Conference

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A Mathematician Looks at Supergravity and AdS/CFT

Kevin Costello Perimeter Institute for Theoretical Physics

October 22, 2014

PIRSA:14100104
Fundamental Physics Without Colliding Particles

Asimina Arvanitaki Perimeter Institute for Theoretical Physics

October 22, 2014

PIRSA:14100103
Spatially coupled quantum LDPC codes

Jean-Pierre Tillich

July 16, 2014

PIRSA:14070015
Measuring the overhead of a quantum error correcting code

Austin Fowler Institute for Quantum Computing (IQC)

July 16, 2014

PIRSA:14070014
Homological product codes

Sergey Bravyi IBM (United States)

July 16, 2014

PIRSA:14070013
Gauge color codes

Hector Bombin PsiQuantum Corp.

July 16, 2014

PIRSA:14070012
Is scalable quantum error correction realistic? Some projects, thoughts and open questions.

Barbara Terhal Delft University of Technology

July 15, 2014

PIRSA:14070010
TBA

John Preskill California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy

July 15, 2014

PIRSA:14070009
Quantum codes – from experimental realizations to quantum foundations

Robert Raussendorf Leibniz University Hannover

July 15, 2014

PIRSA:14070008
Injectivity radius bounds on the minimum distance of quantum LDPC codes

July 15, 2014

PIRSA:14070007
Quantum computing by color-code lattice surgery

Andrew Landahl University of New Mexico

July 15, 2014

PIRSA:14070006
Quantum Error Correction for Ising Anyon Systems

July 14, 2014

PIRSA:14070005

A Mathematician Looks at Supergravity and AdS/CFT

Kevin Costello Perimeter Institute for Theoretical Physics

October 22, 2014

PIRSA:14100104
Fundamental Physics Without Colliding Particles

Asimina Arvanitaki Perimeter Institute for Theoretical Physics

October 22, 2014

PIRSA:14100103
Spatially coupled quantum LDPC codes

Jean-Pierre Tillich

July 16, 2014

PIRSA:14070015

Spatially coupled LDPC were introduced by Felström and Zigangirov in 1999. They might be viewed in the following way, take several several instances of a certain LDPC code family, arrange them in a row and then mix the edges of the codes randomly among neighboring layers. Moreover fix the bits of the first and last layers to zero. It has soon been found out that iterative decoding behaves much better for this code than for the original LDPC code. A breakthrough occurred when it was proved by Kudekar, Richardson and Urbanke that these codes attain the capacity of all binary input memoryless output-symmetric channels.

All these nice features of classical spatially coupled LDPC codes suggest to study whether they have a quantum analogue. The fact that spatially coupled LDPC codes may afford to have large degrees and still perform well under iterative decoding would be quite interesting in the quantum setting, since by the very nature of the quantum construction of stabilizer codes the rows of the parity-check matrix of the quantum code have to belong to the code which is decoded by the iterative decoder. This implies that we should have rather large row weights to avoid severe error-floor phenomena and/or oscillatory behavior of iterative decoding which degrades significantly its performance.

With Andriyanova and Maurice, I showed last year that it is possible to come up with coupled versions of quantum LDPC codes that perform excellently under iterative decoding. For instance we have constructed a spatially coupled LDPC code family of rate $\approx \frac{1}{4}$ which performs well under iterative decoding even for noise values close to the hashing bound $p \approx 0.127$.
This represents a tremendous improvement over all previous known families of quantum LDPC codes of the same rate.
I will discuss in this talk what can be expected from this approach when these spatially coupled LDPC codes are used for performing fault tolerant computation.
Measuring the overhead of a quantum error correcting code

Austin Fowler Institute for Quantum Computing (IQC)

July 16, 2014

PIRSA:14070014

If one's goal is large-scale quantum computation, ultimately one wishes to minimize the amount of time, number of qubits, and qubit connectivity required to outperform a classical system, all while assuming some physically reasonable gate error rate. We present two examples of such an overhead study, focusing on the surface code with and without long-range interactions.
Homological product codes

Sergey Bravyi IBM (United States)

July 16, 2014

PIRSA:14070013

All examples of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good LDPC codes are known that combine constant encoding rate and linear distance. In this talk I will describe the first family of good quantum "almost LDPC" codes. The new codes have a constant encoding rate, linear distance, and stabilizers acting on at most square root of n qubits, where n is the code length. For comparison, all previously known families of good quantum codes have stabilizers of linear weight. The proof combines two techniques: randomized constructions of good quantum codes and the homological product operation from algebraic topology. We conjecture that similar methods can produce good quantum codes with stabilizer weight n^a for any a>0. Finally, we apply the homological product to construct new small codes with low-weight stabilizers.

This is a joint work with Matthew Hastings
Preprint: arXiv:1311.0885
Gauge color codes

Hector Bombin PsiQuantum Corp.

July 16, 2014

PIRSA:14070012

I will describe a new class of topological quantum error correcting codes with surprising features. The constructions is based on color codes: it preserves their unusual transversality properties but removes important drawbacks. In 3D, the new codes allow the effectively transversal implementation of a universal set of gates by gauge fixing, while error-dectecting measurements involve only 4 or 6 qubits. Furthermore, they do not require multiple rounds of error detection to achieve fault-tolerance.
Is scalable quantum error correction realistic? Some projects, thoughts and open questions.

