Southwest Quantum Information and Technology

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

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SESSION 9b: Break-out 2: Quantum Many-Body Physics II
4:00pm - 4:30pm	Sukhbinder Singh, Macquarie University, Sydney
	Tensor networks and Symmetries
	Abstract. Tensors networks methods, which are based on ideas of entanglement and renormalization group, have significantly progressed our understanding of strongly correlated quantum lattice systems in recent years. Examples of popular tensor network states include the matrix product state (MPS)[1], which results naturally from both Wilson’s numerical renormalization group[2] and White’s density matrix renormalization group(DMRG)[3], and the multi-scale entanglement renormalization ansatz (MERA) [4] which is based a specific RG scheme known as entanglement renormalization [5]. These tensor networks have been applied to the exploration of frustrated antiferromagnets, interacting fermions, quantum criticality, topological order and symmetry protected order, and more recently, the MERA has been used to explore[6] the holographic correspondence[7] of string theory. The careful incorporation[8] of lattice symmetries (both spacetime and internal symmetries) in tensor networks is playing an increasingly important role in these applications. In this talk I will outline some aspects of this role in the context of the MPS and the MERA where symmetries have been exploited to (i) target specific quantum number sectors of the Hilbert space, which subsequently also allows for the efficient simulation of lattice systems of anyons[9], (ii) identification of the quantum order of a ground state from its tensor network description[10], and (iii) to realize certain symmetry features of the holographic correspondence in the MERA. References [1] S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995). [2] K.G. Wilson, Rev. Mod. Phys. 47, 4, 773 (1975). [3] S.R. White, Phys. Rev. Lett. 69, 2863 (1992). [4] G. Vidal, Phys. Rev. Lett. 101, 110501 (2008). [5] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007). [6] B. Swingle, Phys. Rev. D 86, 065007 (2012). [7] J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998). [8] S. Singh, R. N. C. Pfeifer, and G. Vidal, Phys. Rev. A 82, 050301 (2010). [9] S. Singh, R. N. C. Pfeifer, G. Vidal, and G. K. Brennen. arXiv:1311.0967 (2013). [10] S. Singh and G. Vidal. Phys. Rev. B 88, 121108(R) (2013).
4:30pm - 5:00pm	Fernando Pastawski, California Institute of Technology
	Optimal dissipative encoding and state preparation for topological order
	Abstract. We study the suitability of dissipative (non-unitary) processes for (a) encoding logical information into a topologically ordered ground space and (b) preparing an (arbitrary) topologically ordered state. We give a construction achieving (a) in time O(L) for the LxL-toric code by evolution under a geometrically local, time-independent Liouvillian. We show that this scaling is optimal: even the easier problem (b) takes at least O(L) time when allowing arbitrary (possibly time-dependent) dissipative evolution. For more general topological codes, we obtain similar lower bounds on the required time for (a) and (b). These bounds involve the code distance and the dimensionality of the lattice. The proof involves Lieb-Robinson bounds, recent cleaning-lemma-type arguments for topological codes, as well as uncertainty relations between complementary observables. By allowing general locality-preserving evolutions (including, e.g., circuits of CPTPMs), our results extend earlier work characterizing unitary state preparation.
5:00pm - 5:30pm	Adolfo del Campo, Los Alamos National Laboratory
	Shortcuts to adiabaticity in many-body systems
	Abstract. The evolution of a system induced by counter-diabatic driving mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary non-local interactions for matter-waves. Here experimentally realizable driving protocols are presented for a large class of single-particle, many-body, and non-linear systems without demanding the spectral properties as an input. The method is applied to the fast decompression of quantum fluids realizing a dynamical quantum microscope, as well as to the fast transport of ion chains.
5:30pm - 6:00pm	Iman Marvian, University of Southern California
	Symmetry-Protected Topological Entanglement
	Abstract. We propose an order parameter for the Symmetry-Protected Topological (SPT) phases which are protected by an Abelian on-site symmetry. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B, two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A and B and the boundaries of the system. In the case of 1-dimensional systems we prove that at the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the non-trivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth local quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Finally, we show that the concept of SPT entanglement leads us to a new interpretation of the string order parameters and based on this interpretation we propose an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters.