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Is scalable quantum error correction realistic? Some projects, thoughts and open questions.
Barbara Terhal Delft University of Technology
PIRSA:14070010Exploring N=1 theories of class S through Higgsing, dualizing and twisting
Jaewon Song University of California, San Diego
TBA
John Preskill California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
PIRSA:14070009Improving Mass Measurements Using Many-Body Phase Space
Can Kilic The University of Texas at Austin
Quantum codes – from experimental realizations to quantum foundations
Robert Raussendorf Leibniz University Hannover
PIRSA:14070008Quantum computing by color-code lattice surgery
Andrew Landahl University of New Mexico
PIRSA:14070006Quantum Error Correction for Ising Anyon Systems
PIRSA:14070005
Homological product codes
Sergey Bravyi IBM (United States)
PIRSA:14070013All 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:1311.0885Gauge color codes
Hector Bombin PsiQuantum Corp.
PIRSA:14070012I 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
PIRSA:14070010Exploring N=1 theories of class S through Higgsing, dualizing and twisting
Jaewon Song University of California, San Diego
We study a class of 4d N=1 SCFTs obtained from partial compactifications of 6d N=(2, 0) theory on a Riemann surface with punctures. We identify theories corresponding to curves with general type of punctures through nilpotent Higgsing and Seiberg dualities. The `quiver tails' of N=1 class S theories turn out to differ significantly from N=2 counterpart and have interesting properties. Various dual descriptions for such a theory can be found by using colored pair-of-pants decompositions. Especially, we find N=1 analog of Argyres-Seiberg duality for the SQCD with various gauge groups. We compute anomaly coefficients and superconformal indices to verify our proposal.TBA
John Preskill California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
PIRSA:14070009Improving Mass Measurements Using Many-Body Phase Space
Can Kilic The University of Texas at Austin
After the 7 and 8 TeV LHC runs, we have no conclusive evidence of physics beyond the Standard Model, leading us to suspect that even if new physics is discovered during run II, the number of signal events may be limited, making it crucial to optimize measurements for the case of low statistics. I will argue that phase space correlations between subsequent on-shell decays in a cascade contain additional information compared to commonly used kinematic variables, and this can be used to significantly improve the precision and accuracy of mass measurements. The improvement is connected to the properties of the volume element of many-body phase space, and is particularly relevant to the case of low signal statistics.Quantum codes – from experimental realizations to quantum foundations
Robert Raussendorf Leibniz University Hannover
PIRSA:14070008This 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).Cosmological Coincidence Problem
I will try to explain how cosmological coincidence of the two values, the matter energy density and the dark energy density, at the present epoch based on a single scalar field model whith a quartic potential, non-mimimally interacting with gravity. Dark energy in this model originates from the potential energy of the scalar field, which is sourced by the appearance of non-relativistic matter at the time z~ 10^10. No fine tuning of parameter are neccessary.Injectivity radius bounds on the minimum distance of quantum LDPC codes
PIRSA:14070007Only 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
PIRSA:14070006In 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.Searching for Other Universes
Matthew Johnson York University
PIRSA:14070025Centuries of astronomy and cosmology have led to an ever-larger picture of our ‘universe’ — everything that we can observe. For just as long, there have been speculations that there are other regions beyond what is currently observable, each with diverse histories and properties, and all inhabiting a ‘Multiverse’. A nexus of ideas from cosmology, quantum gravity, and string theory lead to the prediction that we inhabit one of the most interesting sorts of Multiverses one could imagine: one that arises as a natural consequence of compelling explanations for other physics, and one that at least in principle can be tested with observations. In this talk, I will outline these ideas, and discuss the first observational tests of the Multiverse using data from the Wilkinson Microwave Anisotropy Probe.Quantum Error Correction for Ising Anyon Systems
PIRSA:14070005We 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.