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: 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: 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: Apparatus and methods for performing quantum computations are disclosed. Such quantum computational systems may include quantum computers, quantum cryptography systems, quantum information processing systems, quantum storage media, and special purpose quantum simulators.

Abstract: A computer-implemented method for encryption and decryption using a 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: A computer-implemented method for encryption and decryption using a 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: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice. Various platforms can be used to physically implement such a quantum computer. Platforms include an optical lattice, a Josephson junction array, a quantum dot, and a crystal structure. Each platform comprises an appropriate array of associated sites that can be used to approximate a desired Kagome geometry. A charge controller is desirably electrically coupled to the platform so that the array may be manipulated as desired.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such quantum computational systems may include quantum computers, quantum cryptography systems, quantum information processing systems, quantum storage media, and special purpose quantum simulators.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such quantum computational systems may include quantum computers, quantum cryptography systems, quantum information processing systems, quantum storage media, and special purpose quantum simulators.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice. A topological quantum computer encodes information in the configurations of different braids. The computer physically weaves braids in the 2D+1 space-time of the lattice, and uses this braiding to carry out calculations. A pair of quasi-particles, such as non-abelian anyons, can be moved around each other in a braid-like path. The quasi-particles can be moved as a result of a magnetic or optical field being applied to them, for example.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

Abstract: Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice. A topological quantum computer encodes information in the configurations of different braids. The computer physically weaves braids in the 2D+1 space-time of the lattice, and uses this braiding to carry out calculations. A pair of quasi-particles, such as non-abelian anyons, can be moved around each other in a braid-like path. The quasi-particles can be moved as a result of a magnetic or optical field being applied to them, for example.