Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors3,4,5,6. Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error...
for error-corrected surface code logical qubits3,4,13. Heredis the code distance indicating 2d2 − 1 physical qubits used per logical qubit;pandεdare the physical and logical error rates, respectively; andpthris the threshold error rate of the code. Thus, whenp ≪ pthr, the e...
Finally, if all three bits are flipped so that the original message |000⟩ becomes |111⟩, the recipient has no way of knowing an error occurred. The code distance of a QEC code is the minimum number of errors that change one codeword into another, that is, the number of errors ...
Further, the distance properties of quantum codes are discussed and distance is related to error correction capability. Finally, quantum encoder and decoder implementations are described. 7.3.1 Redundancy and Quantum Error Correction A quantum error correction code (QECC) that encodes K qubits into N...
A stabilizer code is characterized by three parameters [[n,k,d]], where n is the number of physical qubits, k is the number of encoded logical qubits, and d is the minimum distance of the code (the smallest number of simultaneous qubit errors that can transform one valid codeword into ...
More efficient codes are obtained by allowing C_1 to have reduceddistance, and introducing sign changes among the code words in a systematicmanner. This systematic approach leads to single-error correcting codes for 3,4 and 5 information qubits with block lengths of 8, 10 and 11 qubits...
they all have distinct error syndromes. Stabilizer Codes Correct Errors A stabilizer code with distance d corrects (d-1)/2 errors (i.e., to correct t errors, we need d = 2t+1): E and F act the same, so we need not distinguish. Thm.: The code corrects errors for which E †...
*supports the rotated surface code up to distance 11 in real-time. Contact us How Deltaflow works Deltaflow turns unstable physical qubits into error-free logical qubits. It has three main components working in a continuous cycle to process petabytes of data: ...
surface-code AG47 1,385 answered5 hours ago 2votes 0answers 13views Why logical error rates from BP-OSD and MWPM are so different? stim minimum-weight-perfect-matching AG47 1,385 modified5 hours ago 2votes 0answers 31views +100
codeDistance"} } {"qubitParams": {"instructionSet":"Majorana", }"qecScheme": {"name":"surface_code","errorCorrectionThreshold":0.0015,"crossingPrefactor":0.08,"logicalCycleTime":"20 * oneQubitMeasurementTime * codeDistance","physicalQubitsPerLogicalQubit":"2 * codeDistance * codeDistance"} ...