# US 12,762,031 B2 · Adaptive basis based on fusion graph edges and connected components

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- Number: US 12,762,031 B2
- Document ID: US12762031B2
- Status: Granted
- Kind: B2
- Application number: 18/668,863
- Filed: 2024-05-20
- Published: 2026-02-19
- Granted: 2026-10-13
- Earliest claimed: 2020-03-30
- Assignees: Psiquantum, Corp.
- Applicants: PsiQuantum, Corp.
- Inventors: Mihir Pant
- Web page: https://patentgrep.com/patent/US12762031B2

## CPC

- G06F 11/25: Testing of logic operation, e.g. by logic analysers
- G06F 11/1004: {to protect a block of data words, e.g. CRC or checksum (G06F11/1076 takes precedence; security arrangements for protecting computers or computer systems against unauthorized activity G06F21/00)}
- G06N 3/08: Learning methods
- G06N 10/00: Quantum computing, i.e. information processing based on quantum-mechanical phenomena
- G06N 10/40: Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
- G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
- G06F 3/0604: {Improving or facilitating administration, e.g. storage management}
- G06F 3/0659: {Command handling arrangements, e.g. command buffers, queues, command scheduling}
- G06F 3/0679: {Non-volatile semiconductor memory device, e.g. flash memory, one time programmable memory [OTP]}
- H10N 99/05: {Devices based on quantum mechanical effects, e.g. quantum interference devices or metal single-electron transistors}
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- H10N: ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR

## Abstract

A quantum computing system and methods for performing fault-tolerant quantum computing. A fusion controller sequentially performs a series of fusion measurements on different fusion sites of a plurality of fusion sites to obtain a respective series of classical measurement results. The series of fusion measurements is performed on quantum modes of a logical qubit. For respective fusion measurements of the series of fusion measurements, a basis for performing the respective fusion measurement is selected based on classical measurement results of previous fusion measurements. The series of classical measurement results are in the memory medium.

## Claims

### Claim 1

A method comprising:
receiving, by one or more processors, measurement data describing a previous fusion measurement;
updating syndrome data based on the measurement data, the syndrome data comprising a first graph in a primary basis and a second graph in a dual basis that corresponds to the primary basis;
identifying a connected component in the first graph of the primary basis, the connected component comprising a contiguous set of erased edges;
selecting an edge in the primary basis for a subsequent fusion measurement based on the updated syndrome data, the edge being selected based on both ends of the edge being connected to the connected component; and
transmitting instructions to perform the subsequent fusion measurement on the selected edge in the primary basis.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
receiving additional measurement data from application of the subsequent fusion measurement according to the instructions; and
storing the additional measurement data.

### Claim 3 (depends on 1)

The method of claim 1, wherein the measurement data is generated by an external device that applies the previous fusion measurement on a first quantum mode and a second quantum mode.

### Claim 4 (depends on 3)

The method of claim 3, wherein the external device applies the subsequent fusion measurement on the selected edge in the primary basis.

### Claim 5 (depends on 4)

The method of claim 4, wherein a third quantum mode and a fourth quantum mode correspond to the selected edge.

### Claim 6 (depends on 5)

The method of claim 5, wherein the subsequent fusion measurement is applied to the third quantum mode and the fourth quantum mode in the primary basis.

### Claim 7 (depends on 5)

The method of claim 5, wherein a logical qubit comprises the first quantum mode, second quantum mode, third quantum mode, and the fourth quantum mode.

### Claim 8 (depends on 7)

The method of claim 7, wherein a failure result of the subsequent fusion measurement for the edge in the primary basis does not increase a likelihood of logical error in the logical qubit.

### Claim 9 (depends on 3)

The method of claim 3, wherein the instructions for the subsequent fusion measurement are transmitted to the external device.

### Claim 10 (depends on 9)

The method of claim 9, further comprising:
receiving additional measurement data from application of the subsequent fusion measurement according to the instructions,
wherein the measurement data and the additional measurement data are received from the external device.

### Claim 11 (depends on 3)

The method of claim 3, wherein the external device implements a Hadamard gate to perform the subsequent fusion measurement according to the instructions.

### Claim 12

A system comprising:
one or more processors of a machine; and
memory-storing instructions that, when executed by the one or more processors, cause the machine to perform operations comprising:
receive measurement data describing a previous fusion measurement;
update syndrome data based on the measurement data, the syndrome data comprising a first graph in a primary basis and a second graph in a dual basis that corresponds to the primary basis;
identify a connected component in the first graph of the primary basis, the connected component comprising a contiguous set of erased edges;
select an edge in the primary basis for a subsequent fusion measurement based on the updated syndrome data, the edge being selected based on both ends of the edge being connected to the connected component; and
transmit instructions to perform the subsequent fusion measurement on the selected edge in the primary basis.

### Claim 13 (depends on 12)

The system of claim 12, wherein the operations further comprise:
receive additional measurement data from application of the subsequent fusion measurement according to the instructions; and
store the additional measurement data.

### Claim 14 (depends on 12)

The system of claim 12, wherein the measurement data is generated by an external device that applies the previous fusion measurement on a first quantum mode and a second quantum mode.

### Claim 15 (depends on 14)

The system of claim 14, wherein the external device applies the subsequent fusion measurement on the selected edge in the primary basis.

### Claim 16 (depends on 15)

The system of claim 15, wherein a third quantum mode and a fourth quantum mode correspond to the selected edge.

### Claim 17 (depends on 16)

The system of claim 16, wherein the subsequent fusion measurement is applied to the third quantum mode and the fourth quantum mode in the primary basis.

### Claim 18 (depends on 16)

The system of claim 16, wherein a logical qubit comprises the first quantum mode, second quantum mode, third quantum mode, and the fourth quantum mode, and wherein a failure result of the subsequent fusion measurement for the edge in the primary basis does not increase a likelihood of logical error in the logical qubit.

### Claim 19

A machine-readable storage device embodying instructions that, when executed by a machine, cause the machine to perform operations comprising:
receive measurement data describing a previous fusion measurement;
update syndrome data based on the measurement data, the syndrome data comprising a first graph in a primary basis and a second graph in a dual basis that corresponds to the primary basis;
identify a connected component in the first graph of the dual basis, the connected component comprising a contiguous set of erased edges;
select an edge in the dual basis for a subsequent fusion measurement based on the updated syndrome data, the edge being selected based on both ends of the edge being connected to the connected component; and
transmit instructions to perform the subsequent fusion measurement on the selected edge in the dual basis.

### Claim 20 (depends on 19)

The machine-readable storage device of claim 19, wherein the operations further comprise:
receive additional measurement data from application of the subsequent fusion measurement according to the instructions; and
store the additional measurement data.