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PHYS 781 - Lecture 2

Niayesh Afshordi University of Waterloo

September 25, 2014

PIRSA:14090086
14/15 PSI Quantum Theory-14

Joseph Emerson Institute for Quantum Computing (IQC)

September 25, 2014

PIRSA:14090059
14/15 PSI - Relativity- Lecture 14

Neil Turok University of Edinburgh

September 25, 2014

PIRSA:14090063
Fault-tolerant logical gates in quantum error-correcting codes

Beni Yoshida Perimeter Institute for Theoretical Physics
September 24, 2014

PIRSA:14090032
Quantum Physics
14/15 PSI Quantum Theory-13

Joseph Emerson Institute for Quantum Computing (IQC)

September 24, 2014

PIRSA:14090058
14/15 PSI - Relativity- Lecture 13

Neil Turok University of Edinburgh

September 24, 2014

PIRSA:14090062
Lifshitz Field Theories, Anomalies and Hydrodynamics

Shira Chapman University of Amsterdam

September 23, 2014

PIRSA:14090083
PHYS 781 - Lecture 1

Niayesh Afshordi University of Waterloo

September 23, 2014

PIRSA:14090084
14/15 PSI Quantum Theory-12

Joseph Emerson Institute for Quantum Computing (IQC)

September 23, 2014

PIRSA:14090057
14/15 PSI - Relativity- Lecture 12

Neil Turok University of Edinburgh

September 23, 2014

PIRSA:14090061
14/15 PSI Quantum Theory-11

Joseph Emerson Institute for Quantum Computing (IQC)

September 22, 2014

PIRSA:14090056
14/15 PSI - Relativity- Lecture 11

Neil Turok University of Edinburgh

September 22, 2014

PIRSA:14090025

PHYS 781 - Lecture 2

Niayesh Afshordi University of Waterloo

September 25, 2014

PIRSA:14090086
14/15 PSI Quantum Theory-14

Joseph Emerson Institute for Quantum Computing (IQC)

September 25, 2014

PIRSA:14090059
14/15 PSI - Relativity- Lecture 14

Neil Turok University of Edinburgh

September 25, 2014

PIRSA:14090063
Fault-tolerant logical gates in quantum error-correcting codes

Beni Yoshida Perimeter Institute for Theoretical Physics
September 24, 2014

PIRSA:14090032
Quantum Physics
Recently, Bravyi and Koenig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant depth geometrically local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dimensions, locality preserving gates are restricted to a set of unitary gates known as the D-th level of the Clifford hierarchy. In this paper, we elaborate this idea and provide several extensions and applications of their characterization in various directions. First, we present a new no-go theorem for self-correcting quantum memory. Namely, we prove that a three-dimensional stabilizer Hamiltonian with a locality-preserving implementation of a non-Clifford gate cannot have a macroscopic energy barrier. Second, we prove that the code distance of a D-dimensional local stabilizer code with non-trivial locality-preserving m-th level Clifford logical gate is upper bounded by L^{D+1-m}. For codes with non-Clifford gates (m>2), this improves the previous best bound by Bravyi and Terhal. Third we prove that a qubit loss threshold of codes with non-trivial transversal m-th level Clifford logical gate is upper bounded by 1/m. As such, no family of fault-tolerant codes with transversal gates in increasing level of the Clifford hierarchy may exist. This result applies to arbitrary stabilizer and subsystem codes, and is not restricted to geometrically-local codes. Fourth we extend the result of Bravyi and Koenig to subsystem codes. A technical difficulty is that, unlike stabilizer codes, the so-called union lemma does not apply to subsystem codes. This problem is avoided by assuming the presence of error threshold in a subsystem code, and the same conclusion as Bravyi-Koenig is recovered. This is a joint work with Fernando Pastawski. arXiv:1408.1720
14/15 PSI Quantum Theory-13

Joseph Emerson Institute for Quantum Computing (IQC)

