Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session M18: Invited Session: Intersections of Density Functional Theory and Quantum Information |
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Sponsoring Units: DCOMP GQI Chair: Rudy Magyar, Sandia National Laboratories Room: Mission Room 103A |
Wednesday, March 4, 2015 11:15AM - 11:51AM |
M18.00001: From ground-state densities to entangled wave functions: an exploration for the Hubbard model Invited Speaker: Klaus Capelle The fundamental Hohenberg-Kohn theorem of density-functional theory (DFT) guarantees that, in principle, all information about a many-body system is contained in it ground-state density. Most effort in DFT is thus directed at finding ways to reliably calculate this density and to extract useful information from it. Quantum-information theory (QIT), on the other hand, is little concerned with ground-state densities, focusing instead on wave functions and density matrices, with a view on exploiting entangled states in information processing. In spite of these different philosophies, many connections exist between both approaches. In this talk, I review of how some of these connections have been discovered and quantified in the context of the Hubbard model: (i) DFT calculations for a model Hamiltonian serve to relate the entanglement entropy to phase transitions; (ii) a local-density-type approximation can be used to calculate the entanglement entropy of spatially inhomogeneous systems, such as cold atoms in optical traps and large superlattices, where traditional numerical methods encounter difficulties; (iii) a combination of DFT with Bethe-Ansatz techniques allows one to calculate the values of system-specific parameters in expressions for the block-block entanglement that remain undetermined in scaling approaches; (iv) the construction of suitable metrics shines light on how the Hohenberg-Kohn theorem relates densities and wave functions for different systems. [Preview Abstract] |
Wednesday, March 4, 2015 11:51AM - 12:27PM |
M18.00002: Time-Dependent Density Functional Theory for Universal Quantum Computation Invited Speaker: David Tempel In this talk, I will discuss how the theorems of TDDFT can be applied to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, I will discuss how TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. [Preview Abstract] |
Wednesday, March 4, 2015 12:27PM - 1:03PM |
M18.00003: The computational complexity of many-electron problems and Density Functional Theory Invited Speaker: Norbert Schuch Quantum computation and complexity has helped us to sharpen our understanding of the common origin for the difficulty of a wide range of problems in quantum many-body physics. In my talk, I will discuss the implications of quantum complexity theory to understanding systems of interacting electrons, and show how it allows us to determine the fundamental limitations to any numerical method for the simulation of those systems, including our ability to approximate the universal functional in Density Functional Theory. [Preview Abstract] |
Wednesday, March 4, 2015 1:03PM - 1:39PM |
M18.00004: What Density Functional Theory could do for Quantum Information Invited Speaker: Ann Mattsson The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT’s utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Wednesday, March 4, 2015 1:39PM - 2:15PM |
M18.00005: Density Functional Theory and Quantum Computation Invited Speaker: Frank Gaitan |
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