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.
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.
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more accurate and complete theory with new and more powerful possibilities for information processing. The goal of both classical and quantum information theory is to quantify the optimal rates of interconversion of different resources. These rates are usually characterized in terms of entropies.
A central question in quantum computation is to identify which problems can be solved faster on a quantum computer. A Holy Grail of the field would be to have a theory of quantum speed-ups that delineates the physical mechanisms sustaining quantum speed-ups and helps in the design of new quantum algorithms. In this talk, we present such a toy theory for the study of a class of quantum algorithms for algebraic problems, including Shor’s celebrated factoring algorithm. Our theory is an extension of Gottesman’s stabilizer formalism based on elements of group and hypergroup theory.
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.
In this talk I will introduce recent research into quantum clocks of finite dimension, with the focus on their accuracy, as determined by their dimension, coherence, and power consumption.
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. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable.
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.