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.
Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds.
A recent breakthrough in the condensed matter community is the identification and characterization of a rich set of ordered states, known as symmetry protected topological (SPT) phases. These phases are not only fascinating from the perspective of fundamental physics but have also found powerful applications in quantum computation. Very little is known about the thermal stability of SPT ordered systems, or whether their associated computational properties may survive at non-zero temperature.
We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension one, if an SPTO phase supports quantum wire, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation. Joint work with Dongsheng Wang, Abhishodh Prakash, Tzu-Chieh Wei and David Stephen; See arXiv:1609.07549v1
Existing proposals for topological quantum computation have encountered
difficulties in recent years in the form of several ``obstructing'' results.
These are not actually no-go theorems but they do present some serious
obstacles. A further aggravation is the fact that the known topological
error correction codes only really work well in spatial dimensions higher
than three. In this talk I will present a method for modifying a higher
dimensional topological error correction code into one that can be embedded
Given two sets X and Y, we consider synchronous correlations in a two-party nonlocal game with inputs X and outputs Y as a notion of generalized function between these sets (akin to a quantum graph homomorphism). We examine some structures in categories of synchronous classical, quantum, and nonsignalling strategies.
For a family of finite rate stabilizer codes, one can define two distinct error correction thresholds: the usual "block" threshold for the entire code, and the single-qubit threshold, where we only care about the stability of a single encoded qubit corresponding to a randomly chosen conjugate pair of logical X and Z operators. Our main result is that in the case of erasures, for hyperbolic surface codes related to a {p,q} tiling of the hyperbolic plane, it is the latter threshold that coincides exactly with the infinite-graph edge percolation transition. I will also discuss likely genera
We prove that constant-depth quantum circuits are more powerful than their classical counterparts. We describe an explicit (i.e., non-oracular) computational problem which can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates. In contrast, we prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the problem with high probability must have depth logarithmic in the input size. This is joint work with Sergey Bravyi and Robert Koenig (arXiv:1704.00690).
As we get closer to build a quantum computer, the main remaining challenge is handling the noise that aflicts quantum systems.
Topological methods, in their various forms, have become the main contestants in the quest for succesfully overcoming noise. A good deal of their strength and versatility is due to their rather unique physical flavour, which keeps giving rise to surprising developments.
Quantum Field Theories are interacting quantum systems described by an infinite number of degrees of freedom, necessarily living on an infinite-dimensional Hilbert space. Hence, many concepts from Quantum Information Theory have to be adapted before they can be applied to this setting. However, the task is worthwhile as we obtain new tools to understand the entanglement structure of theories describing the fundamental forces of nature. I will outline two approaches along this route, one bottom-down and one bottom-up strategy.
It is commonly believed that quantum information is not lost in a black hole. Instead, it is encoded into non-local degrees of freedom in some clever way; like a quantum error-correcting code. In this talk, I will discuss recent attempts to resolve some paradoxes in quantum gravity by using the theory of quantum error-correction. First, I will introduce a simple toy model of the AdS/CFT correspondence based on tensor networks and demonstrate that the correspondence between the AdS gravity and CFT is indeed a realization of quantum codes.