Physics

In this talk, I will focus on cosmologies that replace the big bang with a big bounce. I will explain how, in these scenarios, the large-scale structure of the universe is determined during a contracting phase before the bounce and will describe the recent development of the first well-behaved classical (non-singular) cosmological bounce solutions.

In recent years there has been quite some effort to apply Matrix Product States (MPS) and more general Tensor Networks (TN) to lattice gauge theories. Contrary to the standard Euclidean-time Monte Carlo approach, which faces a major obstacle in the sign problem, numerical methods based on TN are free from the sign problem and allow to some extent simulating time evolution. Moreover, TN are also a suitable tool to explore proposals for potential future quantum simulators for lattice gauge theories.

In this talk I am going to present some examples where these possibilities allow novel insight into lattice gauge theories. After briefly introducing MPS, I will mainly focus on two models: The first part of the talk is going to be about the Schwinger model. I will show how MPS can help to explore proposals for potential future quantum simulators for this model by studying their spectral properties and simulating adiabatic preparation protocols for the interacting vacuum.

Furthermore, I will show an explicit example where TN allow to overcome the Monte Carlo sign problem in a lattice calculation by studying the zero-temperature phase structure for the two-flavor case at non-zero chemical potential with MPS.

In the second part, I am focusing on a non-Abelian gauge model, namely a 1+1 dimensional SU(2) lattice gauge theory. Using MPS, the phenomenon of string breaking in this theory can be studied in real time, thus allowing to gain new insight into this process. Moreover, I will show how the gauge field can be integrated out for systems with open boundary conditions and how to obtain a formulation which allows to address the model more efficiently with MPS.

Quantum tomography is an important tool for characterizing the parameters of unknown states, measurements, and gates.  Standard quantum tomography is the practice of estimating these parameters with known measurements, states, or both, respectively.  In recent years, it has become important to address the issue of working with systems where the ``devices'' used to prepare states and make measurements both have significant errors.  Of particular concern to me is whether such state-preparation and measurement errors are correlated with each other.  In this talk, I will share a solution to assessing such correlations with an object called a partial determinant.  Further, I will show how this technique suggests a perspective for such correlated quantum states and observables (over the space of device settings) is analogous to the non-holonomic perspectives of thermodynamic heat and work (over the macroscopic state space.)

In this talk I will give a short introduction into Projected Entangled-Pair States (PEPS), and their infinite variant iPEPS, a class of tensor network Ansatz targeted at the simulation of 2D strongly correlated systems. I will present work on two recent

projects: the first will be an application of the iPEPS algorithm to a Kitaev-Heisenberg model, a model which through-out recent years has received a lot of attention due to its potential connection to the physics of a subclass of the so-called Iridate compounds. The second will be work related to the development of the iPEPS method to specifically target cylindrical geometries. Here I will present some preliminary results where we apply the methods to the Heisenberg and Fermi-Hubbard models and evaluate their performance in comparison to infinite Matrix Product States. As a final part of my talk I will, depending on time, elaborate somewhat on potential future topics including (but not restricted to):  the main challenges of iPEPS simulations from a numerical perspective and what pre-steps we have experimented with to tackle these, the possibility of applying recent proposals for finite-temperature calculations within the PEPS framework to frustrated spin systems and the use of Tensor Network Renormalization for the study of RG flows.

To build a fully functioning quantum computer, it is necessary to encode quantum information to protect it from noise. Topological codes, such as the color code, naturally protect against local errors and represent our best hope for storing quantum information. Moreover, a quantum computer must also be capable of processing this information. Since the color code has many computationally valuable transversal logical gates, it is a promising candidate for a future quantum computer architecture.

In the talk, I will provide an overview of the color code. First, I will establish a connection between the color code and a well-studied model - the toric code. Then, I will explain how one can implement a universal gate set with the subsystem and the stabilizer color codes in three dimensions using techniques of code switching and gauge fixing. Next, I will discuss the problem of decoding the color code. Finally, I will explain how one can find the optimal error correction threshold by analyzing phase transitions in certain statistical-mechanical models.

The talk is based on http://arxiv.org/abs/1410.0069, http://arxiv.org/abs/1503.02065 and recent works with M. Beverland, F. Brandao, N. Delfosse, J. Preskill and K. Svore.

In order to create ansatz wave functions for models that realize topological or symmetry protected topological phases, it is crucial to understand the entanglement properties of the ground state and how they can be incorporated into the structure of the wave function.

In this first part of this talk, I will discuss entanglement properties of models of topological crystalline insulators and spin liquids and show how to incorporate topological order, symmetry fractionalization, and lattice symmetry protected topological order into tensor network wave functions.

In the second part of this talk, I will discuss intrinsically fermionic topological phases and an exactly solvable model we built to elucidate the structure of the ground state wave functions in these phases.

References:

https://arxiv.org/abs/1507.00348

https://arxiv.org/abs/1605.06125

I will answer the question in the title. I will also describe a new quantum algorithm for Boolean formula evaluation and an improved analysis of an existing quantum algorithm for st-connectivity. Joint work with Stacey Jeffery.