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.
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.
Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we develop a threshold theorem for quantum supremacy with noisy quantum circuits in the pre-threshold region, where quantum error correction does not work directly.
A research line that has been very active recently in quantum information is that of recoverability theorems. These, roughly speaking, quantify how well can quantum information be restored after some general CPTP map, through particular 'recovery maps'. In this talk, I will outline what this line of work can teach us about quantum thermodynamics.
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 solut
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.
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.