This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
Non-abelian anyons have drawn much interest due to their suspected existence in two-dimensional condensed matter systems and for their potential applications in quantum computation. In particular, a quantum computation can in principle be realized by braiding and fusing certain non-abelian anyons. These operations are expected to be intrinsically robust due to their topological nature. Provided the system is kept at a
Raussendorf introduced a powerful model of fault tolerant measurement based quantum computation, which can be understood as a layering (or “foliation”) of a multiplicity of Kitaev’s toric code. I will discuss our generalisation of Raussendorf’s construction to an arbitrary CSS code. We call this a Foliated Quantum Code. Decoding this foliated construction is not necessarily straightforward, so I will discuss an example in which we foliate a family of finite-rate quantum turbo codes, and present the results of numerical simulations of the decoder performance.
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive proof systems. Specifically, we show that any language in BQP has a quantum interactive proof system with a polynomial-time classical verifier (who can also prepare random single-qubit pure states), and a quantum polynomial-time prover. Here, soundness is unconditional---i.e it holds even for computationally unbounded provers.
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian.
Quantum adiabatic optimization (QAO) slowly varies an initial Hamiltonian with an easy-to-prepare ground-state to a final Hamiltonian whose ground-state encodes the solution to some optimization problem. Currently, little is known about the performance of QAO relative to classical optimization algorithms as we still lack strong analytic tools for analyzing its performance.
I will review a recent proposal for a top-down approach to AdS/CFT by A. Schwarz, which has the advantage of requiring few assumptions or extraneous knowledge, and may be of benefit to information theorists interested by the connections with tensor networks. I will also discuss ways to extend this approach from the Euclidean formalism to a real-time picture, and potential relationships with MERA.
Scalable anyonic topological quantum computation requires the error-correction of non-abelian anyon systems. In contrast to abelian topological codes such as the toric code, the design, modelling, and simulation of error-correction protocols for non-abelian anyon codes is still in its infancy. Using a phenomenological noise model, we adapt abelian topological decoding protocols to the non-abelian setting and simulate their behaviour.
The gauge color code is a quantum error-correcting code with local syndrome measurements that, remarkably, admits a universal transversal gate set without the need for resource-intensive magic state distillation. A result of recent interest, proposed by Bombin, shows that the subsystem structure of the gauge color code admits an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction.
In this talk I address the problem of simultaneously inferring unknown quantum states and unknown quantum measurements from empirical data. This task goes beyond state tomography because we are not assuming anything about the measurement devices. I am going to talk about the time and sample complexity of the inference of states and measurements, and I am going to talk about the robustness of the minimal Hilbert space dimension. Moreover, I will describe a simple heuristic algorithm (alternating optimization) to fit states and measurements to empirical data.