# US 12,602,608 B2 · Method and device for quantum error filtering using quantum error filtering code

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- Number: US 12,602,608 B2
- Document ID: US12602608B2
- Status: Granted
- Kind: B2
- Application number: 18/701,496
- Filed: 2024-01-12
- Published: 2025-07-17
- Granted: 2026-04-14
- Earliest claimed: 2023-07-31
- Assignees: Korea Advanced Institute of Science and Technology
- Applicants: Korea Advanced Institute of Science and Technology
- Inventors: Joonwoo Bae; Hyeokjea Kwon
- Web page: https://patentgrep.com/patent/US12602608B2

## CPC

- G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
- G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers
- B82Y 10/00: Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
- 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

## Abstract

Provided is a method and device for quantum error filtering using a quantum error filtering code that may encode a quantum state for input data, may output, to a quantum circuit, a plurality of logical qubits each implemented as a plurality of physical qubits based on a predefined quantum error filtering code, and may detect a quantum error in one of the input logical qubits based on parities measured from the physical qubits for the logical qubits input through the quantum circuit.

## Claims

### Claim 1

A quantum error filtering device comprising:
an encoder comprising a first quantum circuit configured to output, to a quantum circuit, a plurality of logical qubits each implemented as a plurality of physical qubits based on a predefined quantum error filtering code; and
a filter comprising a second quantum circuit configured to detect a quantum error in one of the input logical qubits based on parities measured from the physical qubits for the logical qubits input through the quantum circuit,
wherein the filter is further configured to determine that a computational result from the quantum circuit is to be discarded based on the detected quantum error,
wherein the quantum error filtering code includes a 2-qubit quantum error filtering code or a 4-qubit quantum error filtering code,
wherein the 2-qubit quantum error filtering code is defined as two logical qubits as shown in the following equation,
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where |0>L represents logical qubit of 0 qubit, |1>L represents logical qubit of 1 qubit, and + and − represent phases, and
wherein the 4-qubit quantum error filtering code is defined as two logical qubits as shown in the following equation,
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where |0>L represents logical qubit of 0 qubit, |1>L represents logical qubit of 1 qubit, 0 and 1 represent bits, and + and − represent phases.

### Claim 2 (depends on 1)

The quantum error filtering device of claim 1, wherein the quantum error filtering code includes the 2-qubit quantum error filtering code, and
wherein the encoder is configured to output two logical qubits each implemented as two physical qubits of the same states based on the 2-qubit quantum error filtering code.

### Claim 3 (depends on 2)

The quantum error filtering device of claim 2, wherein, when the quantum error occurs between the encoder and the filter, the physical qubits for one of the output logical qubits change from the same states to different states.

### Claim 4 (depends on 2)

The quantum error filtering device of claim 2,
wherein the states represent either bits or phases, and
wherein the quantum error is either a bit error as the physical qubits change from the same bits to different bits or a phase error as the physical qubits change from the same phases to different phases.

### Claim 5 (depends on 2)

The quantum error filtering device of claim 2, wherein the filter is configured to,
determine that the quantum error is absent in the input logical qubits if a sum of parities for the input logical qubits is 0, and
determine that the quantum error is present in one of the input logical qubits if the sum of parities for the input logical qubits is 1.

### Claim 6 (depends on 1)

The quantum error filtering device of claim 1, wherein the quantum error filtering code includes the 4-qubit quantum error filtering code, and
wherein the encoder is configured to output two logical qubits each implemented as a combination of a plurality of pairs each including two physical qubits of the same states based on the 4-qubit quantum error filtering code.

### Claim 7 (depends on 6)

The quantum error filtering device of claim 6, wherein, when an error occurs between the encoder and the filter, the physical qubits for one of the pairs in at least one of the output logical qubits change from the same states to different states.

### Claim 8 (depends on 6)

The quantum error filtering device of claim 6,
wherein the states of the physical qubits of each of the pairs represent either bits or phases,
wherein the combination represents a combination of the bits and the phases,
wherein the quantum error includes a bit error as the physical qubits change from the same states to different states and a phase error as the physical qubits change from the same phases to different phases, and
wherein the filter comprises:
a first filter configured to detect the bit error for each of the input logical qubits; and
a second filter configured to detect the phase error for one of the input logical qubits.

