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Fault-Tolerant Quantum Computation with Constant Overhead

Daniel Gottesman University of Maryland, College Park

July 14, 2014

PIRSA:14070004
Spin glass reflection of the decoding transition for space-time codes

Alexey Kovalev University of California, Riverside

July 14, 2014

PIRSA:14070003
Maximum likelihood decoding threshold as a phase transition

Leonid Pryadko University of California, Riverside

July 14, 2014

PIRSA:14070002
Overview of the theory of spin glasses and its applications to quantum codes

Hidetoshi Nishimori Tokyo Institute of Technology

July 14, 2014

PIRSA:14070001
An introduction to quantum LDPC code

David Poulin Université de Sherbrooke

July 14, 2014

PIRSA:14070000
TBA

Cliff Burgess McMaster University

July 09, 2014

PIRSA:14070022
TBA
July 08, 2014

PIRSA:14070018
Condensed Matter
EinsteinPlus 2014 - Cosmology Keynote

Matthew Johnson York University

July 08, 2014

PIRSA:14070020
Numerical investigations of singularities in general relativity

David Garfinkle Oakland University
June 26, 2014

PIRSA:14060052
Cosmology
On Quantum Tunnelling

Neil Turok University of Edinburgh
June 25, 2014

PIRSA:14060051
Cosmology
PSI Ceremony 2014
- John Berlinsky McMaster University
- James Forrest University of Waterloo
June 21, 2014

PIRSA:14060054
Free Discussion

June 19, 2014

PIRSA:14060038

Fault-Tolerant Quantum Computation with Constant Overhead

Daniel Gottesman University of Maryland, College Park

July 14, 2014

PIRSA:14070004

The threshold theorem for fault tolerance tells us that it is possible to build arbitrarily large reliable quantum computers provided the error rate per physical gate or time step is below some threshold value. Most research on the threshold theorem so far has gone into optimizing the tolerable error rate under various assumptions, with other considerations being secondary. However, for the foreseeable future, the number of qubits may be an even greater restriction than error rates. The overhead, the ratio of physical qubits to logical qubits, determines how expensive (in qubits) a fault-tolerant computation is. Earlier results on fault tolerance used a large overhead which grows (albeit slowly) with the size of the computation. I show that using quantum LDPC codes, it is possible in principle to do fault-tolerant quantum computation with low overhead, and with the overhead constant in the size of the computation.
Spin glass reflection of the decoding transition for space-time codes

Alexey Kovalev University of California, Riverside

July 14, 2014

PIRSA:14070003

We introduce space-time quantum code construction which is based on repeating the layers of an arbitrary quantum error correcting code. The error threshold of such space-time construction is shown to be related to the fault tolerant error threshold of the original quantum error correcting code in the presence of errors in syndrome measurements. The decoding transition for space-time codes can be further mapped to random-bond Wegner spin models.
Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z2 gauge models) as well as unexplored earlier and generally non-local disordered spin models with non-trivial phase diagrams that include the spin glass phase.
We apply this construction to the simplest examples of recently discovered hypergraph-product codes and numerically find the fault tolerant threshold in excess of 5% by employing Monte-Carlo simulations.
Maximum likelihood decoding threshold as a phase transition

Leonid Pryadko University of California, Riverside

July 14, 2014

PIRSA:14070002

In maximum likelihood (ML) decoding, we are trying to find the most likely error given the measured syndrome. While this is hardly ever practical, such a decoder is expected to have the highest threshold.
I will discuss the mapping between the ML threshold for an infinite family of stabilizer codes and a phase transition in an associated family of Ising models with bond disorder [1]. This is a generalization of the map between the toric codes and the square lattice Ising model. Quantum LDPC codes produce generally non-local spin models with few-body interactions. A relatively simple Monte Carlo simulation of such a model can give an upper bound on the decoding threshold for the original code family. This can be used to compare code families irrespectively of decoders, and to establish an absolute measure of decoder performance.

