Quantum error correction threshold for surface code

#QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE HOW TO#
#QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE UPDATE#
#QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE CODE#

Reed-Muller codes and transversal quantum gates. The threshold theorem of fault-tolerant quantum computation.

#QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE CODE#

Transversal encoded gates, fault tolerant measurement of code stabilizer, Techniques for fault-tolerant quantum computation - transversal gates, magic state injection, circuits for

#QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE UPDATE#

The Gottesman-Knill theorem: stabilizer update under Pauli measurements. Stabilizer states, Clifford unitaries and Pauli measurements. Surface codes: definition, geometric interpretation of errors and syndrome what is topological here? the use of boundaries. Examples of stabilizerД¬odes: (repitition code, Shor code), 5-qubit code, Steane code, surface codes. Quantum error correction condition for stabilizer codes. Proof of the fact that an error recovery map thatД¬orrects a set ). Proof of the general error correction condition. Definition of 'set of correctable errors'ДЄnd 'error recovery map'. Quantum operations and the Kraus representation unitary freedom in the Kraus representation. With no non-zero threshold (long-range interaction), error discretization. The 9-qubit Shor code, threshold behaviour, code concatenation, a decoherence model The repetition code, first application of the definition of the recovery procedure. Definition of quantum code, CPTP map,ДЄnd error recovery procedure. Background on quantum computation: universality, and the teleportation protocol. Measurement: the Dirac projection postulate and the Born rule.ДЇinishing with the background of quantum mechanics: (c) Quantum measurement: the Dirac projection postulateДЄnd the Born rule. (b) Evolution according to the Schroedinger equation, unitarity. States and Hilbert spaces, the inner product, mixed states and density matrices, entanglement. Mechanics: Quantum states, evolution and observation. Recording of office hour 11: (Friday, Apr 9, 2021). Recording of office hour 10: (Thursday, Apr 1, 2021). Recording of office hour 9: (Friday, Mar 26, 2021). Recording of office hour 8: (Friday, Mar 19, 2021). Recording of office hour 7: (Friday, Mar 12, 2021). Recording of office hour 6: (Friday, Mar 5, 2021). Recording of office hour 5: (Friday, Feb 26, 2021). Recording of office hour 4: (Friday, Feb 12, 2021). Recording of office hour 3: (Friday, Feb 5, 2021). Recording of office hour 2: (Friday, Jan 29, 2021). Recording of office hour 1: (Friday, Jan 22, 2021). Homework Assignment 5, supplemental python file Homework Assignment 4: Posted Mar 27, due April 6, 6 PM. Homework Assignment 3: Posted Mar 7, due Mar 22, 6 PM. Homework Assignment 2: Posted Feb 14, due Mar 1, 6 PM. Homework Assignment 1: Posted Jan 24, due Feb 8, 6 PM. Office hour: My office hour takes place Friday 6-7 PM (Zoom). Grading: 1/3 homework assignments, 1/3 written exam, 1/3 essay/ oral presentation. Takes place Monday + Wednesday 2pm-3:30pm, location: Zoom. Time and location: Term 2 (to Apr 14, 2021). Students of Physics, Computer Science, Engineering and Mathematics. Find them on Piazza (note of Mar 24)!ДЄudience: The course is intended for graduate and senior undergraduate

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Scaling of the overhead for error correction, and fault-tolerance in the presence of architecturalД¬onstraints (short range entangling gates, magic state factories, etc.) Schedule and practical information Per quantum gate is below a critical threshold, then the faulty gates are pretty much as good as prefectДЄfter presenting the TT, the course addresses questions regarding the value of the threshold, the Slightly simplified, if the logical error introduced by decoherence Quantum algorithms can be run efficiently on imperfect quantum computer hardware, as long this hardware So-called Threshold Theorem of Fault-tolerant Quantum Computation (TT).

#QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE HOW TO#

This course teaches those techniques and how to apply them. Of quantum error-correction and fault-tolerant quantum computation. It turns out that decoherence is NOT a fundamental obstacle, rather it can be overcome by the techniques Was thought to be a fundamental obstacle to the physical realization of quantum computation. It is detrimental to quantum computers, and for a long time Quantum systems towards the classical regime. Phys 523B: Fault-tolerant quantum computation Phys 523B: Fault-tolerant quantum computationДecoherence is an ubiquitous effect observed in quantum mechanics, driving

Quantum error correction threshold for surface code