Barbara Terhal Delft University of Technology

July 15, 2014

PIRSA:14070010
TBA

John Preskill California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy

July 15, 2014

PIRSA:14070009
Quantum codes – from experimental realizations to quantum foundations

Robert Raussendorf Leibniz University Hannover

July 15, 2014

PIRSA:14070008

This talk is divided into two parts. In the first part, I discuss a scheme of fault-tolerant quantum computation for a web-like physical architecture of a quantum computer. Small logical units of a few qubits (realized in ion traps, for example) are linked via a photonic interconnect which provides probabilistic heralded Bell pairs [1]. Two time scales compete in this system, namely the characteristic decoherence time T_D and the typical time T_E it takes to provide a Bell pair. We show that, perhaps unexpectedly, this system can be used for fault-tolerant quantum computation for all values of the ratio T_D/T_E.

The second part of my talk is about something entirely different, namely the role of contextuality in quantum computation by magic state distillation. Recently, Howard et al. [2] have shown that contextuality is a necessary resource for such computation on qudits of odd prime dimension. Here we provide an analogous result for 2-level systems.
However, we require them to be rebits. [joint work with Jake Bian, Philippe Guerin and Nicolas Delfosse]

[1] C. Monroe, R. Raussendorf, A. Ruthven, K. R. Brown, P. Maunz4, L.-M.
Duan, and J. Kim, , Phys Rev A 89, 22317 (2014).

[2] Mark Howard, Joel Wallman, Victor Veitch & Joseph Emerson, Nature
doi:10.1038/nature13460 (2014).
Injectivity radius bounds on the minimum distance of quantum LDPC codes

July 15, 2014

PIRSA:14070007

Only a rare number of constructions of quantum LDPC codes are equipped with an unbounded minimum distance. Most of them are inspired by Kitaev toric codes constructed from the a tiling of the torus such as, color codes which are based on 3-colored tilings of surfaces, hyperbolic codes which are defined from hyperbolic tilings, or codes based on higher dimensional manifolds. These constructions are based on tilings of surfaces or manifolds and their parameters depend on the homology of the tiling.

In the first part of this talk, we recall homological bounds on the parameters of these quantum LDPC codes. In particular, the injectivity radius of the tiling provides a general lower bound on the minimum distance of these quantum LDPC codes.

Then, we extend the injectivity radius method to bound the minimum distance of a family of quantum LDPC codes based on Cayley graphs.
Finally, we improve these results by studying a notion of expansion of these Cayley graphs.

This talk is based on a joint work with Alain Couvreur and Gilles Zémor, and a joint work with Zhentao Li and Stephan Tommassé.
Quantum computing by color-code lattice surgery

Andrew Landahl University of New Mexico

July 15, 2014

PIRSA:14070006

In this talk, I will explain how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, I will also show how to improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same time or less than associated defect-braiding methods. Per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement the Hadamard and phase gates in a single transversal step—much faster than surface-code lattice surgery can. I will show that against uncorrelated circuit-level depolarizing noise, color-code lattice surgery uses fewer qubits to achieve the same degree of fault-tolerant error suppression as surface-code lattice-surgery when the noise rate is low enough and the error suppression demand is high enough.
Quantum Error Correction for Ising Anyon Systems

July 14, 2014

PIRSA:14070005

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath, and we propose a phenomenological model to describe the resulting short-time dynamics, including pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of quantum information stored in the code space. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting: one based on Edmond's perfect matching algorithm and one based on the renormalization group. These decoders provably run in polynomial time, and one of them has a provable threshold against a simple iid noise model. Using numerical simulations, we find that the error correction thresholds for these codes/decoders are comparable to similar values for the toric code (an Abelian sub-model consisting of a restricted set of allowed anyons). To our knowledge, these are the first threshold results for quantum codes without explicit Pauli algebraic structure. Joint work with Courtney Brell, Simon Burton, Guillaum Dauphinais, and David Poulin, arXiv:1311.0019.

Title	Speaker(s)	Date	Talk Type	Info link
A Mathematician Looks at Supergravity and AdS/CFT	Kevin Costello	2014-10-22	Conference	View details
Fundamental Physics Without Colliding Particles	Asimina Arvanitaki	2014-10-22	Conference	View details
Spatially coupled quantum LDPC codes	Jean-Pierre Tillich	2014-07-16	Conference	View details
Measuring the overhead of a quantum error correcting code	Austin Fowler	2014-07-16	Conference	View details
Homological product codes	Sergey Bravyi	2014-07-16	Conference	View details
Gauge color codes	Hector Bombin	2014-07-16	Conference	View details
Is scalable quantum error correction realistic? Some projects, thoughts and open questions.	Barbara Terhal	2014-07-15	Conference	View details
TBA	John Preskill	2014-07-15	Conference	View details
Quantum codes – from experimental realizations to quantum foundations	Robert Raussendorf	2014-07-15	Conference	View details
Injectivity radius bounds on the minimum distance of quantum LDPC codes		2014-07-15	Conference	View details
Quantum computing by color-code lattice surgery	Andrew Landahl	2014-07-15	Conference	View details
Quantum Error Correction for Ising Anyon Systems		2014-07-14	Conference	View details

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