#CLIFFORD GROUP QUANTUM ERROR CORRECTION PDF#
#CLIFFORD GROUP QUANTUM ERROR CORRECTION CODE#
#CLIFFORD GROUP QUANTUM ERROR CORRECTION PLUS#

DS codes generalize this idea for simultaneous correction of both data qubits and syndrome bits errors. SM codes protect syndrome with linearly dependent redundant stabilizer measurements. To obtain reliable error syndromes using imperfect physical circuits, we propose syndrome measurement (SM) and quantum data-syndrome (DS) codes. Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of measured error syndromes. Finally, apart from SteaneвЂ™s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered.

#CLIFFORD GROUP QUANTUM ERROR CORRECTION CODE#

The simulation and analytical results explicitly show that by utilizing QTECCs, the fidelity of the quantum gates can be beneficially improved, provided that quantum gates satisfying a certain minimum depolarization fidelity threshold (F_, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when SteaneвЂ™s quantum error correction code is employed. Secondly, we provide examples of the advocated framework by invoking quantum topological error correction codes (QTECCs) for protecting both transversal Hadamard gates and CNOT gates. In this treatise, we approach this problem by firstly presenting the general framework of protecting quantum gates by the amalgamation of the transversal configuration of quantum gates and quantum stabilizer codes (QSCs), which can be viewed as syndrome-based QECCs. In this scenario, the primary challenge is to find the sufficient condition required by each of the quantum gates for beneficially employing QECCs in order to yield reliability improvements given that the quantum gates utilized by the QECCs also introduce quantum decoherence. However, incorporating quantum gates for performing error correction potentially introduces more sources of quantum decoherence into the quantum computers.

Variations on the threshold theorem (e.g.The employment of quantum error correction codes (QECCs) within quantum computers potentially offers a reliability improvement for both quantum computation and communications tasks.

Comparison of thresholds from different codes.

Quantum expander codes or other LDPC codes.

If you want a subject not on this list, let me know and we can discuss if it is acceptable. Recommended length: about 20 pages Possible paper topics

#CLIFFORD GROUP QUANTUM ERROR CORRECTION PLUS#

Then I will discuss with you which research papers (usually 1-3, depending on size) to cover.Дue: April 7, written term paper plus a presentation to the class I recommend that students tell me the subject of their final project by early March. Also, please do not distribute copies of the book outside the class. Please send any comments you may have on it to me (DG). The textbook (a work in progress), Surviving as a Quantum Computer in a Classical World, will be available in class. 17, 24, 31 will be taught by Alex Kubica)

March: Other topics (Note: lectures on Mar.

Shor, Steane, and Knill quantum error correction.

Bounds on quantum error-correcting codes.

#CLIFFORD GROUP QUANTUM ERROR CORRECTION PDF#

Turn in problem sets in class or as PDF (scanned, not picture) by e-mail to and The final project will consist of a paper and presentation of material from research papers on a topic related to the subject of the class. Grading: 70% of the grade will come from problem sets (suitably processed) and 30% from the final project. Office Hours: by appointment, at Perimeter Institute Teaching Assistant: Theerapat Tansuwannont ( ) Quantum Error Correction Quantum Error Correction and Fault ToleranceД¬ourse number: QIC 890, cross-listed as CS 867

Clifford group quantum error correction