Related papers: A geometric view of quantum cellular automata
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
We show that the quantum computational speedup of quantum algorithms is due to their teleological character, their being evolutions toward a goal (the solution of the problem) with an attractor in the very goal they will produce in the…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
Driven by potential exponential speedups in business, security, and scientific scenarios, interest in quantum computing is surging. This interest feeds the development of quantum computing hardware, but several challenges arise in…
The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different…
High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a…
We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…