Southwest Quantum Information and Technology

Sixteenth Annual Meeting, February 20-22, 2014
Santa Fe, New Mexico

Full Program | Thursday | Friday | Saturday | All Sessions

SESSION 4: Quantum Many-Body Physics I
3:45pm - 4:30pm	Thomas Vidick, UC Berkeley (invited)
	A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians
	Abstract. Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an (inverse-polynomial) approximation, expressed as a matrix product state (MPS) of polynomial bond dimension. The algorithm combines many ingredients, including recently discovered structural features of gapped 1D systems, convex programming, insights from classical algorithms for 1D satisfiability, and new techniques for manipulating and bounding the complexity of MPS. Our result provides one of the first major classes of Hamiltonians for which computing ground states is provably tractable despite the exponential nature of the objects involved.
4:30pm - 5:00pm	Akimasa Miyake, University of New Mexico
	Symmetry-protected topological ordered phases and their use for quantum computation
	Abstract. Collective phenomena, like superconductivity and magnetism, are usually robust features of quantum many-body systems. They only depend on a few key parameters of a system Hamiltonian, and often symmetries are sufficient enough to characterize different (quantum) phases associated with different collective behaviors. Through remarkable progress at the crossover between quantum information and quantum many-body physics, it gets more and more clear that certain strongly-correlated ground states could be harnessed for quantum information processing, based on their underlying entanglement structure and thus inherent complexity. For example, some concrete models of topological orders are most known by the application to quantum error correction. Here we address a question: "to what extent computational usefulness of quantum many-body ground states would be determined ubiquitously by symmetries, without the system Hamiltonian specified in detail?" Our approach may be also applicable to how quantum state preparation and verification can be made without detailed knowledge about the system, in the context of quantum simulation. This is a joint work with Jacob Miller.