Seminar

Zero-knowledge proofs are a fundamental building block in classical Cryptography, having far-reaching applications. Recently, there has been some effort in improving our understanding of Zero-knowledge for quantum complexity classes, that will hopefully lead us to striking objects as in the classical case.

This thesis describes quantum algorithms for Hamiltonian simulation,
ordinary differential equations (ODEs), and partial differential
equations (PDEs).
 
Product formulas are used to simulate Hamiltonians which can be
expressed as a sum of terms which can each be simulated individually.
By simulating each of these terms in sequence, the net effect
approximately simulates the total Hamiltonian. We find that the error

According to Feynman, quantum computers will be the most suitable platforms to simulate nature. Although as of today, quantum computers with capability and reliability comparable or beyond those of classical computers do not exist, rapid progress in quantum technologies, and a vast growth in interest and resources in quantum information sciences, promise a future in which quantum computation may play an important role in addressing computationally-challenging problems in all areas of sciences and technology.

We show how to construct fully quantum multi-spin interactions using only two-body Ising interactions plus a uniform transverse field. We then provide an explicit embedding of simple gauge models, such as the surface code, into the D-Wave chimera architecture. Taken as whole this is a way to build topological qubits using existing hardware. The scheme is generalizable to other gauge-like theories, for example those with fractonic topological order such as the X-cube model.

Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few.

The recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware, with promising progress towards simulation of quantum matter and materials. In order to enhance the capabilities of this class of quantum devices, some of the more arduous experimental tasks can be off-loaded to classical algorithms running on conventional computers.

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/r^α in the distance r on a D-dimensional lattice for α ≤ D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking.

The quantum adiabatic theorem governs the evolution of a wavefunction under a slowly time-varying Hamiltonian.

Communication networks have multiple users, each sending and receiving messages. A multiple access channel (MAC) models multiple senders transmitting to a single receiver, such as the uplink from many mobile phones to a single base station. The optimal performance of a MAC is quantified by a capacity region of simultaneously achievable communication rates. We study the two-sender classical MAC, the simplest and best-understood network, and find a surprising richness in both a classical and quantum context.