Abstract: Various embodiments of a modular unit for a topologic qubit and of scalable quantum computing architectures using such modular units are disclosed herein. For example, one example embodiment is a modular unit for a topological qubit comprising 6 Majorana zero modes (MZMs) on a mesoscopic superconducting island. These units can provide the computational MZMs with protection from quasiparticle poisoning. Several possible realizations of these modular units are described herein. Also disclosed herein are example designs for scalable quantum computing architectures comprising the modular units together with gates and reference arms (e.g., quantum dots, Majorana wires, etc.) configured to enable joint parity measurements to be performed for various combinations of two or four MZMs associated with one or two modular units, as well as other operations on the states of MZMs.

Abstract: A fusion outcome quasiparticle may be trapped in a potential well of a topological segment. The fusion outcome quasiparticle may be the product of fusion of a first quasiparticle and a second quasiparticle, where the first and the second quasiparticles are localized at ends of a topological segment. The potential well having the fusion outcome quasiparticle trapped therein and a third quasiparticle may be moved relative to each other such that the potential well and the third quasiparticle are brought toward each other.

Abstract: A fusion outcome quasiparticle may be trapped in a potential well of a topological segment. The fusion outcome quasiparticle may be the product of fusion of a first quasiparticle and a second quasiparticle, where the first and the second quasiparticles are localized at ends of a topological segment. The potential well having the fusion outcome quasiparticle trapped therein and a third quasiparticle may be moved relative to each other such that the potential well and the third quasiparticle are brought toward each other. The quasiparticles may be Majorana modes of a nanowire.

Abstract: Measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge is described. Various issues that would arise when realizing it in fractional quantum Hall systems are discussed.

Abstract: Measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge is described. Various issues that would arise when realizing it in fractional quantum Hall systems are discussed.

Abstract: A fusion outcome quasiparticle may be trapped in a potential well of a topological segment. The fusion outcome quasiparticle may be the product of fusion of a first quasiparticle and a second quasiparticle, where the first and the second quasiparticles are localized at ends of a topological segment. The potential well having the fusion outcome quasiparticle trapped therein and a third quasiparticle may be moved relative to each other such that the potential well and the third quasiparticle are brought toward each other. The quasiparticles may be Majorana modes of a nanowire.

Abstract: Disclosed herein is a protocol that enables the ?/8-gate in chiral topological superconductors in which superconducting stiffness ? has been suppressed. The protocol enables a topologically protected ?/8-gate in any pure Ising system that can be fabricated into genus=1 surface. By adding the ?/8-gate to previously known techniques, a design for universal topologically protected quantum computation which may be implemented using rather conventional materials may be obtained.

Abstract: A twisted track interferometer (TTI) for producing magic states is disclosed. The spin of ½-vortices may be exploited to produce magic states. The disclosed “twisted track interferometer” is a “topological twist” on the conventional Pabre-Pero interferometer adapted to topological superconductors. In the disclosed TTI, the probe particles may be Josephson vortices (JVs). JVs are estimated to be light and will tunnel more easily than Abrikosov vortices. Also, the disclosed TTI does not require multiple tunneling events. Rather, the JVs are propelled down thin insulating tracks within a 2D topological p-wave superconductor by a Magnus force generated by a tunneling supercurrent across the tracks. The JVs encounter tunneling junctions as they pass into the arms of the TTI.

Abstract: A computer-implemented method for encryption and decryption using quantum computational model is disclosed. Such a method includes providing a model of a lattice having a system of non-abelian anyons disposed thereon. From the lattice model, a first quantum state associated with the lattice is determined. Movement of non-abelian anyons within the lattice is modeled to model formation of first and second quantum braids in the space-time of the lattice. The first quantum braid corresponds to first text. The second quantum braid corresponds to second text. A second quantum state associated with the lattice is determined from the lattice model after formation of the first and second quantum braids has been modeled. The second quantum state corresponds to second text that is different from the first text.

Abstract: Disclosed herein are efficient geometries for dynamical topology changing (DTC), together with protocols to incorporate DTC into quantum computation. Given an Ising system, twisted depletion to implement a logical gate T, anyonic state teleportation into and out of the topology altering structure, and certain geometries of the (1,?2)-bands, a classical computer can be enabled to implement a quantum algorithm.

