Use of sack geometry to implement a single qubit phase gate
An implementation of a single qubit phase gate for use in a quantum information processing scheme based on the υ=5/2 fractional quantum Hall (FQH) state is disclosed. Using sack geometry, a qubit consisting of two σ-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 υ=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 π/8 gate may be effected.
1. A method for implementing a single qubit phase gate, the method comprising:
forming a set-off region in a bulk of two-dimensional electron gas, the set-off region defined by an edge of the electron gas;
isolating first and second σ-quasiparticles on respective antidots formed in the set-off region;
allowing an edge current to flow around the edge of the set-off region for an amount of time; and
identifying a phase gate associated with the amount of time for which the edge current is allowed to flow around the edge of the set-off region.
2. The method of claim 1 , wherein forming the set-off region comprises deforming an edge of the electron gas to form a constriction that defines the set-off region.
3. The method of claim 2 , wherein the constriction separates the set-off region from the remainder of the bulk of the electron gas.
4. The method of claim 1 , further comprising:
determining a size of the set-off region, determining a tunneling strength associated with the set-off region, and determining the amount of edge current flowing around the set-off region.
5. The method of claim 4 , wherein the amount of time for which the edge current is allowed to flow around the set-off region is based on the size of the set-off region, the tunneling strength associated with the set-off region, and the amount of edge current flowing around the set-off region.
6. The method of claim 1 , wherein the σ-quasiparticles are non-abelian anyons.
7. The method of claim 6 , wherein the σ-quasiparticles are Ising anyons.
8. The method of claim 1 , wherein the phase gate is a π/8 phase gate.
9. The method of claim 1 , wherein the electron gas is a υ=5/2 fractional quantum Hall fluid.
10. A single qubit phase gate, comprising:
a bulk of two-dimensional electron gas having an edge, a portion of the edge forming a constriction that separates a set-off region of the gas from the remainder of the bulk, wherein first and second σ-quasiparticles are disposed in the set-off region, and an edge current flows around the edge of the set-off region,
wherein the σ-quasiparticles are isolated on respective antidots formed in the electron gas.
11. The phase gate of claim 10 , wherein the σ-quasiparticles define a qubit.
12. The phase gate of claim 10 , further comprising:
current-measuring means for measuring the edge current flowing around the edge of the set-off region.
13. The phase gate of claim 10 , further comprising: edge-deforming means for deforming the edge of the electron gas to alter a size of the constriction.
14. A method for implementing a single qubit phase gate, the method comprising:
isolating a pair of σ-quasiparticles on respective antidots formed in a set-off region in a two-dimensional electron gas in the υ=5/2 fractional quantum Hall state, wherein the set-off region is separated from the remainder of the gas by a constriction, the electron gas in the υ=5/2 fractional quantum Hall state, and the σ-quasiparticles define a qubit; and
inducing a phase gate on the qubit by allowing a number of σ-quasiparticles to traverse an edge of the set-off region.
15. The method of claim 14 , wherein the .sigma.-quasiparticles have topological charges that form |0> and |1> states of the qubit.
16. The method of claim 15 , further comprising:
adjusting a relative phase of the |0> and |1> states of the qubit by altering a size of the constriction.
17. The method of claim 16 , wherein the relative phase advances by an amount that is based on an amount of time over which the size of the constriction is altered, a strength of edge current tunneling at the constriction, an amount of current flowing through the edge, and the area of the electron gas enclosed in the set-off region.
18. The method of claim 17 , further comprising:
allowing the edge current to flow along the edge of the set-off region for a length of time that is based on the tunneling amplitude at the constriction and on an amount by which the phase is advanced due to a σ-quasiparticle traversing the edge of the set-off region.
19. A method for implementing a single qubit phase gate, the method comprising:
forming a set-off region in a bulk of two-dimensional electron gas, the set-off region defined by an edge of the electron gas;
isolating first and second σ-quasiparticles in the set-off region;
allowing an edge current to flow around the edge of the set-off region for an amount of time; and
identifying a π/8 phase gate associated with the amount of time for which the edge current is allowed to flow around the edge of the set-off region.
20. The method of claim 1 , wherein forming the set-off region comprises deforming an edge of the electron gas to form a constriction that defines the set-off region.
21. The method of claim 2 , wherein the constriction separates the set-off region from the remainder of the bulk of the electron gas.
22. The method of claim 1 , further comprising:
determining a size of the set-off region, determining a tunneling strength associated with the set-off region, and determining the amount of edge current flowing around the set-off region.
23. The method of claim 4 , wherein the amount of time for which the edge current is allowed to flow around the set-off region is based on the size of the set-off region, the tunneling strength associated with the set-off region, and the amount of edge current flowing around the set-off region.
24. The method of claim 1 , wherein the σ-quasiparticles are non-abelian anyons.
25. The method of claim 6 , wherein the σ-quasiparticles are Ising anyons.
26. The method of claim 1 , wherein the electron gas is a υ=5/2 fractional quantum Hall fluid.
27. A single qubit phase gate, comprising:
a bulk of two-dimensional electron gas having an edge, a portion of the edge forming a constriction that separates a set-off region of the gas from the remainder of the bulk, and
edge-deforming means for deforming the edge of the electron gas to alter a size of the constriction,
wherein first and second σ-quasiparticles are disposed in the set-off region, and an edge current flows around the edge of the set-off region.
28. The phase gate of claim 27 , wherein the σ-quasiparticles define a qubit.
29. The phase gate of claim 27 , further comprising:
current-measuring means for measuring the edge current flowing around the edge of the set-off region.