### DANIEL GOTTESMAN THESIS

With group and eigenstate, we’ve learned to fix Your quantum errors with our quantum tricks. Quantum Key Distribution Date: Error assumptions for fault tolerance re-examined Other error models, correlated errors, leakage errors, coherent and non-Markovian errors Date: Researchers all over the world are working to build “quantum com Oracle model, Deutsch-Josza algorithm Date: Science 17 May Vol , Issue

Quantum Error Correction 10B Speaker s: Stabilizer codes definition of stabilizer, basic properties of stabilizer, binary vector representation of stabilizer Date: Quantum states to prevent eavesdropping Throughout the moves, Gottesman continued to work on quantum error correction, but he also moved into the field of quantum cryptography, which uses quantum states to prevent eavesdropping. To better spot Those flaws we must avoid, we first must strive To find which ones commute and which do not. In particular, theoretical developments such as fault-tolerant quantum codes and protocols for quantum error correction. Definition of fault tolerance, Shor error correction, fault-tolerant measurement for stabilizer and CSS codes.

Quantum Mechanics for Year Olds Speaker s: In effect, the quantum computer can process all of these states simultaneously, giving it staggering computational power? Shor’s algorithm got around the problem by using different branches of observation and allowing them to interact with each other to produce a theiss interference pattern, which could be observed without disrupting the quantum states.

Quantum Information Review – Lecture 5 Speaker s: A simple proof of the threshold for fault-tolerant quantum computation Speaker s: The two began collaborating while Gottesman was still in graduate school.

# Daniel Gottesman’s Papers

A simple interaction with its environment could cause a qubit to decohere, causing an error that could propagate and drag the quantum computer to a standstill. The quantum Fourier transform circuit.

Daniel GottesmanBeni Yoshida Abstract: Finite field GF 4stabilizer codes as GF 4 codes, perfect quantum codes, definition of Clifford group, sample elements of Clifford group Date: Weight enumerators, quantum MacWilliams identity, quantum shadow enumerator, higher-dimensional Pauli group, stabilizer codes for qudits Date: Still, quantum computers were vulnerable to random collapse even in the absence of external observation.

Quantum Error Correction 10B Speaker s: This built-in secrecy makes quantum error-correcting codes ideal for quantum cryptography,” says Gottesman.

Quantum Error Correction 12B Speaker s: Complexity theory, Church-Turing thesis Date: Non-Abelian ggottesman charges, fusion rules, F and R matrices, pentagon and hexagon equationsFibonacci anyons Date: The catch is that as soon as you observe the quantum states, they collapse or decohere into a random state. The framework “makes it easier to think up new codes and understand how they behave,” says Theiss.

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One of the central critical results in the theory of fault-tolerant quantum computation is that arbitrarily long reliable computation is possible provided the error rate per gate and per time step is below some threshold value. Quantum Error Correction 7A Speaker s: A Quantum Error Correction Sonnet We cannot clone, perforce; instead, we split Coherence to protect it from that wrong That would destroy our valued quantum bit And make our computation take too long.

Quantum Error Correction 5B Speaker s: Quantum Information Review – Lecture 14 Speaker s: Gottesman continued to look for faculty positions, but there were still no openings. Quantum data compression and Schumacher compression. Quantum Error Correction 9A Speaker s: Quantum Error Correction 3A Speaker s: On the other hand, the tech bubble was in the process of bursting.

Quantum Error Correction 9B Speaker s: A s an undergraduate at Harvard, Daniel Gottesman pictured left was interested in physics, but he never liked doing experiments.

That’s where Gottesman came in.

Equivalence of fault-tolerant circuit to less noisy unencoded circuits, threshold theorem, calculation of the threshold. Definition of fault tolerance, Shor error correction, fault-tolerant measurement for stabilizer and CSS codes Date: Quantum Error Correction 10A Speaker s: Applications of the quantum nature of our universe to potential new technologies like quantum cryptography and quantum computation.