Abstract: An implementation of a single qubit phase gate for use in a quantum information processing scheme based on the ?=5/2 fractional quantum Hall (FQH) state is disclosed. Using sack geometry, a qubit consisting of two ?-quasiparticles, which may be isolated on respective antidots, may be separated by a constriction from the bulk of a two-dimensional electron gas in the ?=5/2 FQH state. An edge quasiparticle may induce a phase gate on the qubit. The number of quasiparticles that are allowed to traverse the edge path defines which gate is induced. For example, if a certain number of quasiparticles are allowed to traverse the path, then a ?/8 gate may be effected.

Abstract: A twisted track interferometer (TTI) for producing magic states is disclosed. The spin of ½-vortices may be exploited to produce magic states. The disclosed “twisted track interferometer” is a “topological twist” on the conventional Pabre-Pero interferometer adapted to topological superconductors. In the disclosed TTI, the probe particles may be Josephson vortices (JVs). JVs are estimated to be light and will tunnel more easily than Abrikosov vortices. Also, the disclosed TTI does not require multiple tunneling events. Rather, the JVs are propelled down thin insulating tracks within a 2D topological p-wave superconductor by a Magnus force generated by a tunneling supercurrent across the tracks. The JVs encounter tunneling junctions as they pass into the arms of the TTI.

Abstract: Disclosed herein is a topologically protected ?/8-gate which becomes universal when combined with the gates available through quasi-particle braiding and planar quasi-particle interferometry. A twisted interferometer, and a planar ?/8-gate in CTS, implemented with the help of the twisted interferometer, are disclosed. Embodiments are described in the context of state X (CTS) supported by an ISH, although the concept of a twisted-interferometer is more general and has relevance to all anionic, i.e. quasiparticle systems.

Abstract: Measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge is described. Various issues that would arise when realizing it in fractional quantum Hall systems are discussed.

Abstract: Measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge is described. Various issues that would arise when realizing it in fractional quantum Hall systems are discussed.

Abstract: A computer-implemented method for encryption and decryption using quantum computational model is disclosed. Such a method includes providing a model of a lattice having a system of non-abelian anyons disposed thereon. From the lattice model, a first quantum state associated with the lattice is determined. Movement of non-abelian anyons within the lattice is modeled to model formation of first and second quantum braids in the space-time of the lattice. The first quantum braid corresponds to first text. The second quantum braid corresponds to second text. A second quantum state associated with the lattice is determined from the lattice model after formation of the first and second quantum braids has been modeled. The second quantum state corresponds to second text that is different from the first text.

Abstract: An implementation of a single qubit phase gate for use in a quantum information processing scheme based on the ?=5/2 fractional quantum Hall (FQH) state is disclosed. Using sack geometry, a qubit consisting of two ?-quasiparticles. which may be isolated on respective antidots, may be separated by a constriction from the bulk of a two-dimensional electron gas in the ?=5/2 FQH state. An edge quasiparticle may induce a phase gate on the qubit. The number of quasiparticles that are allowed to traverse the edge path defines which gate is induced. For example, if a certain number of quasiparticles are allowed to traverse the path, then a ?/8 gate may be effected.

Abstract: Disclosed herein is a topologically protected ?/8-gate which becomes universal when combined with the gates available through quasi-particle braiding and planar quasi-particle interferometry. A twisted interferometer, and a planar ?/8-gate in CTS, implemented with the help of the twisted interferometer, are disclosed. Embodiments are described in the context of state X (CTS) supported by an ISH, although the concept of a twisted-interferometer is more general and has relevance to all anionic, i.e. quasiparticle systems.

Abstract: An implementation of a single qubit phase gate for use in a quantum information processing scheme based on the ?=5/2 fractional quantum Hall (FQH) state is disclosed. Using sack geometry, a qubit consisting of two ?-quasiparticles. which may be isolated on respective antidots, may be separated by a constriction from the bulk of a two-dimensional electron gas in the ?=5/2 FQH state. An edge quasiparticle may induce a phase gate on the qubit. The number of quasiparticles that are allowed to traverse the edge path defines which gate is induced. For example, if a certain number of quasiparticles are allowed to traverse the path, then a ?/8 gate may be effected.

Abstract: Disclosed herein is a topologically protected ?/8-gate which becomes universal when combined with the gates available through quasi-particle braiding and planar quasi-particle interferometry. A twisted interferometer, and a planar ?/8-gate in CTS, implemented with the help of the twisted interferometer, are disclosed. Embodiments are described in the context of state X (CTS) supported by an ISH, although the concept of a twisted-interferometer is more general and has relevance to all anionic, i.e. quasiparticle systems.