Scientific Series

We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process, requiring only initial product state preparation. Both the quantum circuit and its input are encoded in an initial canonical basis state of the qudit chain. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time greater than a polynomial in the size of the quantum circuit has passed, the result of the computation can be obtained with high probability by measuring a few qudits in the computational basis. This result also implies that there cannot exist efficient classical simulation methods for generic translationally invariant nearest-neighbor Hamiltonians on qudit chains, unless quantum computers can be efficiently simulated by classical computers (or, put in complexity theoretic terms, unless BPP=BQP). This is joint work with Daniel Nagaj.

The history of human knowledge is often highlighted by our efforts to explore beyond our apparent horizon. In this talk, I will describe how this challenge has now evolved into our quest to understand the physics at/beyond the cosmological horizon, some twenty orders of magnitude above Columbus’s original goal. I also argue why inflationary paradigm predicts the existence of non-trivial physics beyond the cosmological horizon, and how we can use the Integrated Sachs-Wolfe effect in the Cosmic Microwave Background to probe this physics, including the nature of gravity and primordial non-gaussianity on the horizon scale.

We show that the matrix-model for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. The nonabelian gauge fields as well as additional scalar fields couple to a dynamical metric G_ab, which is given in terms of a Poisson structure. This leads to a gravity theory which is naturally related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. Essential features such as gravitational waves and the Newtonian limit are reproduced correctly. UV/IR mixing is understood in terms of an induced gravity action. The framework appears suitable for quantizing gravity.

The renormalization group (RG) is one of the conceptual pillars of statistical mechanics and quantum field theory, and a key theoretical element in the modern formulation of critical phenomena and phase transitions. RG transformations are also the basis of numerical approaches to the study of low energy properties and emergent phenomena in quantum many-body systems. In this colloquium I will introduce the notion of \\\"entanglement renormalization\\\" and use it to define a coarse-graining transformation for quantum systems on a lattice [G.Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. The resulting real-space RG approach is able to numerically address 1D and 2D lattice systems with thousands of quantum spins using only very modest computational resources. From the theoretical point of view, entanglement renormalization sheds new light into the structure of correlations in the ground state of extended quantum systems. I will discuss how it leads to a novel, efficient representation for the ground state of a system at a quantum critical point or with topological order.

The basic problem of much of condensed matter and high energy physics, as well as quantum chemistry, is to find the ground state properties of some Hamiltonian. Many algorithms have been invented to deal with this problem, each with different strengths and limitations. Ideas such as entanglement entropy from quantum information theory and quantum computing enable us to understand the difficulty of various problems. I will discuss recent results on area laws and use these to prove that we can use matrix product states to efficiently represent ground states for one-dimensional systems with a spectral gap, while certain other one-dimensional problems, without the gap assumption, almost certainly have no efficient way for us to even represent the ground state on a classical computer. I will also discuss recent results on higher-dimensional matrix product states, in an attempt to extend the remarkable success of matrix product algorithms beyond one dimension.

We consider a consistent construction of the supersymmetric action for a codimension-two brane in six-dimensional Salam-Sezgin supergravity. When the brane carries a tension, we supersymmetrize the brane tension action by introducing a localized Fayet-Iliopoulos term on the brane and modifying the bulk SUSY transformations. As a result, we find that among the axisymmetric vacua of the system, the unwarped background with football-shaped extra dimensions respects N=1 supersymmetry. We extend the analysis to include the brane multiplets with the couplings to the bulk fields.

In this talk, we will investigate the distinguishability of quantum operations from both discrete and continuous point of view. In the discrete case, the main topic is how we can identify quantum measurement apparatuses by considering the patterns of measurement outcomes. In the continuous case, we will focus on the efficiency of parameter estimation of quantum operations. We will discuss several methods that can achieve Heisenberg Limit and prove in some other cases the impossibility of breaking the Standard Quantum Limit. The general treatment of estimation of quantum operations also allows an investigation of the effect of noise on estimation efficiency.

As physicists, we have become accustomed to the idea that a theory\\\'s content is always most transparent when written in coordinate-free language. But sometimes the choice of a good coordinate system is very useful for settling deep conceptual issues. Think of how Eddington-Finkelstein coordinates settled the longstanding question of whether the event horizon of a Schwarzschild black hole corresponds to a real spacetime singularity or not. Similarly we believe for an information-oriented or Bayesian approach to quantum foundations: That one good coordinate system may (eventually!) be worth more than a hundred blue-in-the-face arguments. This talk will motivate and chronicle the search for one such candidate coordinate system---the so-called Symmetric Informationally Complete Measurement---which has caught the attention of a handful of us here at PI and a handful of our visitors.

I shall review the potential relevance of antisymmetric tensor fields in physics, perhaps the most intriguing being a massive antisymmetric tensor as dark matter. Next, based on the most general quadratic action for the antisymmetric tensor field, I shall discuss what are possible extensions of Einstein\\\'s theory which include antisymmetric tensor field and thus torsion in a dynamical fashion.

Bell\\\'s theorem is commonly understood to show that EPR correlations are not explainable via a local hidden variable theory. But Bell\\\'s theorem assumes that the initial state of the particles is independent of the final detector settings. It has been proposed that this independence assumption might be undermined by a relativistically-allowed form of \\\"backward causation\\\", thereby allowing construction of a local hidden-variable model after all. In this talk, I will show that there is no backward causation model which yields the desired correlations. However, there are other physical scenarios yielding nontrivial nonlocal correlations which violated Bell\\\'s independence assumption. I will present two.