[1] A. A. Kovalev and L. P. Pryadko, "Spin glass reflection of the decoding transition for quantum error correcting codes," unpublished,
arXiv:1311.7688 (2013).
Overview of the theory of spin glasses and its applications to quantum codes

Hidetoshi Nishimori Tokyo Institute of Technology

July 14, 2014

PIRSA:14070001

I will review the theory of spin glasses with an emphasis on gauge symmetry. A number of exact results will be shown to be derived, some of which are useful to discuss the properties of quantum LDPC codes. Also will be explained is the combination of gauge symmetry, replica method, and duality argument to predict the precise location of a multicritical point, which is equivalent to the error-tolerance limit of toric code.
An introduction to quantum LDPC code

David Poulin Université de Sherbrooke

July 14, 2014

PIRSA:14070000

In this talk, I will cover some basic notions of quantum LDPC codes, focusing on the similarities and distinctions with their classical cousins. Topics will include definitions of stabilizer quantum LDPC codes (CSS and general), iterative decoding algorithms, dual spin models, and obstructions caused by error degeneracy. The talk will be informal and a good occasion to ask questions.
TBA

Cliff Burgess McMaster University

July 09, 2014

PIRSA:14070022
TBA
July 08, 2014

PIRSA:14070018
Condensed Matter
EinsteinPlus 2014 - Cosmology Keynote

Matthew Johnson York University

July 08, 2014

PIRSA:14070020
Numerical investigations of singularities in general relativity

David Garfinkle Oakland University
June 26, 2014

PIRSA:14060052
Cosmology
The singularity theorems of general relativity tell us that spacetime singularities form in gravitational collapse, but tell us very little about the precise nature of these singularities. More information can be found using analytic approximations and numerical simulations. It is conjectured that inside black holes are two types of singularities: one that is spacelike, local, and oscillatory, and the other that is null and weak. This talk will review what numerical simulations of singularities have been done and the extent to which the above conjecture has been verified by the simulations.
On Quantum Tunnelling

Neil Turok University of Edinburgh
June 25, 2014

PIRSA:14060051
Cosmology
One of the most basic but intriguing properties of quantum systems is their ability to `tunnel' between configurations which are classically disconnected. That is, processes which are classically impossible, are quantum allowed. In this talk I will outline a new, first-principles approach combining the semiclassical approximation with the concepts of post-selection and weak measurement. Its main virtue is to provide a real-time description within which sharp answers can be given to questions such as 'how long did the tunneling take' and 'where was the particle while it was tunneling?' Potential applications span a vast range, from laboratory tests to understanding black hole evaporation, the stability of the electroweak Higgs vacuum and the future of our universe, and the validity (or otherwise) of the "inflationary multiverse" scenario.
PSI Ceremony 2014
- John Berlinsky McMaster University
- James Forrest University of Waterloo
June 21, 2014

PIRSA:14060054
Free Discussion

June 19, 2014

PIRSA:14060038

Title	Date	Collection	Type	Info
Fault-Tolerant Quantum Computation with Constant Overhead	2014‑07‑14	International Workshop on Quantum LDPC Codes	Conference	View details
Spin glass reflection of the decoding transition for space-time codes	2014‑07‑14	International Workshop on Quantum LDPC Codes	Conference	View details
Maximum likelihood decoding threshold as a phase transition	2014‑07‑14	International Workshop on Quantum LDPC Codes	Conference	View details
Overview of the theory of spin glasses and its applications to quantum codes	2014‑07‑14	International Workshop on Quantum LDPC Codes	Conference	View details
An introduction to quantum LDPC code	2014‑07‑14	International Workshop on Quantum LDPC Codes	Conference	View details
TBA	2014‑07‑09	EinsteinPlus 2014		View details
TBA	2014‑07‑08	Quantum Matter	Scientific Series	View details
EinsteinPlus 2014 - Cosmology Keynote	2014‑07‑08	EinsteinPlus 2014		View details
Numerical investigations of singularities in general relativity	2014‑06‑26	Cosmology and Gravitation	Scientific Series	View details
On Quantum Tunnelling	2014‑06‑25	Colloquium	Scientific Series	View details
PSI Ceremony 2014	2014‑06‑21		Other	View details
Free Discussion	2014‑06‑19	New ideas in low-energy tests of fundamental physics	Conference	View details

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