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We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues:(1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

In this Letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics--one of the hallmark characteristics of the Moore-Read state expected to describe the observed fractional quantum Hall effect plateau at nu = 5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et al. are also addressed.

We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.PACS numbers: 03.67. Lx, 03.65.Vf, 03.67.Pp, 05.30.Pr Topological quantum computation (TQC) is an approach to quantum computing that derives fault-tolerance from the intrinsically error-protected Hilbert spaces provided by the nonlocal degrees of freedom of non-Abelian anyons [1,2,3,4]. To be computationally universal, the anyon model describing a topologically ordered system must be intricate enough to permit operations capable of densely populating the computational Hilbert space. At its conception, the primitives envisioned as necessary for implementing TQC were:1. Creation of the appropriate non-Abelian anyons, which will encode topologically protected qubits in their non-local, mutual multi-dimensional state space.2. Measurement of collective topological charge of anyons, for qubit initialization and readout.3. Adiabatic transportation of computational anyons around each other, to produce braiding transformations that implement the desired computational gates.In an effort to simplify, or at least better understand the TQC construct and what is essential to its architecture, we reconsider the need for physically braiding computational anyons. We demonstrate that it is not a necessary primitive by replacing it with an adaptive series of non-demolitional topological charge measurements. Naturally, this "measurementonly" approach to TQC draws some analogy with other measurement-only approaches of quantum computing [5,6,7,8], but has the advantage of not expending entanglement resources, thus allowing for computations of indefinite length (for fixed resource quantities).In this letter, we only consider orthogonal, projective measurements [9] of topological charge, for which the probability and state transformation for outcome c is given bySuch measurements potentially include Wilson loop measurements in lattice models, energy splitting measurements in fractional quantum Hall (FQH) and possibly other systems, and (the asymptotic limit of) interferometry measurements when the measured charge c is Abelian. Though these may involve or be related to the motion of some anyons, the measured anyons are not moved (at least not around each other).We use a diagrammatic representation of anyonic states and operators acting on them, as described by an anyon model (for definitions, including normalizations, see e.g. [10,11]). Through a set of combinatorial rules, these diagrams encode the purely topological properties of anyons, independent of any particular physical representation. Using this formalism, we show how projective measurement of the topological charge of pairs of anyons enables quantum state teleportation. We then show that repeated applications of ...