Abstract: A quantum device is fabricated by forming a network of nanowires oriented in a plane of a substrate to produce a Majorana-based topological qubit. The nanowires are formed from combinations of selective-area-grown semiconductor material along with regions of a superconducting material. The selective-area-grown semiconductor material is grown by etching trenches to define the nanowires and depositing the semiconductor material in the trenches. A side gate is formed in an etched trench and situated to control a topological segment of the qubit.

Abstract: The disclosure concerns fabricating a quantum device. In an embodiment, a method is disclosed comprising: providing a substrate and an insulator formed on the substrate; from combinations of selective-area-grown semiconductor material along with regions of a superconducting material, forming a network of nanowires oriented in a plane of the substrate which can be used to produce a Majorana-based topological qubit; and fabricating a side gate for controlling a topological segment of the qubit; wherein the selective-area-grown semiconductor material is grown on the substrate, by etching trenches in the insulator formed on the substrate to define the nanowires and depositing the semiconductor material in the trenches defining the nanowires; and wherein the fabricating of the side gate comprises etching the dielectric to create a trench for the side gate and depositing the side gate in the trench for the side gate.

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: 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: A quantum phase estimator may include at least one phase gate, at least one controlled unitary gate, and at least one measurement device. The quantum phase estimator receives at least one ancillary qubit and a calculational state comprised of multiple qubits. The phase gate may apply random phases to the ancillary qubit, which is used as a control to the controlled unitary gate. The controlled unitary gate applies a second random phase to the calculational state. The measurement device may measure a state of the ancillary qubit from which a phase of the calculational state may be determined.

Abstract: A quantum computer may include topologically protected quantum gates and non-protected quantum gates, which may be applied to topological qubits. The non-protected quantum gates may be implemented with a partial interferometric device. The partial interferometric device may include a Fabry-Pérot double point contact interferometer configured to apply “partial” interferometry to a topological qubit.

Abstract: A quantum computer may include topologically protected quantum gates and non-protected quantum gates, which may be applied to topological qubits. The non-protected quantum gates may be implemented with a partial interferometric device. The partial interferometric device may include a Fabry-Pérot double point contact interferometer configured to apply “partial” interferometry to a topological qubit.

Abstract: A quantum phase estimator may include at least one phase gate, at least one controlled unitary gate, and at least one measurement device. The quantum phase estimator receives at least one ancillary qubit and a calculational state comprised of multiple qubits. The phase gate may apply random phases to the ancillary qubit, which is used as a control to the controlled unitary gate. The controlled unitary gate applies a second random phase to the calculational state. The measurement device may measure a state of the ancillary qubit from which a phase of the calculational state may be determined.

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: A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for ?=5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |?>. This is a NOT gate on the {|1>, |?>} qubit and is effected by braiding of an electrically charged quasi particle ? which carries an additional SU(2)-charge. Read-out is accomplished by ?-particle interferometry.

Abstract: Experiments suggest that the mathematically weakest non-abelian TQFT may be physically the most robust. Such TQFT's—the v=5/2 FQHE state in particular—have discrete braid group representations, so one cannot build a universal quantum computer from these alone. Time tilted interferometry provides an extension of the computational power (to universal) within the context of topological protection. A known set of universal gates has been realized by topologically protected methods using “time-tilted interferometry” as an adjunct to the more familiar method of braiding quasi-particles. The method is “time-tilted interferometry by quasi-particles.” The system is its use to construct the gates {g1, g2, g3}.

Abstract: A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for ?=5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |?>. This is a NOT gate on the {|1>, |?>} qubit and is effected by braiding of an electrically charged quasi particle ? which carries an additional SU(2)-charge. Read-out is accomplished by ?-particle interferometry.

Abstract: A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for ?=5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |?>. This is a NOT gate on the {|1>, |?>} qubit and is effected by braiding of an electrically charged quasi particle a which carries an additional SU(2)-charge. Read-out is accomplished by ?-particle interferometry.

Abstract: A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for ?= 5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |?>. This is a NOT gate on the {|1>, |?>} qubit and is effected by braiding of an electrically charged quasi particle ? which carries an additional SU(2)-charge. Read-out is accomplished by ?-particle interferometry.

Abstract: Experiments suggest that the mathematically weakest non-abelian TQFT may be physically the most robust. Such TQFT's—the ?=5/2 FQHE state in particular—have discrete braid group representations, so one cannot build a universal quantum computer from these alone. Time tilted interferometry provides an extension of the computational power (to universal) within the context of topological protection. A known set of universal gates has been realized by topologically protected methods using “time-tilted interferometry” as an adjunct to the more familiar method of braiding quasi-particles. The method is “time-tilted interferometry by quasi-particles.” The system is its use to construct the gates {g1, g2, g3}.

Abstract: A quantum computer can only function stably if it can execute gates with extreme accuracy. “Topological protection” is a road to such accuracies. Quasi-particle interferometry is a tool for constructing topologically protected gates. Assuming the corrections of the Moore-Read Model for v= 5/2's FQHE (Nucl. Phys. B 360, 362 (1991)) we show how to manipulate the collective state of two e/4-charge anti-dots in order to switch said collective state from one carrying trivial SU(2) charge, |1>, to one carrying a fermionic SU(2) charge |?>. This is a NOT gate on the {|1>, |?>} qubit and is effected by braiding of an electrically charged quasi particle ? which carries an additional SU(2)-charge. Read-out is accomplished by ?-particle interferometry.

Abstract: The present invention provides a method for determining binding of a receptor to one or more ligands. The method consists of contacting a collective receptor variant population with one or more ligands and detecting binding of one or more ligands to the collective receptor variant population. The collective receptor variant population can be further divided into two or more subpopulations, one or more of the two or more subpopulations can be contacted with one or more ligands and one or more receptor variant subpopulations having binding activity to one or more ligands can be detected. The steps of dividing, contacting and detecting can be repeated one or more times. The invention also provides methods for identifying a receptor variant having optimal binding activity to one or more ligands. The invention additionally provides a method for determining binding of a ligand to one or more receptors.

Abstract: The present invention provides a method for determining binding of a receptor to one or more ligands. The method consists of contacting a collective receptor variant population with one or more ligands and detecting binding of one or more ligands to the collective receptor variant population. The collective receptor variant population can be further divided into two or more subpopulations, one or more of the two or more subpopulations can be contacted with one or more ligands and one or more receptor variant subpopulations having binding activity to one or more ligands can be detected. The steps of dividing, contacting and detecting can be repeated one or more times. The invention also provides methods for identifying a receptor variant having optimal binding activity to one or more ligands. The invention additionally provides a method for determining binding of a ligand to one or more receptors.