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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 Information
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
Algebraic characterization of entanglement classes

Markus Grassl Max Planck Institute for the Science of Light
September 19, 2014

PIRSA:14090070
Quantum Information

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 Information
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
Algebraic characterization of entanglement classes

Markus Grassl Max Planck Institute for the Science of Light
September 19, 2014

PIRSA:14090070
Quantum Information
Entanglement is a key feature of composite quantum system which is directly related to the potential power of quantum computers. In most computational models, it is assumed that local operations are relatively easy to implement. Therefore, quantum states that are related by local operations form a single entanglement class. In the case of local unitary operations, a finite set of polynomial invariants provides a complete characterization of the entanglement classes. Unfortunately, one faces the problem of combinatorial explosion so that computing such a complete set of invariants becomes difficult already for quite small system. The two main problems in this context are to compute invariants and to decide completeness, i.e., whether a given set of invariants generates the full invariant ring. Important tools are both univariate and multivariate Hilbert series which are already difficult to compute. We will also address computational aspects of these problems and techniques for showing completeness of a set of invariants.

Title	Date	Collection	Type	Info
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
Algebraic characterization of entanglement classes	2014‑09‑19	Perimeter Institute Quantum Discussions	Scientific Series	View details

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