### Claim 9

A quantum error filtering method of a computer device, the quantum error filtering method comprising:
outputting, to a quantum circuit, a plurality of logical qubits each implemented as a plurality of physical qubits based on a predefined quantum error filtering code;
detecting a quantum error in one of the input logical qubits based on parities measured from the physical qubits for the logical qubits input through the quantum circuit; and
determining that a computational result from the quantum circuit is to be discarded based on the detected quantum error,
wherein the quantum error filtering code includes a 2-qubit quantum error filtering code or a 4-qubit quantum error filtering code,
wherein the 2-qubit quantum error filtering code is defined as two logical qubits as shown in the following equation,
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where |0>L represents logical qubit of 0 qubit, |1>L represents logical qubit of 1 qubit, and + and − represent phases, and
wherein the 4-qubit quantum error filtering code is defined as two logical qubits as shown in the following equation,
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L
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where |0>L represents logical qubit of 0 qubit, |1>L represents logical qubit of 1 qubit, 0 and 1 represent bits, and + and − represent phases.

### Claim 10 (depends on 9)

The quantum error filtering method of claim 9, wherein the quantum error filtering code includes the 2-qubit quantum error filtering code, and
wherein the outputting to the quantum circuit comprises outputting two logical qubits each implemented as two physical qubits of the same states based on the 2-qubit quantum error filtering code.

### Claim 11 (depends on 10)

The quantum error filtering method of claim 10, wherein, when the quantum error occurs between an encoder comprising a first quantum circuit and a filter comprising a second quantum circuit, the physical qubits for one of the output logical qubits change from the same states to different states.

### Claim 12 (depends on 10)

The quantum error filtering method of claim 10, wherein the states represent either bits or phases, and
wherein the quantum error is either a bit error as the physical qubits change from the same bits to different bits or a phase error as the physical qubits change from the same phases to different phases.

### Claim 13 (depends on 10)

The quantum error filtering method of claim 10, wherein the detecting of the quantum error comprises:
determining that the quantum error is absent in the input logical qubits if a sum of parities for the input logical qubits is 0; and
determining that the quantum error is present in one of the input logical qubits if the sum of parities for the input logical qubits is 1.

### Claim 14 (depends on 9)

The quantum error filtering method of claim 9, wherein the quantum error filtering code includes the 4-qubit quantum error filtering code, and
wherein the outputting to the quantum circuit comprises outputting two logical qubits each implemented as a combination of a plurality of pairs each including two physical qubits of the same states based on the 4-qubit quantum error filtering code.

### Claim 15 (depends on 14)

The quantum error filtering method of claim 14, wherein, when an error occurs between an encoder comprising a first quantum circuit and a filter comprising a second quantum circuit, the physical qubits for one of the pairs in at least one of the output logical qubits change from the same states to different states.

### Claim 16 (depends on 14)

The quantum error filtering method of claim 14, wherein the states of the physical qubits of each of the pairs represent either bits or phases,
wherein the combination represents a combination of the bits and the phases,
wherein the quantum error includes a bit error as the physical qubits change from the same states to different states and a phase error as the physical qubits change from the same phases to different phases, and
wherein the detecting of the quantum error comprises:
detecting the bit error for each of the input logical qubits; and
detecting the phase error for one of the input logical qubits.

### Claim 17

A non-transitory computer-readable recording medium storing instructions that, when executed by a processor, cause the processor to perform a quantum error filtering method on a computer device, the quantum error filtering method comprising:
outputting, to a quantum circuit, a plurality of logical qubits each implemented as a plurality of physical qubits based on a predefined quantum error filtering code;
detecting a quantum error in one of the input logical qubits based on parities measured from the physical qubits for the logical qubits input through the quantum circuit; and
determining that a computational result from the quantum circuit is to be discarded based on the detected quantum error,
wherein the quantum error filtering code includes a 2-qubit quantum error filtering code or a 4-qubit quantum error filtering code,
wherein the 2-qubit quantum error filtering code is defined as two logical qubits as shown in the following equation,
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>
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,
❘
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>
L
=
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>
where |0>L represents logical qubit of 0 qubit |1>L represents logical qubit of 1 qubit, and + and − represent phases, and
wherein the 4-qubit quantum error filtering code is defined as two logical qubits as shown in the following equation,
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where |0>L represents logical qubit of 0 qubit, |1>L represents logical qubit of 1 qubit, 0 and 1 represent bits, and + and − represent phases.