Christina Knapp
University of California, Santa Barbara
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Featured researches published by Christina Knapp.
Physical Review B | 2017
Torsten Karzig; Christina Knapp; Roman M. Lutchyn; Parsa Bonderson; Matthew B. Hastings; Chetan Nayak; Jason Alicea; Karsten Flensberg; Stephan Plugge; Yuval Oreg; C. M. Marcus; Michael H. Freedman
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.
Physical Review X | 2016
Christina Knapp; Michael P. Zaletel; Dong E. Liu; Meng Cheng; Parsa Bonderson; Chetan Nayak
Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry’s matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error.
Annals of Physics | 2017
Parsa Bonderson; Christina Knapp; Kaushal Patel
We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.
arXiv: Quantum Physics | 2018
Christina Knapp; Michael E. Beverland; Dmitry I. Pikulin; Torsten Karzig
Majorana-based quantum computing seeks to use the non-local nature of Majorana zero modes to store and manipulate quantum information in a topologically protected way. While noise is anticipated to be significantly suppressed in such systems, finite temperature and system size result in residual errors. In this work, we connect the underlying physical error processes in Majorana-based systems to the noise models used in a fault tolerance analysis. Standard qubit-based noise models built from Pauli operators do not capture leading order noise processes arising from quasiparticle poisoning events, thus it is not obvious {\it a priori} that such noise models can be usefully applied to a Majorana-based system. We develop stochastic Majorana noise models that are generalizations of the standard qubit-based models and connect the error probabilities defining these models to parameters of the physical system. Using these models, we compute pseudo-thresholds for the
Physical Review B | 2018
Christina Knapp; Torsten Karzig; Roman M. Lutchyn; Chetan Nayak
d=5
arXiv: Strongly Correlated Electrons | 2018
Christina Knapp; Eric Spanton; Andrea Young; Chetan Nayak; Michael P. Zaletel
Bacon-Shor subsystem code. Our results emphasize the importance of correlated errors induced in multi-qubit measurements. Moreover, we find that for sufficiently fast quasiparticle relaxation the errors are well described by Pauli operators. This work bridges the divide between physical errors in Majorana-based quantum computing architectures and the significance of these errors in a quantum error correcting code.
Physical Review B | 2018
Christina Knapp; Torsten Karzig; Roman M. Lutchyn; Chetan Nayak
Archive | 2018
Roman Lutchyn; Parsa Bonderson; Michael Freedman; Torsten Karzig; Chetan Nayak; Jason Alicea; Christina Knapp
Bulletin of the American Physical Society | 2018
Torsten Karzig; Christina Knapp; Roman M. Lutchyn; Chetan Nayak
Bulletin of the American Physical Society | 2017
Christina Knapp; Torsten Karzig; Roman M. Lutchyn; Parsa Bonderson; Matthew B. Hastings; Chetan Nayak; Jason Alicea; Karsten Flensberg; Stephan Plugge; Yuval Oreg; C. M. Marcus; Michael H. Freedman