# US 12,112,240 B2 · Fault correction for Clifford circuits > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,112,240 B2 - Document ID: US12112240B2 - Status: Granted - Kind: B2 - Application number: 17/820,701 - Filed: 2022-08-18 - Published: 2024-02-22 - Granted: 2024-10-08 - Earliest claimed: 2022-07-29 - Assignees: Microsoft Technology Licensing, LLC - Applicants: Microsoft Technology Licensing, LLC - Inventors: Nicolas Guillaume Delfosse; Adam Edward Paetznick - Web page: https://patentgrep.com/patent/US12112240B2 ## CPC - G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers - G06N 10/70: Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation - G06N 10/40: Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control - G06N 20/00: Machine learning - H03M 13/159: {Remainder calculation, e.g. for encoding and syndrome calculation} - H03M 13/611: {Specific encoding aspects, e.g. encoding by means of decoding} - G06N 3/08: Learning methods - G06N 3/084: Backpropagation, e.g. using gradient descent - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C) ## Abstract A method to correct a fault in application of a Clifford circuit to a qubit register of a quantum computer comprises: (A) receiving circuit data defining the Clifford circuit; (B) emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register; and (C) emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and on the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register. ## Claims ### Claim 1 A method to correct a fault in application of a Clifford circuit to a qubit register of a quantum computer, the method comprising: receiving circuit data defining the Clifford circuit; emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register; and emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and on the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register. ### Claim 2 (depends on 1) The method of claim 1 wherein the Clifford circuit includes one or more Clifford gates. ### Claim 3 (depends on 1) The method of claim 1 wherein the Clifford circuit includes one or more Pauli measurements. ### Claim 4 (depends on 1) The method of claim 1 wherein the Clifford circuit includes redundant measurements. ### Claim 5 (depends on 1) The method of claim 1 wherein the Clifford circuit is an error-syndrome extraction circuit. ### Claim 6 (depends on 1) The method of claim 1 wherein the space-time quantum code is a quantum-stabilizer code. ### Claim 7 (depends on 1) The method of claim 1 wherein each of the check operators is a stabilizer generator of the space-time quantum code, and wherein measurement of each stabilizer generator returns a result of a corresponding outcome check of the outcome code. ### Claim 8 (depends on 1) The method of claim 1 further comprising: building a lookup decoder for the space-time quantum code; and decoding the space-time quantum code via the lookup decoder to correct the fault in the application of the Clifford circuit to the qubit register. ### Claim 9 (depends on 1) The method of claim 1 further comprising: emitting low-density parity-check (LDPC) space-time quantum code based on the circuit data, the outcome code, and the space-time quantum code, the LDPC space-time quantum code including connected stabilizers of the space-time quantum code up to a predetermined weight; and decoding the LDPC space-time quantum code in an LDPC decoder to correct the fault in the application of the Clifford circuit to the qubit register. ### Claim 10 (depends on 9) The method of claim 9 wherein emitting the LDPC space-time quantum code comprises receiving the space-time quantum code in D dimensions and producing local stabilizer generators in D+1 dimensions. ### Claim 11 (depends on 9) The method of claim 9 wherein emitting the LDPC space-time quantum code comprises: constructing a space-time graph of the Clifford circuit; and constructing a set of stabilizer generators of the space-time code that are supported on local regions of the space-time graph. ### Claim 12 A computer system coupled operatively to a quantum computer, the computer system comprising: a processor; and operatively coupled to the processor, computer memory holding instructions that cause the processor to correct a fault in application of a Clifford circuit to a qubit register of the quantum computer, the instructions comprising: instructions (A) for receiving circuit data defining the Clifford circuit; instructions (B) for emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register; and instructions (C) for emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register. ### Claim 13 (depends on 12) The computer system of claim 12 wherein the Clifford circuit includes redundant measurements. ### Claim 14 (depends on 12) The computer system of claim 12 wherein the Clifford circuit is an error-syndrome extraction circuit. ### Claim 15 (depends on 12) The computer system of claim 12 wherein the space-time quantum code is a quantum-stabilizer code. ### Claim 16 (depends on 12) The computer system of claim 12 wherein each of the check operators is a stabilizer generator of the space-time quantum code, and wherein measurement of each stabilizer generator returns a result of a corresponding outcome check of the outcome code. ### Claim 17 (depends on 12) The computer system of claim 12 further comprising: instructions for emitting low-density parity-check (LDPC) space-time quantum code based on the circuit data, the outcome code, and the space-time quantum code, the LDPC space-time quantum code including connected stabilizers of the space-time quantum code up to a predetermined weight; and instructions for decoding the LDPC space-time quantum code in an LDPC decoder to correct the fault in the application of the Clifford circuit to the qubit register. ### Claim 18 (depends on 17) The computer system of claim 17 wherein emitting the LDPC space-time quantum code comprises receiving the space-time quantum code in D dimensions and producing local stabilizer generators in D+1 dimensions. ### Claim 19 (depends on 17) The computer system of claim 17 wherein emitting the LDPC space-time quantum code comprises: constructing a space-time graph of the Clifford circuit; and constructing a set of stabilizer generators of the space-time code that are supported on local regions of the space-time graph. ### Claim 20 A method to correct a fault in application of a Clifford circuit to a qubit register of a quantum computer, the method comprising: receiving circuit data defining the Clifford circuit; emitting outcome code based on the circuit data, the outcome code including a series of outcome checks each corresponding to an anticipated error syndrome of the application of the Clifford circuit to the qubit register; emitting space-time quantum code corresponding to the Clifford circuit based on the circuit data and on the outcome code, the space-time quantum code including a series of check operators that support quantum-error correction, thereby enabling fault correction in the application of the Clifford circuit to the qubit register; emitting low-density parity-check (LDPC) space-time quantum code based on the circuit data, the outcome code, and the space-time quantum code, the LDPC space-time quantum code including connected stabilizers of the space-time quantum code up to a predetermined weight; and decoding the LDPC space-time quantum code in an LDPC decoder to correct the fault in the application of the Clifford circuit to the qubit register.