# US 9,517,931 B2 · Measurement-only topological quantum computation

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- Number: US 9,517,931 B2
- Document ID: US9517931B2
- Status: Granted
- Kind: B2
- Application number: 13/465,374
- Filed: 2012-05-07
- Published: 2012-08-30
- Granted: 2016-12-13
- Earliest claimed: 2007-09-07
- Assignees: Microsoft Technology Licensing, LLC
- Applicants: Michael Freedman; Chetan Nayak; Parsa Bonderson
- Inventors: Michael Freedman; Chetan Nayak; Parsa Bonderson
- Web page: https://patentgrep.com/patent/US9517931B2

## CPC

- G06N 20/00: Machine learning
- B82Y 10/00: Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- G01B 2290/55: Quantum effects
- G06N 5/02: Knowledge representation; Symbolic representation
- G06N 20/10: using kernel methods, e.g. support vector machines [SVM]
- G06Q 10/10: Office automation; Time management
- G06Q 30/02: Marketing; Price estimation or determination; Fundraising
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- B82Y: SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G06Q: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR

## 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.

## Claims

### Claim 1

A quantum computer, comprising:
an array of computational anyons;
an array of entanglement anyons situated so that at least one entanglement anyon is situated between each adjacent pair of computational anyons;
a fractional quantum Hall (FQH) fluid; and
a plurality of contacts coupled to the FQH fluid so as define at least one interferometer formed in an edge of the FQH fluid for measuring a current associated with coupling of a selected computational anyon to at least one associated entanglement anyon or a coupling of adjacent entanglement anyons, wherein a quantum computation is defined at least in part by the current measurement.

### Claim 2 (depends on 1)

The quantum computer of claim 1, wherein a result of the quantum computation is based on a quantum state associated with the FQH fluid after the current has been measured.

### Claim 3 (depends on 1)

The quantum computer of claim 1, wherein the FQH fluid is in a first quantum state before the current is measured, and a result of the quantum computation is based on a second quantum state associated with the FQH fluid after the current has been measured.

### Claim 4 (depends on 1)

The quantum computer of claim 1, wherein measuring the current affects the quantum state of at least one of the computational or entanglement anyons.

### Claim 5 (depends on 1)

The quantum computer of claim 1, wherein the measured current is associated with a collective quantum state of at least one computational anyon, at least one entanglement anyon, or a combination thereof.

### Claim 6 (depends on 5)

The quantum computer of claim 5, wherein a result of the quantum computation is a braiding transformation.

### Claim 7 (depends on 1)

The quantum computer of claim 1, wherein at least one of the array of computational anyons and the array of entanglement anyons are defined as least energy excitations of a system of real particles on which the fractional quantum Hall effect fluid is formed.

### Claim 8 (depends on 1)

The quantum computer of claim 1, wherein computational anyons are stationary anyons.

### Claim 9 (depends on 1)

The quantum computer of claim 1, wherein the quantum computation includes a braiding transformation.

### Claim 10

A quantum computer, comprising:
a fractional quantum Hall (FQH) fluid;
an array of computational anyons;
an array of entanglement anyons situated so that at least one entanglement anyon is situated between each adjacent pair of computational anyons; and
a plurality of contacts coupled to the FQH fluid so as define at least:
a first interferometer situated to measure a current associated with a first quantum state based on a coupling of a first computational anyon and at least a first entanglement anyon situated adjacent the first computational anyon;
a second interferometer formed in an edge of the FQH fluid situated to measure a current associated with a coupling of adjacent entanglement anyons; and
a third interferometer situated to measure a current associated with a second quantum state associated with the FQH fluid based on a coupling of a second computational anyon and at least a second entanglement anyon situated adjacent the second computational anyon.

### Claim 11 (depends on 10)

The quantum computer of claim 10, wherein the second interferometer is situated so that the current associated with a coupling of adjacent entanglement anyons is measured after the current associated with the first computational anyon and at least the first entanglement anyon situated adjacent the computational anyon is measured.

### Claim 12 (depends on 11)

The quantum computer of claim 11, wherein the current associated with the first quantum state is measured before the current associated with the coupling of adjacent entanglement anyons is measured.

### Claim 13 (depends on 11)

The quantum computer of claim 11, wherein the entanglement anyons are provided by excitations in the edge current.

### Claim 14 (depends on 10)

The quantum computer of claim 10, wherein the first and second quantum states associated with the FQH fluid are topological quantum states.

### Claim 15 (depends on 10)

The quantum computer of claim 10, wherein computational anyons are stationary anyons.

### Claim 16

A quantum computing method for performing anyonic quantum computation, the method comprising:
performing a sequence of edge-current measurements in an interferometer, the sequence of edge-current measurements defining a braiding transformation, each said edge-current measurement being associated with one or more probe anyons defined by a fractional quantum Hall (FQH) effect fluid, wherein the probe anyons are associated with at least one edge current of the fractional quantum Hall effect fluid.

### Claim 17 (depends on 16)

The quantum computing method of claim 16, wherein each edge-current measurement includes deforming an edge of the FQH fluid to form an interferometer in the FQH fluid, then performing the edge current measurement to provide an interferometry measurement, and then destructing the deformed edge to remove the interferometer.

### Claim 18 (depends on 16)

The quantum computing method of claim 16, wherein each collection of non-abelian anyons includes no more than eight non-abelian anyons, each non-abelian anyon in each collection is adjacent to at least one other non-abelian anyon in the collection, and each collection is bounded in a physical region in the FQH fluid.

### Claim 19 (depends on 16)

The quantum computing method of claim 16, wherein a quantum computation is defined at least in part by each of the edge-current measurements.

### Claim 20 (depends on 16)

The quantum computing method of claim 16, wherein a quantum computation is defined by the sequence of edge-current measurements.

### Claim 21 (depends on 16)

The quantum computing method of claim 16, wherein the non-abelian anyons include stationary anyons.