aqora

Quantum Error Correction

S. Rajasekar, R. Velusamy

Realization of long distance quantum cryptography requires quantum error correction (QEC) of the errors introduced by noise on communication channels. This chapter begins with presenting common sources of errors in QEC. For quantum information processing qubits using photons, trapped ions, superconducting circuits and spins in semiconductors have been considered. Coherent quantum errors arise due to the errors associated with system controls and/or characterization where imprecise operation on the qubit introduces inaccurate Hamiltonian dynamics. The basic principle involved in classical error correction is to increase the number of bits more than is required for a given amount of information. Digitization of quantum errors makes it possible to correct any quantum error using the ability to correct a finite set of errors. The use of stabilizer codes to describe QEC codes is highly useful. It allows for easy synthesis of correction circuits and also shows how logical operations can be performed directly on encoded data.Realization of long distance quantum cryptography requires quantum error correction (QEC) of the errors introduced by noise on communication channels. This chapter begins with presenting common sources of errors in QEC. For quantum information processing qubits using photons, trapped ions, superconducting circuits and spins in semiconductors have been considered. Coherent quantum errors arise due to the errors associated with system controls and/or characterization where imprecise operation on the qubit introduces inaccurate Hamiltonian dynamics. The basic principle involved in classical error correction is to increase the number of bits more than is required for a given amount of information. Digitization of quantum errors makes it possible to correct any quantum error using the ability to correct a finite set of errors. The use of stabilizer codes to describe QEC codes is highly useful. It allows for easy synthesis of correction circuits and also shows how logical operations can be performed directly on encoded data.

CRC Press eBooksOct 5, 20220 citations

QECirc: A Community-Driven, FAIR Library of Quantum Error Correction Circuits

Ludwig Schmid, Tom Peham, Robert Wille

Quantum error correction (QEC) underpins fault-tolerant quantum computing, but the circuits that realize QEC codes (encoders, logical state-preparation and gate routines, and syndrome-extraction schedules) are scattered across papers and one-off repositories in incompatible formats, often documented too sparsely to reconstruct or reuse. We present QECirc (https://qecirc.com/), a community-driven, open library that makes QEC circuits Findable, Accessible, Interoperable, and Reusable (FAIR). Each entry links to its underlying code, ships in Stim and OpenQASM with interactive visualizations, and is checked for correctness before publication. In short, where a catalog such as the Error Correction Zoo describes the codes, QECirc provides the concrete circuits that realize them.Quantum error correction (QEC) underpins fault-tolerant quantum computing, but the circuits that realize QEC codes (encoders, logical state-preparation and gate routines, and syndrome-extraction schedules) are scattered across papers and one-off repositories in incompatible formats, often documented too sparsely to reconstruct or reuse. We present QECirc (https://qecirc.com/), a community-driven, open library that makes QEC circuits Findable, Accessible, Interoperable, and Reusable (FAIR). Each entry links to its underlying code, ships in Stim and OpenQASM with interactive visualizations, and is checked for correctness before publication. In short, where a catalog such as the Error Correction Zoo describes the codes, QECirc provides the concrete circuits that realize them.

quant-pharXiv:2609.20182Jul 29, 20260 citations

Realization of quantum error correction

John Chiaverini, Dietrich G. Leibfried, Tobias Schaetz +9 more

NatureDec 1, 2004517 citations

Quantum Computing | NIST

Emanuel H. Knill

NatureJan 28, 20100 citations

Quantum Metrology | NIST

R. Harris, J. Niemeyer

Nov 11, 20110 citations

Correct Implementation of NIST SP 800-22 Statistical Tests for Quantum Random Number Generator Validation

Will Daoud

We identify four implementation error classes in NIST SP 800-22 statistical tests: (1) run-counting substituted for Berlekamp-Massey in Test 10, (2) p-value boosting in Test 12, (3) chi-squared deflation in Test 14, (4) unconditional health test passes. Corrected implementations produce genuine 15/15 PASS on PHM quantum entropy. Hardware validation reveals that IBM superconducting qubit readout asymmetry (0.39%) causes NIST failures at 1M bits, requiring readout error mitigation for certification. IBM job: d8e3t73o3njc73eu7880. Note: Also available on IACR ePrint https://eprint.iacr.org/2026/109748We identify four implementation error classes in NIST SP 800-22 statistical tests: (1) run-counting substituted for Berlekamp-Massey in Test 10, (2) p-value boosting in Test 12, (3) chi-squared deflation in Test 14, (4) unconditional health test passes. Corrected implementations produce genuine 15/15 PASS on PHM quantum entropy. Hardware validation reveals that IBM superconducting qubit readout asymmetry (0.39%) causes NIST failures at 1M bits, requiring readout error mitigation for certification. IBM job: d8e3t73o3njc73eu7880. Note: Also available on IACR ePrint https://eprint.iacr.org/2026/109748

May 31, 20260 citations

Realization of quantum error correction | NIST

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