Related papers: From Geometry to Quantum Computation
We review the field of Optical Quantum Computation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and…
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
We in this paper consider a further generalization of the (optical) holonomic quantum computation proposed by Zanardi and Rasetti (quant-ph/9904011), and reinforced by Fujii (quant-ph/9910069) and Pachos and Chountasis (quant-ph/9912093).…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum…
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
Experimental realization of a universal set of quantum logic gates with high-fidelity is critical to quantum information processing, which is always challenging by inevitable interaction between the quantum system and environment. Geometric…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling,…
We present a new model of quantum computation rooted in the representation theory of the mass less sector of unitary irreducible representations of the extended Poincare group developed in [1].
This is a sequel to the papers (quant-ph/9910063) and (quant-ph/0004102). The aim of this paper is to give mathematical foundations to Holonomic Quantum Computation (Computer) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
Due to its geometric nature, holonomic quantum computation is fault-tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open…
We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This…