An in-depth introduction to quantum error correction, fault-tolerant quantum computing, and related topics. Covers stabilizer codes, CSS codes, higher-dimensional codes, specific code constructions, entanglement purification protocols, and quantum channel capacity. Also bounds on quantum error correction: quantum Hamming bound, quantum Singleton bound, linear programming bounds and the quantum MacWilliams identity; and principles of fault-tolerant quantum computation: fault-tolerant error measurement, fault-tolerant gate design, the threshold for fault-tolerant quantum computation, and topological fault-tolerance. http://pirsa.org/podcast/C07001 Science 2012 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 09 Feb 2012 04:39:28 -0500 sbradwell@perimeterinstitute.ca Thu, 09 Feb 2012 04:39:28 -0500 G 180 pirsa-admin@perimeterinstitute.ca Steve Bradwell's - Podcast Generator Administrative introduction, quantum operations, examples of quantum channels, quantum code correcting bit flip errors, quantum code correcting phase errors Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/bb744a90-ca94-4d1a-8ac8-efc73a334695.mp3 Science http://streamer.perimeterinstitute.ca/mp3/bb744a90-ca94-4d1a-8ac8-efc73a334695.mp3 Tue, 09 Jan 2007 15:30:00 -0500 9-qubit Shor code, definition of a quantum error-correcting code, correcting linear combinations of errors, quantum error correction conditions, definition of distance Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/219784ab-0ccc-488d-ae97-01b9efb5bc5a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/219784ab-0ccc-488d-ae97-01b9efb5bc5a.mp3 Tue, 09 Jan 2007 17:00:00 -0500 Stabilizer codes (definition of stabilizer, basic properties of stabilizer, binary vector representation of stabilizer) Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/26bb6877-4886-47d8-a84d-da361cb64333.mp3 Science http://streamer.perimeterinstitute.ca/mp3/26bb6877-4886-47d8-a84d-da361cb64333.mp3 Tue, 16 Jan 2007 15:30:00 -0500 5-qubit code, logical Pauli group for stabilizer codes, classical linear codes (generator and parity check matrices, Hamming codes), CSS codes (definition, 7-qubit code) Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/9089b716-9058-4824-8f2c-d305f54b3561.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9089b716-9058-4824-8f2c-d305f54b3561.mp3 Tue, 16 Jan 2007 17:00:00 -0500 Finite field GF(4), stabilizer codes as GF(4) codes, perfect quantum codes, definition of Clifford group, sample elements of Clifford group Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/bd8c51cb-ee9f-47d0-98dd-183bdcae87dd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/bd8c51cb-ee9f-47d0-98dd-183bdcae87dd.mp3 Tue, 23 Jan 2007 15:30:00 -0500 Clifford group as symplectic group, generators of the Clifford group & encoding circuits for stabilizer codes, efficient simulation of Clifford group circuits, efficient simulation of Pauli measurements Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/4692deab-0b40-49b2-8989-df9c035bdb15.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4692deab-0b40-49b2-8989-df9c035bdb15.mp3 Tue, 23 Jan 2007 17:00:00 -0500 Guest lecturer Raymond Laflamme: experimental quantum error correction Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/32eeeb63-6b71-4e64-a1d7-401e83fc8e04.mp3 Science http://streamer.perimeterinstitute.ca/mp3/32eeeb63-6b71-4e64-a1d7-401e83fc8e04.mp3 Tue, 30 Jan 2007 15:30:00 -0500 Guest lecturer Robert Raussendorf: graph states Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/59c75ec2-ca07-45c1-be9d-896e59e8b042.mp3 Science http://streamer.perimeterinstitute.ca/mp3/59c75ec2-ca07-45c1-be9d-896e59e8b042.mp3 Tue, 30 Jan 2007 17:00:00 -0500 Generators of symplectic group, quantum Gilbert-Varshamov bound, quantum Hamming bound, quantum Singleton bound Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/ba9bb900-305e-47e7-8404-c425e03f22ae.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ba9bb900-305e-47e7-8404-c425e03f22ae.mp3 Tue, 06 Feb 2007 15:30:00 -0500 Weight enumerators, quantum MacWilliams identity, quantum shadow enumerator, higher-dimensional Pauli group, stabilizer codes for qudits Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/70058cd2-c668-4fc9-abee-226d9cab769f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/70058cd2-c668-4fc9-abee-226d9cab769f.mp3 Tue, 06 Feb 2007 17:00:00 -0500 Examples of qudit stabilizer codes, polynomial codes, Clifford group for qudits, introduction to fault-tolerance, definition of transversal gates, definition of fault-tolerant gates Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/2826b433-445d-4291-a215-a0dd565055fd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2826b433-445d-4291-a215-a0dd565055fd.mp3 Tue, 13 Feb 2007 15:30:00 -0500 Transversal Pauli group, transversal Clifford group for 7-qubit code, transversal gates for 5-qubit code, overview of fault-tolerant protocols. Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/dbcfcf95-7e9a-4950-a4e6-a7542f1d683c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/dbcfcf95-7e9a-4950-a4e6-a7542f1d683c.mp3 Tue, 13 Feb 2007 17:00:00 -0500 Definition of fault tolerance, Shor error correction, fault-tolerant measurement for stabilizer and CSS codes Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/0b0f2d3a-6a89-4898-946e-d6be46ad0782.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0b0f2d3a-6a89-4898-946e-d6be46ad0782.mp3 Tue, 20 Feb 2007 15:30:00 -0500 Fault-tolerant stabilizer state preparation, Steane error correction, universal fault-tolerant set of gates through gate teleportation, magic state distillation Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/3c579eca-dc15-483d-83e2-0d86164a6bd1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3c579eca-dc15-483d-83e2-0d86164a6bd1.mp3 Tue, 20 Feb 2007 17:00:00 -0500 Assumptions for fault tolerance, extended rectangles, good, bad, and correct rectangles. Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/b9af4d05-24dc-43e1-b802-44dad087db23.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b9af4d05-24dc-43e1-b802-44dad087db23.mp3 Tue, 27 Feb 2007 15:30:00 -0500 Equivalence of fault-tolerant circuit to less noisy unencoded circuits, threshold theorem, calculation of the threshold. Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/a47194e8-b91e-46a9-9a6c-5da944c11666.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a47194e8-b91e-46a9-9a6c-5da944c11666.mp3 Tue, 27 Feb 2007 17:00:00 -0500 Circuit assumptions for fault tolerance re-examined (other universal gate sets, local gates, fresh ancillas, no measurements, parallelism) Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/dbf12f1b-b229-4d4a-b248-ef10ec6bdbad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/dbf12f1b-b229-4d4a-b248-ef10ec6bdbad.mp3 Tue, 06 Mar 2007 15:30:00 -0500 Error assumptions for fault tolerance re-examined (Other error models, correlated errors, leakage errors, coherent and non-Markovian errors) Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/e34a5c1f-e6d4-4897-8d8c-b4ea61556ee9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e34a5c1f-e6d4-4897-8d8c-b4ea61556ee9.mp3 Tue, 06 Mar 2007 17:00:00 -0500 One- and two-way entanglement distillation protocols, twirling, stabilizer EDPs, definition of quantum channel capacity Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/28a2fd97-3e76-4e65-beee-e5f3976a6361.mp3 Science http://streamer.perimeterinstitute.ca/mp3/28a2fd97-3e76-4e65-beee-e5f3976a6361.mp3 Tue, 13 Mar 2007 15:30:00 -0400 One- and two-way quantum capacities for the erasure channel, upper and lower bounds on the quantum capacities for the depolarizing channel, coherent information Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/c9daf8cf-461c-44cf-978c-3595aebf0fc7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c9daf8cf-461c-44cf-978c-3595aebf0fc7.mp3 Tue, 13 Mar 2007 17:00:00 -0400 Toric code (definition, fault-tolerance, particle model of errors), definition of qudit toric code Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/2e0079ed-f018-4c23-a629-ca70162e9732.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2e0079ed-f018-4c23-a629-ca70162e9732.mp3 Tue, 20 Mar 2007 15:30:00 -0400 Behavior of particles in qudit toric code, braid group, basic idea of fault tolerance with non-Abelian anyons Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/ddd7dc4a-c329-48ea-a831-3a040e1bcb44.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ddd7dc4a-c329-48ea-a831-3a040e1bcb44.mp3 Tue, 20 Mar 2007 17:00:00 -0400 Non-Abelian anyons (charges, fusion rules, F and R matrices, pentagon and hexagon equations), Fibonacci anyons Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/e528e878-5a22-4ecf-a682-bebfd2f7fbcb.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e528e878-5a22-4ecf-a682-bebfd2f7fbcb.mp3 Tue, 27 Mar 2007 15:30:00 -0400 Universality of Fibonacci anyons, operator quantum error correction, Bacon-Shor codes Daniel Gottesman http://streamer.perimeterinstitute.ca/mp3/55b2bc7d-a97e-4e42-b959-fc62e16a914d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/55b2bc7d-a97e-4e42-b959-fc62e16a914d.mp3 Tue, 27 Mar 2007 17:00:00 -0400