Quantum Matter

In 2014 Hartnoll proposed that the diffusion constants of incoherent metals should be bounded as $ D \geq \hbar v^2/ (k_B T)$, where v is a characteristic velocity. In this talk I will describe a large class of holographic theories that saturate such a bound, with $v$ being the velocity of the butterfly effect. Our results suggest a novel connection between transport at strong coupling and the field of quantum chaos.

Non-relativistic geometries that violate hyperscaling have been used as holographic laboratories for probing strongly coupled phases with anomalous scalings. In this talk I will discuss holographic computations of DC conductivities in gravitational systems that exhibit such scalings, and allow for momentum dissipation. I will also comment on the cases in which one obtains a linear temperature dependence for the resistivity.

Ultracold atomic Fermi gases near Feshbach resonances or in optical lattices realize paradigmatic, strongly interacting forms of fermionic matter. Topological excitations and spin-charge correlations can be directly imaged in real time. In resonant fermionic superfluids, we observe the cascade of solitonic excitations following a pi phase imprint. A planar soliton decays, via the snake instability, into vortex rings and long-lived solitonic vortices. For fermions in optical lattices, realizing the Fermi-Hubbard model, we detect charge and antiferromagnetic spin correlations with single-site resolution. At low fillings, the Pauli and correlation hole is directly revealed. In the Mott insulating state, we observe strong doublon-hole correlations, which should play an important role for transport.

Quantum many-body systems are challenging to study because of their exponentially large Hilbert spaces, but at the same time they are an area for exciting new physics due to the effects of interactions between particles. For theoretical purposes, it is convenient to know if such systems can be expressed in a simpler way in terms of some nearly-free quasiparticles, or more generally if one can construct a large set of operators that approximately commute with the system’s Hamiltonian. In this talk I will discuss two ways of using the entanglement spectrum to tackle these questions. In the first part, I will show that strongly disordered systems in the many-body localized phase have a universal power-law structure in their entanglement spectra. This is a consequence of their local integrability, and distinguishes such states from typical ground states of gapped systems. In the second part, I will introduce a notion of “interaction distance” and show that the entanglement spectrum can be used to quantify “how far” an interacting ground state is from a free

(Gaussian) state. I will discuss some examples of quantum spin chains and outline a few future directions.

 

[1] M. Serbyn, A. Michailidis, D. Abanin, Z. Papic, arXiv:1605.05737.

[2] C. J. Turner, K. Meichanetzidis, Z. Papic, and J. K. Pachos, arXiv:1607.02679.

This talk presents a quantum algorithm for performing persistent homology, the identification of topological features of data sets such as connected components, holes and voids. Finding the full persistent homology of a data set over n points using classical algorithms takes time O(2^{2n}), while the quantum algorithm takes time O(n^2), an exponential improvement. The quantum algorithm does not require a quantum random access memory and is suitable for implementation on small quantum computers with a few hundred qubits.

In a fair comparison of the performance of a quantum algorithm to a classical one it is important to treat them on equal footing, both regarding resource usage and parallelism. We show how one may otherwise mistakenly attribute speedup due to parallelism as quantum speedup. As an illustration we will go through a few quantum machine learning algorithms, e.g. Quantum Page Rank, and show how a classical parallel computer can solve these problems faster with the same amount of resources. Our classical parallelism considerations are especially important for quantum machine learning algorithms, which either use QRAM, allow for unbounded fanout, or require an all-to-all communication network.