Physical Hilbert space for the affine group formulation of 4D, gravity of Lorentzian signature.
Eyo Ita US Naval Academy and Cambridge University (DAMTP)
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Asymmetric Hawking Radiation : Baryogenesis from Hawking Radiation
Anson Hook University of Maryland, College Park
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Space-Time Circuit-to-Hamiltonian construction and Its Applications
Barbara Terhal Delft University of Technology
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Supersymmetric AdS5 solutions in M-theory and Class S SCFT's
Ibrahima Bah University of Southern California (USC)
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Life as a Physicist
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Natalia Toro Stanford University
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Philip Schuster Stanford University
PIRSA:14070027 -
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Can Quantum Correlations be Explained Causally?
Robert Spekkens Perimeter Institute for Theoretical Physics
PIRSA:14070026 -
Inferring causal structure: a quantum advantage
Katja Ried Universität Innsbruck
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Measuring the overhead of a quantum error correcting code
Austin Fowler Institute for Quantum Computing (IQC)
PIRSA:14070014 -
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Physical Hilbert space for the affine group formulation of 4D, gravity of Lorentzian signature.
Eyo Ita US Naval Academy and Cambridge University (DAMTP)
The authors have revealed a fundamental structure which has been hidden within the Wheeler-DeWitt (WDW) constraint of four dimensional General Relativity (GR) of Lorentzian signature in the Ashtekar self-dual variables. The WDW equation can be written as the commutator of two geometric entities, namely the imaginary part of the Chern-Simons functional Q and the local volume element V(x) of 3-space. Upon quantization with cosmological constant, the WDW equation takes on the form of the Lie algebra of the affine group of transformations of the straight line, with Q and V(x) playing the role of the generators for the Lie algebra. The generators are Hermitian, which addresses the issue of the implementation of the reality conditions of GR at the quantum level. Additionally, the irreducible unitary representations (IUR) implement the positivity of the spectrum of the volume operator V(x) at the quantum level This development has led to the existence of elements of the physical Hilbert space for four dimensional gravity of Lorentzian signature, the full theory, in the form of irreducible, unitary representations of the affine group of transformations of the straight line. The affine Lie algebraic structure of the WDW equation remains intact even in the presence of nongravitational fields. This feature has led to the extension of the affine group formulation to elements of the physical Hilbert space for gravity coupled to the full Standard Model of particle physics, quantized on equal footing. Work on the physical interpretation of the states with respect to gauge-diffeomorphism invariant observables, and spacetime geometries solving the Einstein equations is in progress. The journal reference for these results are as follows: - The first result has been published in CQG 30 (2013) 065013 - The second result has just been published in Annals of Physics Journal Vol.343, pages 153-163, April 2014 -
Asymmetric Hawking Radiation : Baryogenesis from Hawking Radiation
Anson Hook University of Maryland, College Park
We show that in the presence of a chemical potential, black hole evaporation generates baryon number. If the inflaton or Ricci scalar is derivatively coupled to the B-L current, the expansion of the universe acts as a chemical potential and splits the energy levels of particles and their anti-particles. The asymmetric Hawking radiation of primordial black holes can thus be used to generate a B-L asymmetry. If dark matter is produced by the same mechanism, the coincidence between the mass density of visible and dark matter can be naturally explained. -
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Space-Time Circuit-to-Hamiltonian construction and Its Applications
Barbara Terhal Delft University of Technology
The circuit-to-Hamiltonian construction translates a dynamics (a quantum circuit and its output) into statics (the groundstate of a circuit Hamiltonian) by explicitly defining a quantum register for a clock. The standard Feynman-Kitaev construction uses one global clock for all qubits while we consider a different construction in which a clock is assigned to each point in space where a qubit of the quantum circuit resides. We show how one can apply this construction to one-dimensional quantum circuits for which the circuit Hamiltonian realizes the dynamics of a vibrating string. We discuss how the construction can be used (1) in quantum complexity theory to obtain new and stronger results in QMA and (2) how one can realize, based on this construction, universal quantum adiabatic computation and a universal quantum walk using a 2D interacting particle Hamiltonian. See http://arxiv.org/abs/1311.6101 -
What’s Interesting These Days (With Gravity)?
Latham Boyle University of Edinburgh
PIRSA:14070028Many of the most interesting open issues in physics today are related in one way or another to gravity. For the past 100 years, we have described spacetime and gravity via Einstein's theory of "General Relativity." But when we try to mesh General Relativity with the rest of physics, and use it to describe the cosmos, we encounter a range of puzzles. I'll describe some of these puzzles, and some routes to attacking them that look exciting to me. -
Supersymmetric AdS5 solutions in M-theory and Class S SCFT's
Ibrahima Bah University of Southern California (USC)
We provide a framework for describing gravity duals of four-dimensional N=1 superconformal field theories obtained by compactifying a stack of M5-branes on a Riemann surface. The gravity solutions are completely specified by two scalar potentials whose pole structures on the Riemann surface correspond to the spectrum of punctures that labels different theories. We discuss how to identify these puncture in gravity. -
Life as a Physicist
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Natalia Toro Stanford University
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Philip Schuster Stanford University
PIRSA:14070027Ever wonder what a day in the life of a theoretical physicist is like?, Life as a Physicist is an opportunity to ask questions of two Perimeter Institute Faculty members. -
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Can Quantum Correlations be Explained Causally?
Robert Spekkens Perimeter Institute for Theoretical Physics
PIRSA:14070026There is a strong correlation between the sun rising and the rooster crowing, but to say that the one causes the other is to say more. In particular, it says that making the rooster crow early will not precipitate an early dawn, whereas making the sun rise early (for instance, by moving the rooster eastward) can lead to some early crowing. Intervening upon the natural course of events in this manner is a good way of discovering causal relations. Sometimes, however, we can't intervene, or we'd prefer not to. For instance, in trying to determine whether smoking causes lung cancer, we'd prefer not to force any would-be nonsmokers to smoke. Fortunately, there are some clever tricks that allow us to extract information about what causes what entirely from features of the observed correlations. One of these tricks was discovered by the physicist John Bell in 1964. In a groundbreaking paper, he used it to demonstrate the seeming impossibility of providing a causal explanation of certain quantum correlations. This revealed a fundamental tension between quantum theory and Einstein's theory of relativity --the two central pillars of modern physics. It is a tension that is still with us today. -
Inferring causal structure: a quantum advantage
Katja Ried Universität Innsbruck
A fundamental question in trying to understand the world -- be it classical or quantum -- is why things happen. We seek a causal account of events, and merely noting correlations between them does not provide a satisfactory answer. Classical statistics provides a better alternative: the framework of causal models proved itself a powerful tool for studying causal relations in a range of disciplines. We aim to adapt this formalism to allow for quantum variables and in the process discover a new perspective on how causality is different in the quantum world. Causal inference is a central task in the context of causal models: given observed statistics over a set of variables, one aims to infer how they are causally related. Yet in the seemingly simple case of just two classical variables, this is impossible (unless one makes additional assumptions). I will show how the analogous task for quantum variables can be solved. This quantum advantage is reminiscent of the advantages that quantum mechanics offers in computing and communication, and may lead to similarly rich insights. Our scheme is corroborated by data obtained in collaboration with Kevin Resch's experimental group. Time permitting, I will also address other applications of the quantum causal models. arXiv:1406.5036 -
Spatially coupled quantum LDPC codes
PIRSA:14070015Spatially 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)
PIRSA:14070014If 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)
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:1311.0885