Seminar

Several tasks in quantum-information processing involve quantum learning. For example, quantum sensing, quantum machine learning and quantum-computer calibration involve learning and estimating unknown parameters from measurements of many copies of a quantum state that depends on those parameters. This type of metrological information is described by the quantum Fisher information matrix, which bounds the average amount of information learnt about the parameters per measurement of the state.

The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we investigate the hardness of classically simulating the QSVT. A recent result by Chia, Gilyén, Li, Lin, Tang and Wang (STOC 2020) showed that the QSVT can be efficiently "dequantized" for low-rank matrices, and discussed its implication to quantum machine learning.

In this talk I will discuss ongoing progress in two projects. The first project is related to implementing the time-evolution operator corresponding to the Kogut-Susskind formulation of Lattice Gauge Theories (U(1), SU(2), and SU(3)), and an improvement thereof called the Loop-String-Hadron formulation. We give a simple, generic method of decomposing a Hamiltonian into a minimal sum of easily-diagonalizable summands, suitable to plug into Trotter- or Block-Encoding-based Hamiltonian simulation methods.

The so-called Welded Tree Problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm (https://arxiv.org/pdf/quant-ph/0209131.pdf). Given the name of a special ENTRANCE vertex, a quantum walk can find another distinguished EXIT vertex using polynomially many queries, though without finding any particular path from ENTRANCE to EXIT.

Real-time control software and hardware is essential for operating modern quantum systems. In particular, the software plays a crucial role in bridging the gap between applications and real-time operations on the quantum system. Unfortunately, real-time control software is an often underexposed area, and many well-known software engineering techniques have not propagated to this field. As a result, control software is often hardware-specific at the cost of flexibility and portability.

Quantum error correction is an indispensable ingredient for scalable quantum computing. We discuss a particular class of quantum codes called "quantum low-density parity-check (LDPC) codes." The codes we discuss are alternatives to the surface code, which is currently the leading candidate to implement quantum fault tolerance. We discuss the zoo of quantum LDPC codes and discuss their potential for making quantum computers robust with regard to noise.

Semidefinite Programming (SDP) is a class of convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization, machine learning and operational research. In this talk, I will discuss how SDP can be used to address two major challenges in quantum computing research: near-term quantum advantage and device certification.

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 c

Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations such as constructing quantum states or performing unitary transformations.

Motivated by recent experimental demonstrations of Floquet topological insulators, there have been several theoretical proposals for using structured light, either spatial or spectral, to create other properties such as flat band and vortex states. In particular, the generation of vortex states in a massive Dirac fermion insulator irradiated by light carrying nonzero orbital angular momentum (OAM) has been proposed recently. Here, we evaluate the orbital magnetization and  optical conductivity as physical observables for such a system.