Measurement-only topological quantum computation
View Patent ↗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.
1. A method for performing measurement-only anyonic quantum computation, the method comprising:
measuring a first quantum state associated with a fractional quantum Hall (FQH) fluid;
measuring a first current associated with a first collective quantum state of a first collection of non-abelian anyons emergent in the FQH fluid, wherein a computation is defined at least in part by the first current measurement;
measuring a second quantum state associated with the FQH fluid after the first current has been measured; and
determining a result of the computation based on the second quantum state.
2. The method of claim 1 , wherein measuring the current affects the collective quantum state of the collection of non-abelian anyons.
3. The method of claim 2 , further comprising:
identifying a second collection of non-abelian anyons based on the collective quantum state of the first collection of non-abelian anyons after the first current has been measured; and
measuring a second current associated with the second collection of non-abelian anyons.
4. The method of claim 3 , wherein the second collection of non-abelian anyons is identified based on the computation.
5. The method of claim 1 , wherein the first and second quantum states of the FQH fluid are measured interferometrically.
6. The method of claim 5 , wherein an outcome of the interferometric measurement is determined by measuring an edge current in the FQH fluid.
7. The method of claim 6 , wherein the interferometric measurement is carried out by one or more probe anyons.
8. The method of claim 7 , wherein the probe anyons are provided by excitations in the edge current.
9. The method of claim 1 , wherein each non-abelian anyon in the first collection is adjacent to at least one other non-abelian anyon in the first collection.
10. The method of claim 1 , wherein the first collection of non-abelian anyons is bounded in a physical region in the FQH fluid.
11. The method of claim 1 , wherein the first collection includes no more than eight non-abelian anyons.
12. The method of claim 1 , wherein the non-abelian anyons emerge as least-energy excitations of a system of real particles on which the fractional quantum Hall effect fluid is formed.
13. The method of claim 1 , wherein the first and second quantum states associated with the FQH fluid are topological quantum states.
14. A method for performing measurement-only anyonic quantum computation, comprising:
measuring a first quantum state associated with a fractional quantum Hall (FQH) fluid;
performing a sequence of edge-current measurements, the sequence of edge-current measurements defining a computation, each said edge-current measurement being associated with a respective collection of non-abelian anyons emergent in the FQH fluid, wherein the non-abelian anyons emerge as least-energy excitations of a system of real particles on which the fractional quantum Hall effect fluid is formed;
measuring a second quantum state associated with a fractional quantum Hall (FQH) fluid after the sequence of edge-current measurements have been performed; and
determining a result of the computation based on the second quantum state.
15. The method of claim 14 , wherein the sequence of edge-current measurements includes a first edge-current measurement associated with a first collection of non-abelian anyons, and a second edge-current measurement associated with a second collection of non-abelian anyons, and wherein the non-abelian anyons that form the second collection are determined from an outcome of the first edge-current measurement.
16. The method of claim 14 , wherein the first and second quantum states of the FQH fluid are measured via interferometry, and an outcome of the interferometry measurement is determined by measuring the edge current in the FQH fluid.
17. The method of claim 16 , wherein each interferometry measurement includes: first deforming an edge of the FQH fluid to form an interferometer in the FQH fluid, then performing the edge current measurement that gives the interferometry measurement, and then un-deforming the deformed edge to remove the interferometer.
18. The method of claim 14 , wherein each collection of non-abelian anyons includes no more than eight non-abelian anyons, wherein each non-abelian anyon in each collection is adjacent to at least one other non-abelian anyon in the collection, and wherein each collection is bounded in a physical region in the FQH fluid.
19. A measurement-only anyonic quantum computer, the quantum computer comprising:
means for measuring a first quantum state associated with a fractional quantum Hall (FQH) fluid;
means for measuring a first current associated with a first collective quantum state of a first collection of non-abelian anyons emergent in the FQH fluid, wherein a computation is defined at least in part by the first current measurement;
means for measuring a second quantum state associated with the FQH fluid after the first current has been measured; and
means for determining a result of the computation based on the second quantum state.
20. The quantum computer of claim 19 , wherein the means for measuring the first current comprises an interferometer formed in an edge of the FQH fluid.