404917012702. Measurementbased quantum computation has emerged from the physics community as a new apporach to quantum computation. Measurementbased quantum computation with trapped ions. Measurementbased quantum computation mbqc is a novel approach to quantum computation where the notion of measurement is the main driving force of computation. Since measurementbased quantum computation is inherently distributed, this allows us to extend naturally several concepts of the measurement calculus 2, a formal model for such computations.
In every step of the computation, a local measurement is performed on the quantum state and the result is fed into the classical. Quantum computation offers a promising new kind of information processing, where the nonclassical features of quantum mechanics. The new paradigm of measurementbased quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state, is particularly exciting in this regard. The 2d aklt state is universal for measurementbased. Although these models have been shown to be formally equivalent, their underlying elementary concepts and the. Give some details to understand basic ingredients of measurementbased quantum computation. A calculus for measurementbased quantum computation 3 3. Measurementbased quantum computation beyond the oneway. Measurementbased and universal blind quantum computation. Measurementbased quantum computation with cluster states. Universal quantum computing with arbitrary continuousvariable encoding 6.
While quantum circuits are still widely considered as a convenient formalism for describing algorithms, using measurements to steer quantum computation is considered a serious alternative. We introduce schemes for quantum computing based on local measurements on entangled resource states. We develop a formal model for distributed measurementbased quantum computations, adopting an agentbased view, such that computations are described locally. Downloadchiu2012fermionic measurementbased quantum computation. This state forms a universal resource for quantum computation, i. Mqc is a means of utilising an entangled resource state to perform computation using. Measurementbased quantum computation on cluster states. Contextuality as a resource for measurementbased quantum. Every lecture is accompanied by readings that support and expand on what was covered in the lecture.
Quantum computation offers a promising new kind of information processing, where the nonclassical features of quantum mechanics can be harnessed and exploited. Measurementbased quantum computation and resource states mbqc is a quantum computing method that uses a resource state, allowing all computations to be done using only single qubit operations. A introduction traditionally, the main framework to explore quantum computation has been the circuit model deu89, based on unitary evolution. Measurementbased quantum computation ubc library open. Topos logic in measurementbased quantum computation. Introduction measurementbased quantum computation, and. A quantum circuit is translated to a singlequbit measurement pattern on the resource state. Generalized flow and determinism in measurementbased. The outcome of each individual measurement is random, but they are related in such a way that.