September 24, 2014

PIRSA:14090058
14/15 PSI - Relativity- Lecture 13

Neil Turok University of Edinburgh

September 24, 2014

PIRSA:14090062
Lifshitz Field Theories, Anomalies and Hydrodynamics

Shira Chapman University of Amsterdam

September 23, 2014

PIRSA:14090083

I will review various aspects of field theories that posses a Lifshitz scaling symmetry. I will detail our study of the cohomological structure of anisotropic Weyl anomalies (the equivalent of trace anomalies in relativistic scale invariant field theories). I will also analyze the hydrodynamics of Lifshitz field theories and in particular of Lifshitz superfluids which may give insights into the physics of high temperature superconductors.
PHYS 781 - Lecture 1

Niayesh Afshordi University of Waterloo

September 23, 2014

PIRSA:14090084
14/15 PSI Quantum Theory-12

Joseph Emerson Institute for Quantum Computing (IQC)

September 23, 2014

PIRSA:14090057
14/15 PSI - Relativity- Lecture 12

Neil Turok University of Edinburgh

September 23, 2014

PIRSA:14090061
14/15 PSI Quantum Theory-11

Joseph Emerson Institute for Quantum Computing (IQC)

September 22, 2014

PIRSA:14090056
14/15 PSI - Relativity- Lecture 11

Neil Turok University of Edinburgh

September 22, 2014

PIRSA:14090025

Title	Date	Collection	Type	Info
PHYS 781 - Lecture 2	2014‑09‑25	PHYS 781 - Fundamentals of Astrophysics	Course	View details
14/15 PSI Quantum Theory-14	2014‑09‑25	14/15 PSI - Quantum Theory	Course	View details
14/15 PSI - Relativity- Lecture 14	2014‑09‑25	14/15 PSI -Relativity	Course	View details
Fault-tolerant logical gates in quantum error-correcting codes	2014‑09‑24	Perimeter Institute Quantum Discussions	Scientific Series	View details
14/15 PSI Quantum Theory-13	2014‑09‑24	14/15 PSI - Quantum Theory	Course	View details
14/15 PSI - Relativity- Lecture 13	2014‑09‑24	14/15 PSI -Relativity	Course	View details
Lifshitz Field Theories, Anomalies and Hydrodynamics	2014‑09‑23	Quantum Fields and Strings	Scientific Series	View details
PHYS 781 - Lecture 1	2014‑09‑23	PHYS 781 - Fundamentals of Astrophysics	Course	View details
14/15 PSI Quantum Theory-12	2014‑09‑23	14/15 PSI - Quantum Theory	Course	View details
14/15 PSI - Relativity- Lecture 12	2014‑09‑23	14/15 PSI -Relativity	Course	View details
14/15 PSI Quantum Theory-11	2014‑09‑22	14/15 PSI - Quantum Theory	Course	View details
14/15 PSI - Relativity- Lecture 11	2014‑09‑22	14/15 PSI -Relativity	Course	View details

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Format results

PHYS 781 - Lecture 2

14/15 PSI Quantum Theory-14

14/15 PSI - Relativity- Lecture 14

Fault-tolerant logical gates in quantum error-correcting codes

14/15 PSI Quantum Theory-13

14/15 PSI - Relativity- Lecture 13

Lifshitz Field Theories, Anomalies and Hydrodynamics

PHYS 781 - Lecture 1

14/15 PSI Quantum Theory-12

14/15 PSI - Relativity- Lecture 12

14/15 PSI Quantum Theory-11

14/15 PSI - Relativity- Lecture 11

PHYS 781 - Lecture 2

14/15 PSI Quantum Theory-14

14/15 PSI - Relativity- Lecture 14

Fault-tolerant logical gates in quantum error-correcting codes

14/15 PSI Quantum Theory-13

14/15 PSI - Relativity- Lecture 13

Lifshitz Field Theories, Anomalies and Hydrodynamics

PHYS 781 - Lecture 1

14/15 PSI Quantum Theory-12

14/15 PSI - Relativity- Lecture 12

14/15 PSI Quantum Theory-11

14/15 PSI - Relativity- Lecture 11