QuICS Special Seminar

Abstract: Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the global effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima.

Abstract: While quantum walk frameworks make it easy to design quantum algorithms, as evidenced by their wide application across domains, the major drawback is that they can achieve at most a quadratic speedup over the best classical algorithm.  In this work, we generalise the electric network framework – the most general of quantum walk frameworks, into a new framework that we call the multidimensional quantum walk framework, which no longer suffers from the aforementioned drawback, while still maintaining the original classical walk intuition.

Abstract: Traditional stabilizer codes operate over prime power local-dimensions. For instance, the 5-qubit code and 9-qubit code operate over local-dimension 2. In this presentation we discuss extending the stabilizer formalism using the local-dimension-invariant framework to import stabilizer codes from these standard local-dimensions to other cases.

Abstract: Interacting fermionic systems can model real world physical phenomenon directly. Many people are working on finding efficient and practical ways to determine properties of these quantum simulators. Specifically, estimating correlation functions, that reveal important properties such as coulomb-coulomb interaction strength and entanglement spreading, is a crucial goal. The well know classical shadows formalism allows one to find linear properties of a quantum state by reusing outcomes from simple basis measurements.

Abstract: A quantum state that depends on a parameter is a commonly studied structure in quantum physics. Examples include the ground state of a Hamiltonian with a parameter or Bloch states as functions of the quasimomentum. The change in the state as the parameter varies can be characterized by such geometric objects as the Berry phase or the quantum distance which has led to many insights in the understanding of quantum systems.

Abstract: In this talk, I will focus on topological order and error correction on fractal geometries.  Firstly, I will present a no-go theorem that Z_N topological order cannot survive on any fractal embedded in two spatial dimensions and then show that for fractal lattice models embedded in 3D or higher spatial dimensions, Z_N topological order survives if the boundaries on the holes condense only loop or membrane excitations.  Next, I will discuss fault-tolerant logical gates in the Z_2 version of these fractal models, which we name as fractal surface codes, using their connection to glob

The position states of the harmonic oscillator describe the location of a particle moving on the real line. Similarly, the phase difference between two superconductors on either side of a Josephson junction takes values in the configuration space of a particle on a circle. More generally, many physical systems can be described by a basis of "position states," describing a particle moving on a more general configuration or state space. Most of this space is usually ignored due to the energy cost required to pin a particle to a precise "position".

Entanglement is a critical resource for a useful quantum computer. There is a not a consensus on whether large-scale entanglement is physically possible, and entanglement on mixed states at non-zero temperature is poorly understood.  We discuss theoretical and computable bounds on how much entropy a quantum system can tolerate and still be useful for computation, and some directions for further exploration.  This is not a research talk, but rather a review of interesting results.

Matrix syntax is a formal model of syntactic relations, based on a conservative and a radical assumption. The conservative assumption dates back to antiquity: that the fundamental divide in human language is between nouns and verbs, which are “conceptually at right angles” (as different as substantive words can be). The radical assumption is that such a conceptual orthogonality could be treated as a formal orthogonality in a vector space, with all its consequences.

Quantum dots formed in silicon heterostructures have emerged as a promising candidate for creating qubits, the building blocks of quantum computing. Their small size, ease of control, and compatibility with modern semiconductor processes make them especially enticing. However, the intrinsic near-degeneracy (valley splitting) of the conduction band electrons that form these quantum dots poses a serious concern for the viability of these qubits, but may also hold the solution.