QuICS seminar

Abstract: There is a rich connection between classical and quantum codes and holographic correspondence connecting 2d CFTs and abelian 3d Chern-Simons theories. In the 3d language the codes emerge as a way to parametrize condensable anyons. Upon condensation 3d topological field theory gives rise to 2d CFT at the boundary. This provides a way to construct 2d CFTs from codes - the so called "code CFTs." This construction of code CFT has a natural interpretation in terms of a CSS quantum code (defined in terms of the original classical code, defining the CFT).

Abstract: I will discuss recent advances in improving and costing quantum algorithms for linear differential equations. I will introduce a stability-based analysis of Berry et al.’s 2017 algorithm that greatly extends its scope and leads to complexities sublinear in time in a broad range of settings – Hamiltonian simulation being a boundary case that prevents this kind of broad fast-forwarding. I illustrate these gains via toy examples such as the linearized Vlasov-Possion equation, networks of coupled, damped, forced harmonic oscillators and quadratic nonlinear systems of ODEs.

Abstract: Finding the ground energy of a quantum system is a fundamental problem in condensed matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical description, i.e. a poly-size classical circuit for computing the amplitude. Notable examples of succinct states encompass matrix product states, contractible projected entangled pair states, and states that can be represented by classical neural networks. We study the complexity of the local Hamiltonian problem with succinct ground state.

Abstract: Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. I will begin with a quick introduction to the general framework of quantum resource theories, in particular motivating it and explaining why the convertibility of resourceful states is at its core.

Abstract: Quantum measurements are critical to virtually any aspect of quantum information processing--for example: quantum error correction, distillation protocols, or state preparation.  We discuss the evolution of quantum information under Pauli measurement circuits.  We define "local reversibility" in context of measurement circuits, which guarantees that quantum information is preserved and remain "localized" after measurement.  We find that measurement circuits can exhibit a richer set of behaviour in comparison to their unitary counterparts.  For example, a

Abstract: I will talk about:

. New efficient algorithms for quantum state tomography (the quantum analogue of estimating a probability distribution).

. Why you should care about the difference between total variation distance and Hellinger distance and KL divergence and chi-squared divergence.

. Quantum-inspired improvements to the classical problem of independence testing.

Includes joint work with Steven T. Flammia (Amazon)

Abstract: In the last few years, a number of works have proposed and improved provably efficient algorithms for learning the Hamiltonian from real-time dynamics. In this talk, I will first provide an overview of these developments, and then discuss how the Heisenberg limit, the fundamental precision limit imposed by quantum mechanics, can be reached for this task. I will show that reaching the Heisenberg limit requires techniques that are fundamentally different from previous ones.

Abstract: Quantum cryptography leverages unique features of quantum mechanics in order to construct cryptographic primitives which are oftentimes impossible for digital computers. Cryptographic applications of quantum computers therefore have the potential for useful quantum advantage – entirely without computational speed-ups. In this talk, I will focus on two fundamental questions: First, is it possible to certify that private data has been deleted? And second, is it possible to revoke a cryptographic key?

Abstract: How hard is it to compress a quantum state? To fast-forward the evolution of a local Hamiltonian? To unscramble the Hawking radiation of a black hole? Traditional complexity theory -- which is centered around decision problems and tasks with classical inputs and outputs -- appears inadequate for reasoning about the complexity of such tasks involving quantum inputs and outputs.

Abstract: In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model.