# US 2020/0401478 A1 · Topological quantum error correction using a data bus

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- Number: US 2020/0401478 A1
- Document ID: US20200401478A1
- Status: Published application
- Kind: A1
- Application number: 16/451,713
- Filed: 2019-06-25
- Published: 2020-12-24
- Earliest claimed: 2019-06-21
- Assignees: Turing Inc.
- Applicants: Turing Inc.
- Inventors: Michele Reilly; Simon Devitt
- Web page: https://patentgrep.com/patent/US20200401478A1

## CPC

- G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
- G06F 11/1068: {in sector programmable memories, e.g. flash disk (G06F11/1072 takes precedence)}
- G06F 13/4027: {using bus bridges (G06F13/4022 takes precedence)}
- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- G06N 10/40: Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
- G11C 29/52: Protection of memory contents; Detection of errors in memory contents
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G11C: STATIC STORES (semiconductor memory devices H10B)

## Abstract

Described herein is a Quantum Computing device comprising a first and a second square patch of qubits, each of the first and second square patch of qubits representing a logical qubit and being in a joint quantum state corresponding to a surface code, the surface code having a distance of two or more. The first and second square patch of qubits have a side-length equal to the distance plus one qubits. The device furthermore comprises one or more chain of qubits prepared in a joint GHZ state serving as a data bus. The chain of qubits neighbors both the first and the second square patch of qubits and has a length equal to or greater than the sum of the two side-lengths.

## Claims

### Claim 1

A quantum computing device comprising:
two or more logical qubits each consisting of a square patch of (d+1)×(d+1) qubits in a joint quantum state corresponding to a surface code, the qubits of each square patch being classified as either data qubits or syndrome qubits and the surface code having a distance d of two or more,
one or more rectangular patches of N×m qubits serving as a data bus with a length N>=2 and a width m>=1, the qubits of the data bus being in a joint quantum state, wherein the data bus connects the first and the second square patch of qubits in that each of the two or more square patches of qubits contains a qubit that is adjacent to a qubit of the data bus, wherein two qubits are adjacent if there are means for performing two qubit CNOT operations between them.

### Claim 2 (depends on 1)

The device of claim 1, wherein there are three or more logical qubits.

### Claim 3 (depends on 1)

The device of claim 1, wherein there is more than one data bus.

### Claim 4 (depends on 1)

The device of claim 1, wherein the distance d of the surface code is greater than two.

### Claim 5 (depends on 2)

The device of claim 2, wherein one of the one or more data buses connects more than two logical qubits.

### Claim 6 (depends on 1)

The device of claim 1, wherein the four or more square patches of qubits are arranged into an array.

### Claim 7 (depends on 2)

The device of claim 2, wherein the data bus connects all logical qubits.

### Claim 8 (depends on 1)

The device of claim 1, wherein the width m of the data bus is m=1.

### Claim 9 (depends on 8)

The device of claim 8, wherein the length N of the data bus is greater or equal to the sum of the side lengths of the square qubit patches encoding the logical qubits, i.e. N>=2(d+1).

### Claim 10 (depends on 9)

The device of claim 9, wherein the N qubits of the data bus are in a joint GHZ-state.

### Claim 11

A method for implementing a merge operation by performing an arbitrary length fault tolerant parity check in surface code quantum computing comprising:
a) preparing a first and a second logical qubit each in the form of square patch of qubits in a joint quantum state corresponding to a surface code with distance d, the square patches of qubits each having a side-length of (d+1) qubits, the qubits of the square patches being classified as either data qubits or syndrome qubits,
b) preparing a chain of N data bus qubits with N>=2 in a joint GHZ-state, wherein the chain of data qubits connects the first and second logical qubit in that each of the logical qubits contains one or more data qubits that is adjacent to a qubit of the data bus,
c) for each data qubit of the first and second logical qubit adjacent to a data bus qubit, performing a transversal CNOT operation between that data qubit and the qubit of the data bus to which it is adjacent,
d) measuring all qubits of the data bus,
e) repeating steps b)-d) d times, and
f) obtaining an error corrected measurement result by a majority vote over the individual measurement results of step d).

### Claim 12 (depends on 11)

The method of claim 11, wherein during step b the qubits of the data bus are kept protected against bit flip errors.

### Claim 13 (depends on 12)

The method of claim 12, wherein the qubits of the data bus are kept protected against bit flip errors by performing d cycles of error correction.

### Claim 14 (depends on 11)

The method of claim 11, wherein at least two CNOT operations are performed simultaneously.

### Claim 15 (depends on 14)

The method of claim 14, wherein all CNOT operations are performed simultaneously.